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FORECASTING BUSINESS FAILURES USING A POISSON REGRESSION MODEL
Vasanthakumar N. Bhat
Lubin School of Business, Pace University, New York, NY 10038
In this paper, we present a Poisson regressioo model for business failure rates in the United States. The yearly
business failure rates follow a skewed probability distribution fimction with nonnegative values. There are many business
estab1ishments and probability that a particular business establishment will close is very small. These facts conform to a
Poisson specification. The empirical results suggest that the percentage change in gross national product, money supply,
and inventmy to sales ratio inversely and the average nmnber of businesses formed in the previous five years as a proportion
of current existing businesses and unemployment rate directly effect failme rates. The Poisson regression ana1ysis is an
extremely usefUl method to model Poisson dependent variables such as claim rates in insurance, mortality rates in health
care and so on.
Business failures ire of siguificant concern to
policy makers. Business failures represent inability of
businesses to endure financial difficulties. Businesses,
particularly small ones, are the nation's job generators.
Therefore, failures of businesses can significantly affect
employment and consumer coDfidence. The purpose of
this paper is to examine the macroeconomic determinants
of business failures in the United Stales. We also evaluate
the effect of the Bankruptcy Reform Act of 1978 on
business closings. In this paper, we deal with business
failures per 10,000 establishments covered by the Dun
and BradsIreet Corporation. Business fajlures denote the
number of estabHshments that close because they owe
money to creditors. Such businesses include those which
close because of comt proceedings such as foreclosure,
bankruptcy and attachment or receivership. Businesses
which close voluntarily either with some arrangements
with creditors or by leaving 1IIlpaid debts are also
included in this category of business failures. One
common feature about all these failures is that these
establishments close withont fully paying their creditors.
Therefore, businesses which close due to lack of capital,
inadequate profits, poor health or retirement of the owner
and change of name or location are excluded from our
analysis.
Dun and Bradstreet COIporation publishes
business failure data weekly, monthly and quarterly. This
data is based on a UDiverse count· of firms and
consequently does not have any sampling errors. The
failure data denotes the number of corporations and
llDincorporated businesses which go out of business
owing money to creditors. The data is collected from
court records, credit management groups and
newspapers. The failure data published by Dun and
BradsIreet differs ftom banknlptcy statistics published by
the Adminislrative Office of the U.S. Court because d!ey
are based on case numbers. For example. when a
partnership firm goes bankrupt, Dun and Bradstreet
counts that as one business failure though each partner
might have been assigned one case number. Similarly,
the courts may classify a bllllkruptcy as business though
it might not have been actually in business. Dun and
Bradstreet does not include tax shelter firms,
establishments represented by persons moonlighting on
second job and so on. The universe of businesses in the
Dun and Bradstreet data base is therefore smaller than
thenumber of taxable firms in Internal Revenue Service
statistics.
There are only a few studies that analyze
various factors that influence business failures. Hudson
and Cuthbertson(I993) present a general autoregressive
dislributedlag (ADL) model for personal bankruptcies in
the UK using data from 1971 to 1988. Shepard(1984)
presents an ordinary least square regression model for
nonbusiness bankruptcies in the United States for the
period 1948-1979. Hudson(I986) analyzes reasons for
companies to go into banlauptcy and provides a
regression model for voluntary and compuIsoty
liquidations in UK
In Exhibit 1, we indil:ate businesses failure rates
in different years from 1946 to 1991. Approximately
97,000 busin ems failed in 1992. lhat n:plesents failures
ofahout 11000+ ss:sper 10,000. There are about 8.82
miI1ion businesses in the U.S. The probability that a
particular establishment will fail is very low and is only
0.011 in 1992. In Exhibit 2, we present empirical
disCribution of failure rates per 10,000 firms in clifferent
years. This distribution is neither normally nor
symmeIricaIIy disIributed deosity function. The empirical
distribution is skewed. Since the failure rate is not
normally distributed, ordinary least square regression
models cannot be used to ideatifY macroeconomic factors
which affect failure rates. Failure rates do not take
negative values. They are not symmetricaJly distributed.
The probability that a particular firm will fail in a year is
veJY sman and there are many firms that can fail. Poisson
disbibuti.on is ex1remely suited to model such random
variables. We therefore, use Poisson regression to model
business failure rates.
This papeI" is organized into five sections. In the
next section, we briefly describe Poisson regression
model. We discuss various macroeconomic factors that
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atIect failure rates of businesses. We use changes in the
gross national product to represent changes in the
economicvitality of a nation. The percentage changes in
the gross national product should be inversely related to
failure rates.
Unlike large films, most small firms depend on
credit for their capital requjrements. Therefore,
availability of credit and its costs can significantly affect
weD-being of a firm. Fast growing firms and marginally
profitable firms require ample credit for their survival.
Therefore, lack ofcredit can drive many firms, especially
the small ones, to failure. There are several measures that
can be a proxy for credit availability. Money supply is
one of1he measures of credit availability. We use money
Sllpply M-2 published for the month of June of each year
as a measure to lepn:sent credit availability in this paper.
Unemployment measures number of persons
withont jobs actively seeking work. It inclndes an
persons 16 years and older who lost or quit previous jobs
and others who reenter workforce. The unemployment
rate denotes the percentage of unemployed in the labor
fcirce. Since the unemployment rate measures the
proportion of people seeking jobs, this is one of the most
important indWators of economic vitality. High
unemployment rates can dampen consumer confidence
and spending which in turn can increase failure rates.
Consequently, the unemployment rates are directly
related to the business failure rates.
Inventcuy to sales ratio has direct affect on the
future production levels. The inventory-sales ratio is
calculated by dividing inventory by sales. Two different
measures of inventory-sales ratios are published. The
inventory to sales ratio published by the Census Bureau
deal with inventories and sales of manufacturers,
merchant wholesalers and retailers. The inventory-sales
ratio published by the Bureau of Economic Analysis
include only final sales to consumers, businesses,
government and foreigners and omits raw materials,
supplies and semi-finished products. In this paper, we
use the inwntoIyto sales ratio compiled by the Bureau of
Census for the month of June of each year.
Capital JlI8Iket retom is an excellent indicator of
future economic activity. Rising stock prices increase
weaII:h and improve consumer confidence. FaDing stock
prices, on the other hand, hamper new capital issues
'Mlk::h in tum discourage spending. There are a variety of
stock market indexes. The stock market indexes
oompiledby the New York Stock Exchange. Standard &.
Poots Corporation, Dow Jones and Wilshire Associates
are some of the popular ones. In this paper, we use total
stock market return for each year as compiled. by
Ibbotson Associates. Since stock market return is a
leading indicator, we use stock market retnrns of the
previous year as our independent variable.
The early years of a business are its most
affect failure rates in the subsequent section. We then
discuss results. We close this paper with conclusions in
the last section.
Poisson Regression Model
Poissson regression has been extensively used
to model the aualysis of discrete count data. Multiple
linear regRSSion is typically used to identify relationships
between a dependent variable and several independent
variables. However, in many settings, the dependent
variable we wish to model may be discrete rather than
contiauous. In addition, the dependent variable may take
only DOIIlleg8Iive values. Therefore, the dependent
variable may not have normal distribution which is
continuous and can take negative values. Therefore, we
could improve multiple linear regression with a model
that accounts for these characteristi.cs. From Exhibit 2,
it is obvious that failure rate per 10,000 businesses are
Uwed towards right. Poisson distribution is well suited
to model such situations. In this model, the failure rates
are assumed to be arising from a Poisson distribution.
This disIribu1ion accounts for the iofrequent and discrete
nature offailures. Ifwe assume that each firm has some
probability ofbeiog faikd, the expected rate of failures in
year t, A,. can be modeled as a function of failure rate per
10,000 businesses and the number of businesses in
10,000's. We can formulate failure rates as an
exponential function of macroeconomic factors which
ensure that the failure rates are nonnegative. If the
macroeconomic variables are denoted by the vector X. ,
the failure rate can be written as:
A, = exp(XP)·
If failure rates are assumed to be Poisson, then the
parameters can efficiently and consistently estimated by
JIIaYimmn likelihood techniques. Poisson regression has
been used to model accident rates of ships [McCullagh
and NeIder(1983»), highway fatalities [Michener and
Tlghe(I992)] and airline accidents [Rose(1990)]. One
drawback ofPoisson regRSSion is its implicit assumption
that the variance equals the mean. Uulike ordinaJy least
square regression method, Poisson regression tends to
give the largest observation more weight than the smaller
ones.
Macroeconomic Factors
The purpose of this paper is to identify
macroeconomic factors that worsen failures of
businesses. The following macroeconomic factors are
considered to cause business failures:
Percentage change in the gross national product,
Credit availability,
Unemployment,
lnventcuy-sa1es ratios,
Capital market retnrns, and
Business survival.
Overall business acIivity can influence sales and
pro.fits of an enterprise. Economic health of a nation can
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critical periods. About half the busmesses do not survive
beyond five years. By the end often years, about two in
three businesses fail. In Exhibit 3, we present survival
rates ofbuslnesses by age of businesses for 1980, 1985
aod 1990. We find that business failure rates are high in
early years and 1hen 1hey flatten out with time. Therefore.
longer a business survives, higher are its chances that it
will outlive still longer. In order to account for 1his
phenomenon, we take average number of businesses
formed in 1he previous five years as a proportion of total
businesses for each year as an independent variable.
Bankruptcy laws have significant effect on
business failores. The Bankruptcy Act of 1978 (official1y
Public Law 95-598) is a major revision since 1938 when
1he Baokruptcy Act of 1898 was amended. In addition to
sUeamJioing adminisIrative mechanism in the bankruptcy
code, this code reforms and consolidates various
provisions into 1hree chapters 7, 11 and 13. A single
pelSOIl or a family in financial trouble can either resort to
Chapter 7 or Chapter 13. Chapter 7 deals with straight
bankruptcies in which a debtor discharges his debt for
paying something to creditors. Chapter 13 allows a
debtor to keep his assets and but promise payment of
debt over three to five years. According to Chapter 13, it
is no longer necessaxy to have approval of creditors for
repayments plans. The courts and debtors have
CODSiderable discretion on this matter. New chapter 11
deals with matters relating to corporate capital structure
reorgauization, arrangement with unsecured creditors,
non-corporate real estate cases and railroad
reorganizatious. Chapter 11 gives exclusive monopoly to
the company management to propose a plan of
reorganization within 120 days. The bankruptcy courts
can extend this management's exclusive privilege
indefinitely. Therefore, the management of a company
does not have to fear that they will lose control of their
orgauization if it opts for baukruptcy. Small businesses
can use Chapter 13 and enjoy some ·of its liberalized
provisions. In short, the new law has made business
closings attractive.
Regression Results
We use business failure rates as reported by
Dun and Bradstreet in its Bwiness Failure Records as a
depeudent variable. The failure data were expanded in
1984 by adding agriculture. forestly and fishing; finance,
iDsaraoce, and real estate", and an services. To account for
these changes, we use a dummy variable D84 whose
value will be 0 if year is smaller than 1984 and 1 for
years greater than 1983. We also use dummy variable
BD to account for the Bankruptcy Reform Act of 1978
which wmt into effect on 1st October 1979. The dummy
variable BD is 1 for years 1980 and greater and 0 for
years less than. 1980.
We use business failure rates as a dependent
variable and percentage change in the gross national
product, M-2 money supply, inventory"sa1es ratio,
tmemploymeDt, stockrelumin the previous year, average
number of businesses formed in the last five years as a
proportion of existing total businesses and dummy
variables to account for revisions in the data in 1984 and
passage of Bankruptcy Reform Act of 1978. All
variables, o1her than the dmnmy variables, are expressed
in 1heir logarithms to base 10. Exhibit 4 displays variable
definitions and their sources. The mean and standard
deviations of ctifferent variables are given in Exhibit 5.
In Exhibit 6, we present Poisson and ordinary
least squares (OLS) regression outputs. The dependent
variable in the OLS regression model is the logarithm of
failurerates. We indicate parameter name, the estimated
parametervalue, and p-value associated with Waid Chisquare and t statistics for testing the significance of the
parameter in Poisson and OLS models. Since the
estimated parameters are elasticities, the coefficients
should be directly comparable. One of the implicit
assumption in a Poisson regression model is that the
variance equals its mean. However, there could be either
overdispersion or underdispersion of data in the fitted
model. One way to test for over or underdispersion is to
verify whether Deviauce divided by degrees of freedom
is close to 1 (SAS, 1993). In our case, we get deviance
per degrees of freedom of 1.0716 which is close to 1.
Therefore, Poisson regression analysis is an appropriate
method to model business failure rates. We compare
appropriatenessofPoisson model against OLS model. In
OLS model, we get an R2 of 0.9067. The R2 for Poisson
model is 0.99. In addition, we also evaluate DurbinWatson statistics in both cases to verify autocorrelation
betweenresidnals The Durbin-Watson statistic for OLS
model is 1.070 and for Poisson model 1.23 again
indicating suitability of Poisson model.
Both Poisson and OLS models have identical
signs for coefficients of various independent variables.
Accordingtotheresu1ts presented in Exhit 6, we find the
percentage change in GNP, money supply, inventory to
sales ratio, and stock retums in the preceding year
inversely affect the business failure rates. The
unemployment rate and businesses formed in the
preceding five years as a proportion of total existing
business increase failure rates. The dummy variable
representing the passage of Bankruptcy Reform Act of
1978 has a positive coefficient indicating increase in
failure rates as a consequence of this act. The dummy
variable is also statistica1ly sigDificant at 0.05 level in
both models. This suggests that the Bankruptcy Act of
1978 has exaceroated business failures. The coefficient
for BD in the OLS model is .3129 and in the Poisson
model.2860. Based OllPoisson Regression model, out of
11742 businesses closed in 1980, 2936 business closings
can be attributed to the passage of the Bankruptcy
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Quality:Economic Determinants of Airline Safety
Refonn Act of 1978. The average liability of businesses
closed in 1989 is about $0.395 million. Therefore
closings attributed to the passage of the bankruptcy code
can be estimated to be $1.132 billion in 1980 alone.
There are several statistical models for
predicting failure of a business establishment. A good
description of failure prediction models for small
businesses can be fonud in Storey et aI. (1987) and
statistical models for baukmptcy prediction in
Altman(l981). However, many of these models use
company specific information and do not consider
macroeconomic factors. Our regression model indicates
that IlIlICl'OeIXIJlC factors do worsen business failures.
It is therefore important that 1end.ing institutions such as
banks do consider future economic environment in
addition to staIisIicaI. failure prediction models when they
make lending decisions. Effects of macroeconomic
factors on failure rates of varions industries are going to
be different. Therefore, it is essential to combine
IDIlC1'OeCOIlOD factors along with industry and company
specific information to improve the 8CClll'acy of failure
prediction models.
Conclusions
In this paper, we present Poisson and OLS
regression models of business failures. Unlike a multiple
regression model, Poisson regression considers skewness
in the probability density function and nonnegativity of
failure rates. Poisson specification conforms to the fact
that the probability of a failure of a business
establishment is very low and at the same time the
number of establishments that can fail is Vel)' high. Our
Poisson regressionmodel indicates that economic factors
do affect failure rates and therefore it is important to
incorporate them in the failure prediction models. The
Bankruptcy Reform Act of 1978 has adversely affected
business closings.
Performance," Journal ofPolitical Economy, 98 (1990)
944-64.
SAS., Bas Technical Report P-243 SASlSTAT
Software:The GENMOD Procedure, Release 6.09, Cary,
NC:SAS Institute Inc,
Shepard, L, Personal failures and the bankruptcy reform
act of 1978, Journal of Law & Economies, xxvn
(1984) 419-437.
Storey,D.,K~,K., Watson,R, Wynarczyk,P., The
performance ofsmal/firms, London:Routledge, 1989.
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References
Altman, E.I. Avery, RE. SiDky, J.F., Application of
classification techniques in business banking and
finance, Greenwich, CT, USA:Jai Press Inc, 1981.
American Enterprise Institute., Bankruptcy Reform,
Washington, DC:American Enterprise Institute, 1978.
Hudson, J., An analysis of company liquidations, Applied
Economics, 18 (1986), 219-235.
Hudson, J., Cuthbertson, The determinants of
bankruptcies in the U.K.:1971-1988, The Manchester
Schoo/Vol.LXI (1993), 65-81.
McCuIIagb, P., and J.Nelder Genera/ized Linear Models,
London:Chapmau andHaU, 1989.
Michener, R, and C.Tighe "A Poisson Regression Model
of Highway Fatalities," American Economic Review,
Papers and Proceedings, 82 (1992), 452-456.
Rose, Nancy L., "Profitability and Product
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Exhibit 4
Variable
BFAIL
GNPCH
MONEY
UNEMP
INVSAL
PTOCK
NEWS
BD
D84
Exhibit 5
Variable
BFAIL
GNPCH
MONEY
INVSAL
PTOCK
NEWB
Variables and their data sources
Description
Number of businesses failed per
year per 10,000 businesses
Change in GNP + 1
Source
Dun and Bradstreet Failures
Record
Survey of Current Business
(Bureau of Economic Analysis)
Federal Reserve Board Bulletin
Monthly Labor Review
(Bureau of Labor Statistics)
Survey of Current Business
(Bureau of the Census)
Ibbotson Associates
Money supply M2
Unemployment rate
Inventory-Sales
Ratios
Total Stock Market Return
(for preceding year) + 1
Average number of businesses
Business Failures Record
formed in the previous five
(Dun andBradstreet
Years/Total businesses
Corporation)
Dummy variable 1 if year is greater than 1979 (to
account for Bankruptcy Reform Act of 1979 which
went into effect on October 1, 1979) otherwise 0
Dummy variable 1 if year is greater than 1983 (to account for
inclusion of agriculture, forestry and fishing, finance,
insurance, and real estate; and all services to failure data)
otherwise o.
Means and standard deviations of various variables.
N
45
45
45
44
44
41
Mean
0.0055
0.0729
7.2575
0.4248
0.1126
-0.6930
std. Dev.
0.0027
0.0317
0.3844
0.0487
0.1516
0.4738
Minimum
0.0014
-0.0050
6.6619
0.3075
-0.3075
-1. 7824
Maximum
0.0120
0.1450
7.8128
0.5365
0.4228
-0.0594
All variables except BFAIL are expressed as logarithm to base 10.
Exhibit 6 Poisson and OLS Regression Results for 1946-91
POISSON
OLS
Variable
Coefficient
Pr>Chi
Coefficient
Dependent Variable: Failure Rates.
Intercept
GNPCH
MONEY
INVSAL
UNEMP
PTOCK
BD
D84
NEWS
N
9.8970
-4.8152
-1.6968
-3.6688
0.1057
-0.0409
0.2860
0.9190
1.2350
0.0000
0.0001
0.0000
0.0000
0.0595
0.8389*
0.0192
0.0000
0.0000
+9.6993
-4.6531
-1.6724
-3.7711
0.0891
-0.0950
0.3129
0.6946
1.1767
41
0.99
Durbin-Watson
1.23
Deviance
34.2909
Degrees of Freedom
32
Deviance/Degrees of freedom 1. 0716
Pr>t
0.0008
0.0010
0.0001
0.0001
0.1118*
0.6722*
0.0360
0.0001
0.0001
41
0.91
1.07
R2
Not significant at the 10-percent level.
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