Industry equilibrium with random exit or default

• Published date: 01 August 2019
• Date: 01 August 2019
• Author: Piin‐Hueih Chiang,Svetlana Boyarchenko
• DOI: http://doi.org/10.1111/jpet.12381

J Public Econ Theory. 2019;21:650–686.wileyonlinelibrary.com/journal/jpet650

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© 2019 Wiley Periodicals, Inc.

Received: 12 November 2018

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Revised: 10 May 2019

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Accepted: 11 May 2019

DOI: 10.1111/jpet.12381

ORIGINAL ARTICLE

Industry equilibrium with random exit

or default

Svetlana Boyarchenko

1

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Piin‐Hueih Chiang

2

1

Department of Economics,

The University of Texas at

Austin, Austin, Texas

2

Department of Economics, National

Chengchi University, Taipei, Taiwan

Correspondence

Svetlana Boyarchenko, Department of

Economics, The University of Texas at

Austin, 2225 Speedway Stop C3100,

Austin, Texas 78712.

Email: sboyarch@utexas.edu

Abstract

An industry consisting of a large number of small price

taking firms subject to idiosyncratic productivity shocks

is considered. At the moment of entry, a firm takes on

debt. We show that in a competitive equilibrium, some

firms exit and pay out their debt while others choose to

default. The outcome depends on the realization of firm‐

specific shocks. The paper demonstrates that if the firms

self‐select between exit with debt repayment and

default, then the default region is disconnected from

the exit region. The methodological contribution of the

paper is the analytical characterization of the long‐run

equilibrium for two scenarios of the initial distribution

of productivity shocks. We consider two public policy

mechanisms—contract enforcement and creditor pro-

tection. Our policy recommendation is that regulators

need to reduce the contract enforcement if they want to

decrease the long‐run default rate.

KEYWORDS

endogenous default, endogenous exit, heterogeneous firms, industry

equilibrium

JEL CLASSIFICATION

C61; D81; G31; H32

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INTRODUCTION

1.1

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Motivation

Small businesses are an important part of the economy of virtually every nation. The importance of

small firms’growth for economic development has been recognized in policy‐oriented literature

(see, e.g., Beck, Demirguc‐Kunt, Laeven, & Levine, 2008). According to the US Small Business

Administration, small firms produce more than half of US nonfarm output, employ 50% of workers,

and pay 45% of total private payroll. Small firms represent 99.7% of all employer firms. Small firms

are an important source of income for the poor in developing countries. Ninety nine percent of the

firms in many poor countries have 10 or fewer workers (see, McKenzie, 2017). Many micro

enterprises in developing countries have high returns to capital, but also face risky revenue streams

(see de Mel, McKenzie, & Woodruff, 2019). In principle, equity offers several advantages over debt

when financing investments of this nature, but the use of equity in practice has been largely limited

to investments in much larger firms. Although there is a lot of optimism about the power of finance

for small‐scale business development, a growing literature (see, e.g., de Mel et al., 2019; Inekwe,

2019; McKenzie & Paffhausen, 2018) shows that success cannot be taken for granted and may

critically depend both on the entrepreneur’s personal characteristics and on institutions.

The goal of this paper is to understand how small firms’entry and exit decisions are affected

by industry‐wide and firm‐specific exogenous parameters and procedures and to provide policy

recommendations. We leave for the future analysis of the optimal business tax policy as in

Becker and Schneider (2017).

Small firms rely heavily on external finance. Picard and Rusli (2018) emphasize the

importance of private debt financing in reducing government transfers and information costs.

Small firms have historically faced significant difficulties in accessing funding for positive net

present value (NPV) projects due to lack of credible information about them by potential

providers of funds. Maybe due to creditors’cautiousness, bankruptcy rate (at least in the United

States) is low: The average annual default rate on small business administration (SBA) loans is

3.5% according to Glennon and Nigro (2005). Hillegeist, Keating, Cram, and Lundstedt (2004)

document that the average annual bankruptcy rate for US firms was 1% from 1980 to 2000.

Mester (1997) estimates the annual default rate for business loans as ranging between 1% and

3%. Herranz, Krasa, and Villamil (2015) use the Survey of Small Business Finances

administered by The Board of Governors of the Federal Reserve System and the US Small

Business Administration, data and find a large percentage of entrepreneurs who inject personal

funds to keep their firms alive. This may seem puzzling because incorporated firms are

protected by limited liability in case of bankruptcy. Negative equity and low default rates

indicate that bankruptcy is a strategic decision.

In the United States, businesses can file Chapter 7 or 11 for bankruptcy. Chapter 11 is

designed for large firms, or corporations negotiating debt restructuring while continuing their

operations. Chapter 7 is primarily intended as a bankruptcy procedure for consumers, but it is

also de facto a bankruptcy procedure for small firms. After filing for Chapter 7, an entrepreneur

“gets a fresh start”in the sense that debts are discharged and all future earnings are exempt

from debt payments.

Death or exit rates of small firms are fairly high. McKenzie and Paffhausen (2018) find that small

firms die at an average rate of 8.2% per year. Due to high exit rates of small firms, creditors face not

only default risk, but also prepayment risk, that is why it is really important to understand why

some small businesses partially financed by debt choose to exit and pay out their debt, while others

file for bankruptcy as well as creditor protection and contract enforcement mechanisms.

1.2

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Contribution and results

The main contribution of this paper is to derive an equilibrium model for a competitive industry

that, due to technological reasons, is composed of small firms and to demonstrate how small

BOYARCHENKO AND CHIANG

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firms self‐select between default and exit with debt prepayment. Our numerical results produce

the exit rate at least two times higher than the default rate, which agrees with empirical findings

listed above. Our model also shows that when exit and default are strategic decisions, firms are

making negative profits before liquidation. Hence, the entrepreneurs have to inject their own

money to cover business losses. This agrees with empirical findings of Herranz et al. (2015).

We derive analytical expressions for equilibrium output price, debt coupon rate, entry rate of

new firms, and stationary distribution of active firms. We also describe analytically the

following four state space regions.

1. The good luck zone (the upper tail of the initial distribution of shocks): Firms in this zone

are the most productive ones. Eventually, they will exit, but they never default.

2. The exit zone (adjacent to the left boundary of the good luck zone): The entrepreneur finds

out that her own prospects are not too good but the investment project has sufficiently high

scrap value, so that it makes sense to sell the firm’s assets and pay back the debt.

3. The default zone (the lower tail of the initial distribution of shocks): The entrepreneur

observes that the future is too bleak and defaults immediately.

4. The Buridan zone (an interval that separates the default and exit zones): The entrepreneur

observes that her prospects are not great, but it is optimal to remain active, so she goes on

producing. If eventually the shock enters the default zone first, the firm defaults. If instead

the shock enters the exit zone first, then the firm pays the debt and exits. While the

entrepreneur is indecisive, her behavior resembles the behavior of the famous animal placed

between two piles of hay.

The novelty of prediction of our dynamic model is that the default zone is disconnected from

the exit zone, so that there are relatively unproductive firms that remain active for some time.

The dynamics of the firms inside the Buridan zone suggests that the firms may leave the

industry after a sequence of favorable productivity shocks. The reader must keep in mind that

the initial productivity shock of a firm in the Buridan zone is rather low. Had the entrepreneur

invested only her own assets in the project, she would have sold the firm immediately and

exited the industry. Since the project is partially financed by debt, the entrepreneur cannot sell

the firm immediately, because the value she will recover is insufficient to pay back the debt. At

the same time, the entrepreneur is too good to file for bankruptcy. She can always do this later if

her productivity worsens. So she needs a sequence of successful realizations of revenues to be

able to sell the firm at the scrap value that will at least be high enough to pay back the debt.

Exit from the Buridan zone with debt repayment can be interpreted as an intraindustry

liquidation. Fleming and Moon (1995) find that many liquidating firm assets are sold to firms

operating in the same industry. They describe such voluntary liquidations as an interesting

example of efficient and orderly asset reallocation. Since a voluntary liquidation is conducted at

management’s discretion, managers choose to liquidate when financial factors make it value‐

increasing for the firm. Fleming and Moon (1995) also document that liquidating firms

experience positive abnormal returns in the period preceding liquidation announcement. They

suggest that the market anticipates the firm’s liquidation and responds to this value enhancing

action.

Being able to characterize equilibrium values analytically is very important, because

comparative statics analysis becomes possible. In particular, we study how equilibrium values

depend on parameters that comprise contract enforcement and creditor protection mechanisms.

The contract enforcement is captured in our model by a penalty for debt prepayment, and

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