An empirical analysis of the business failure process for large and small firms.

Campbell, Steven V. ; Choudhury, Askar H.

ABSTRACT

This paper investigates endogenous dependence in the business failure process for large and small businesses. After controlling for systemic growth, we find the momentum in business failures from their cumulative lagged effect over time influences other distressed business to fail and creates a domino-effect. For both large and small businesses, endogenous dependence is most effectual in the months immediately prior to failure and then gradually dissipates to a level of insignificance within a two year lag. We also find new business formations counterbalance to some degree the domino-effect of business failures; however, the lag effect for new business formations is twice as long for large firms compared to small firms. Our results suggest theories of business failure and bankruptcy prediction models would be enhanced by incorporating endogenous dependence in the business failure process as an explanatory variable.

INTRODUCTION

Empirical evidence suggests business failure is a combination of firm-specific (micro) factors (e.g.; Altman, 1968, 1971; Hambrick & Crozier, 1985; Duchesneau & Gartner, 1990; Lussier, 1996; Perry, 2001; Carland et al., 2001) and external (macro) factors related to the business cycle (e.g;. Altman, 1971; Carroll & Delacroix, 1982; Rose et al., 1982; Yrle et al., 2001). The common thread running through these prior studies is their focus on the exogenous determinants of business failure, which the literature suggests are many. As Carland et al. (2001) observe, "The study of small business failure has been so institutionalized, that the causes of failure have become cliches: managerial incompetence, undercapitalization, etc" [p.78].

The purpose of this paper is to analyze endogenous dependence in the business failure process. Specifically, we present evidence of lead times in two forces affecting the number of large and small business failures. One force is business failure momentum which we characterize as a domino-effect: one firm's failure causes other firms to fail which cause still more firms to fail and so on. We also present evidence of lead times in the competing force of new business formations: the formation of a new business prevents other established firms from failing which prevent still more firms from failing and so on. Research along these lines could add an important new dimension to the existing body of business failure research by enhancing existing bankruptcy prediction models, improving managerial decision making, and helping auditors, bankers, and financial analysts assess the failure risk of their clients.

While some specific hypotheses can be generated, our limited understanding of business failure endogenicity suggests an exploratory, inductive research approach is appropriate and this study takes such an approach. For our empirical analysis we use quarterly and monthly business failure data for the period January 1986 to September 1998. Separate regressions are estimated for large business failures and small business failures, and for each regression various lead-lag relationships are tested in order to determine the highest statistical correlation, on a multivariate basis, between variables. To control for systemic growth, our regression analysis includes a linear time trend control variable and, where appropriate, we adjust for the affects of autocorrelation.

Overall our evidence indicates significant endogenous dependence in the business failure process for both large and small firms, with the stronger correlations occurring in the case of small firms. For both large and small firms, endogenous dependence is most influential in the months immediately prior to failure then gradually dissipates to a level of insignificance within two years. Our results further suggest new business formations counterbalance to some degree the domino-effect of business failure momentum; however, the lag effect for new business formations is twice as long for large firms compared to small firms. Specifically, for large businesses we find the counterbalancing influence of new business formations is most powerful at sixteen months prior to failure and then diminishes rapidly, while for small businesses we find new business formations have their greatest influence eight months before failure. The diminishing impact of new business formations mark the onset of the death struggle identified by Hambrick and D'Aveni's (1988), and our evidence suggests once a firm begins a death struggle, it must be very lucky to overcome endogenous dependence in the business failure process.

The next section summarizes the related literature on business failures and develops the study's hypotheses. This is followed by a section discussing the sample selection and research design. The results are presented next and in the final section of the paper we summarize our findings and conclusions.

HYPOTHESES DEVELOPMENT

Bankruptcy is a serious economic problem in the United States and the bankruptcy literature is vast. One of the most extensive areas of study in the bankruptcy literature has been bankruptcy prediction research. An accurate bankruptcy prediction model offers many economic benefits and as Jones (1987, p.131) observes:

 The continued strong interest in bankruptcy prediction indicates
 the importance of the topic. An accurate prediction of bankruptcy
 can benefit a variety of interested parties. For example, investors
 may seek to avoid losses associated with bankruptcy....Lenders may
 use bankruptcy prediction techniques to help assess the risk on
 loan default. Auditors must issue a qualified opinion when there is
 substantial uncertainty about an entity's continued existence. A
 bankruptcy prediction model could warn an auditor about a company's
 vulnerability and protect the auditor from lawsuits arising from a
 failure to disclose the possibility of bankruptcy. Management may
 choose to defend a proposed merger against antitrust charges on the
 basis that an acquired company was failing. Employees or their
 unions may want to assess the risk of bankruptcy and the resulting
 threat to continued employment. Academicians have used bankruptcy
 prediction models to demonstrate the information value of cash flow
 and price-level adjusted data.

Most of the bankruptcy prediction studies produced in the 1960s, 1970s, and 1980s are well summarized in a number of publications (e.g.; Altman et al., 1981; Scott, 1981; Altman, 1983; Zavgren, 1983; Jones, 1987; Platt & Platt, 1990). The better known multivariate studies use multiple discriminate analysis (e.g.; Altman, 1968; Altman et al., 1977), regression modeling (e.g.; Edminster, 1972), logit analysis (e.g.; Olson, 1980; Zavgren, 1983), probit analysis (e.g.; Zmijewski, 1984), and recursive partitioning (e.g.; Frydman, et al., 1985). While some of these methodologies have resolved certain statistical issues, the classification results one year prior to failure are fairly invariant and somewhat disappointing. Corporate failure models described as having good predictive ability generally report out-of-sample classification results that are ten or more percentage points lower than the ex post results.

Bankruptcy prediction studies have documented numerous exogenous determinants of business failure, including many firm-specific (micro) predictors. Most researchers have selected financial ratios as predictor variables because of their popularity and predictive success in previous studies (e.g.; Beaver, 1966; Altman, 1968; Olson, 1980; Frydman et al., 1985; Casey & Bartczak, 1985; Hambrick & Crozier, 1985; Duchesneau & Gartner, 1990; Lussier, 1996; Perry, 2001). Other researchers have examined macroeconomic predictors under the assumption that any given firm may have a higher propensity to fail in times of economic recession than in times of economic prosperity. These researchers generally have selected popular economic indicators as predictor variables (e.g.; Rose et al., 1982; Carroll & Delacroix, 1982; Yrle et al., 2001). Although this approach to variable selection has had little success in developing an integrated theory of business failure, there has been success in using such variables to distinguish between bankrupt and nonbankrupt firms.

Where the interest is in understanding bankruptcy rather than simply predicting it, there must be the ability to apply economic interpretations to the prediction models. The present study is aimed at providing insights into the process of business failure for large and small businesses in the context of aggregate business failures. While most of the bankruptcy literature has concentrated on identifying exogenous factors related to failure, only a few studies (e.g.; Hambrick & D'Aveni, 1988; Venkataraman et al., 1990) have investigated the process of failure within the firm, and no study to our knowledge has investigated endogenous dependence among failed firms. Understanding such interrelationships among failed firms is fundamental to developing an integrated theory of business failure and advancing our understanding of bankruptcy prediction.

Hambrick and D'Aveni (1988) document the dynamics of large corporate failure by using a matched pair design of 57 large bankruptcies and 57 matched survivors. Perhaps their most striking finding is that the bankrupts showed signs of relative weakness very early, as far back as ten years before they failed. From years t-10 to t-2, the bankrupts maintained cushions comparable to their matched firm survivors for meeting current obligations, but at the same time that their profitability was suffering and their potential slack was depleting. In the end their cushion of short-term resources collapsed and failure resulted. Hambrick and D'Aveni concluded the failure process for large companies is a long protracted downward spiral consisting of four phases. The final stage they termed the "death struggle" (years t-2 and t-1 for the firms in their sample). It is in this final stage that the firm's slack and performance deteriorate sharply, and death occurs.

Regarding the failure process for small firms, Venkataraman et al. (1990) investigated the interaction between environmental volatility and the liabilities of newness and smallness. Contrary to the drawn-out downward spiral documented for large firms by Hambrick and D'Aveni (1988), Venkataraman et al. (1990) found new small firm failure is generally abrupt and catastrophic. Under their process model, whether a new small business succeeds or fails depends on the nature, formation, and dissolution of specific transactions. The authors observe:

New firms in many industries often lack the collateral or bonding requirements for engaging in transactions.... Under such situations some firms use a transaction with an established other partner as a source of legitimacy. We call the strategy of using transactions, with one or two legitimate external parties as collateral, to attract and engage in transactions with other resource suppliers, leveraging. However, leveraging renders the overall set of transactions of the firm tightly coupled, by making the fulfillment of each transaction highly contingent upon the fulfillment of the others. And, therefore, when any one transactions in the set fails, the whole set could fail in domino-effect fashion (Venkataraman et al., 1990, p.287).

Small business failure is thus triggered by the breakdown of a key contractual relationship or transaction at a time when the small firm lacks accumulated slack. By the laws of chance some proportion of transactions fail, terminate, or are unfulfilled, due to environmental turbulence which means small business failure is partly within the control of an entrepreneur and partly a random process beyond the entrepreneur's control.

The present study extends the work of Hambrick and D'Aveni (1988) and Venkataraman et al. (1990) by examining interdependence among firms in the business failure process. While Venkataraman et al. (1990) document the interdependence among a particular firm's set of transactions; we examine the interdependence among firms as a source of transaction failure. Our first hypothesis extends the idea of coupling transactions from being an intra-firm phenomenon to include inter-firm dependence. Thus, the failure of an important transaction can have a domino-effect causing numerous other businesses to fail. This process of protracted time dependence in past business failures can be characterized as a long memory of business failures stemming from a series of failed transactions.

H1: The number of business failures is positively influenced by lag
 effects from prior business failures.

Counterbalancing the domino-effect of business failure is new business formations. New business formations create new transactions which allow existing businesses to implement risk reducing strategies such as diversifying or accumulating slack. These actions make the firm less vulnerable to the failure of any particular transaction in its set of transactions. The number of new business formations thus is a proxy for economic activities that prevent existing businesses from failing. However, once a firm begins what Hambrick and D'Aveni (1988) describe as the "death struggle" phase of business failure, new business formations will be ineffectual in stemming the rapid disintegration of transactions. Thus, our second hypothesis is:

H2: The number of business failures is negatively influenced by lag
 effects from new business formations.

RESEARCH DESIGN

Both quarterly and monthly business failure data were accumulated from Dun and Bradstreet's commercial failures data for the period of January 1986 to September 1998. This sample period was one of necessity, rather than choice. In the mid-1980s Dunn and Bradstreet's decided to expand the compilation of business closing statistics in certain industry groups and this resulted in 20 months of missing data in the data set. Beginning the sample period in January 1986 avoided this missing data problem. The sample period ends in September 1998 because at this time Dun and Bradstreet reorganized its internal operations and ceased reporting business formation and business failure statistics altogether.

Table 1 presents summary statistics for large and small business failures for the sample period January 1986--September 1998. A "failure" is defined as, "a concern that is involved in a court proceeding or voluntary action that is likely to end in a loss to creditors" (Dun and Bradstreet's measures of failures, 1955-1998). All industrial and commercial enterprises petitioned into the Federal Bankruptcy Courts are included in the failure records. Also included are: 1) concerns forced out of business through such actions in the State courts as foreclosures, executions, and attachments with insufficient assets to cover all claims; 2) concerns involved in court actions such as receiverships, reorganizations, or arrangements; 3) voluntary discontinuations with a known loss to creditors; and 4) voluntary out of court compromises with creditors. Table 1 indicates the average number of small business failures is more than double the average number of large business failures. Specifically, during the sample period the number of small business failures averaged 4085 per month compared to 1898 failures per month for large businesses. A small business is defined as a concern having less than $100,000 in current liabilities; a large business is defined as a concern having more than $100,000 in current liabilities (Dun and Bradstreet's measures of failures, 1955-1998).

Table 1 also reports the average amount of current liabilities for large and small business failures for the sample period. Current liabilities include all accounts and notes payable, whether secured or unsecured, known to be held by banks, officers, affiliated companies, suppliers, or the Government. They do not include long-term publicly held obligations (Dun and Bradstreet's measures of failures, 1955-1998). The amount of current liabilities is of interest because it is one of the few directly observable measures of business failure costs. A large proportion of these liabilities will never be paid, and consequently, they must be absorbed as losses by other business and non-business entities. Current liabilities for large firm failures are 50 times larger on average than the current liabilities for small firm failures.

We hypothesize (1) a positive association between lag effects of prior business failures and current business failures and (2) a negative association between lag effects of new business formations and current business failures. To test these hypotheses we regress the number of business failures on lagged business failures and lagged new business incorporations. The analysis becomes complicated because the number of business failures depends not only on past business failures and new business formations but also on many other factors including population growth and market expansions. To control for this systemic growth, the regression includes a linear time trend control variable, defined as a time series starting at one and growing at a constant amount B=1 each time period.

We estimated separate regressions for large and small business failures and do not combine large firms and small firms in the same model. For each regression we examined various lag relationships in order to determine the highest statistical correlation, on a multivariate basis, between variables. We also tested various lag relationships between large firm failures and small firm failures, and visa versa; however, these latter regressions did not improve explanatory power, and therefore, are not reported.

From the various lag combinations of quarterly data, the final specification using ordinary least squares regression is of the following form for large firm failures and small firm failures respectively:

LGFAI[L.sub.t] = [[beta].sub.0] + [[beta].sub.1]TREN[D.sub.t] +
[[beta].sub.2]LGFAI[L.sub.t-1] + [[beta].sub.3]NE[W.sub.t-6] +
[v.sub.t] (1)

SMFAI[L.sub.t] = [[beta].sub.0] + [[beta].sub.1]TREN[D.sub.t] +
[[beta].sub.2]SMFAI[L.sub.t-1] + [[beta].sub.3]NE W.sub.t-3] +
[v.sub.t] (2)

Where:

TREN[D.sub.t] = a series starting at 1 and growing at a constant amount
 B=1 each time period t;
SMFAI[L.sub.t-1] = the number small firm failures lagged one quarter
 back in time t;
LGFAI[L.sub.t-1] = the number large firm failures lagged one quarter
 back in time t; and
NE[W.sub.t-k] = the number of new business incorporations lagged k
 quarters back in time t.

After estimating equations (1) and (2) with quarterly data, we employed the same procedure to estimate e similar regressions using monthly data. This provided a detailed time series of monthly lags around points of highest statistical correlation. From the various lag combinations of monthly data, the final specification using ordinary least squares regression is of the following form for large firm failures and small firm failures respectively:

LGFAI[L.sub.t] = [[beta].sub.0] + [[beta].sub.1]TREN[D.sub.t] +
[[beta].sub.2]LGFAI[L.sub.t-1] + [[beta].sub.3]LGFAI[L.sub.t-2] +
[[beta].sub.3]LGFAI[L.sub.t-3] + [[beta].sub.5]NE[W.sub.t-16] +
[[beta].sub.6]NE[W.sub.t-17] + [[beta].sub.7]NE[W.sub.t-18] + vt (3)

SMFAI[L.sub.t] = [[beta].sub.0] + [[beta].sub.1]TREN[D.sub.t] +
[[beta].sub.2]SMFAI[L.sub.t-1] + [[beta].sub.3]SMFAI[L.sub.t-2] +
[[beta].sub.4]SMFAI[L.sub.t-3] + [[beta].sub.5]NE[W.sub.t-16] +
[[beta].sub.6]NE[W.sub.t-17] + [[beta].sub.7]NE[W.sub.t-18] + vt (4)

Where:

TREN[D.sub.t] = a series starting at 1 and growing at a constant amount
 B=1 each time period t;
SMFAI[L.sub.t-J] = the number small firm failures lagged J months back
 in time t;
LGFAI[L.sub.t-J] = the number large firm failures lagged J months back
 in time t; and
NE[W.sub.t-k] = the number of new business incorporations lagged k
 months back in time t.

Because of the autocorrelative nature of the data, we performed a time series analysis based on the Box-Jenkins approach (Box & Jenkins, 1976). Autocorrelation induces unreliability in assessing the least squares estimators in a regression model (see Choudhury, 1994). Based on the time series analysis, it was necessary to adjust for autocorrelation with regard to the quarterly data only. We evaluated the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the regression residuals using SAS procedure PROC ARIMA (see SAS/ETS User's Guide, 1988) to observe the degree of autocorrelation and to identify the order of the model that sufficiently described the autocorrelation. A seventh order autoregressive (AR) model (1 - [[phi].sub.7] [B.sup.7]) [v.sub.t] = [[epsilon].sub.t] has been identified for large firms model and sixth order autoregressive (AR) model (1 - [[phi].sub.6] [B.sup.6]) [v.sub.t] = [[epsilon].sub.t] has been identified for small firms. These models were estimated using the maximum likelihood technique with SAS procedure PROC AUTOREG.

Autoregressive parameters for both the large and small firm quarterly data models were statistically significant at the .05 level. An adjustment was therefore introduced and the final specification using generalized least squares regression is of the following form for large and small firm failures:

LGFAI[L.sub.t] = [[beta].sub.0] + [[beta].sub.1]TREN[D.sub.t] +
[[beta].sub.2]LGFAI[L.sub.t-1] + [[beta].sub.3]NE[W.sub.t-6] +
[v.sub.t][v.sub.t] = [[phi].sub.7] [v.sub.t-7] + [[epsilon].sub.t]; (5)

SMFAI[L.sub.t] = [[beta].sub.0] + [[beta].sub.1]TREN[D.sub.t] +
[[beta].sub.2]SMFAI[L.sub.t-1] + [[beta].sub.3]NE[W.sub.t-3] +
[v.sub.t][v.sub.t] = [[phi].sub.6] [v.sub.t-6] + [[epsilon].sub.t]; (6)

Where:

TREN[D.sub.t] = a series starting at 1 and growing at a constant amount
 B=1 each time period t;
SMFAI[L.sub.t-1] = the number small firm failures lagged one quarter
 back in time t;
LGFAI[L.sub.t-1] = the number large firm failures lagged one quarter
 back in time t; and
NE[W.sub.t-k] = the number of new business incorporations lagged k
 quarters back in time t.

RESULTS

In this section we report the results of tests investigating endogenous dependence in large and small business failures. Table 2 reports correlations between the number of business failures and their monthly lags. Consistent with the first hypothesis, significant positive correlations are observed in the monthly lags for both large and small business failures. The strongest correlations, .73 for large firms and .85 for small firms, occur after a one month lag. Subsequently the monthly correlations weaken over time to the point insignificance by 24 months. The results in Table 2 also suggest the memory of business failure is longer for small firms compared to large firms.

Table 3 reports the results of the regression equations using quarterly data. The timing relationships reported in Table 3 were empirically determined in order to maximize the explanatory power of the regression model. Thus, maximum explanatory power was achieved for the large firm regression when large business failures were lagged one quarter and new business formations were lagged six quarters. In contrast, maximum explanatory power was achieved for the small firm regression when small business failures were lagged one quarter and new business formations were lagged three quarters. The Durbin-Watson statistics on the initial estimates indicated marginally significant autocorrelation among error terms; and therefore, Table 3 also reports the estimated generalized regression equations that are corrected for autocorrelation.

The coefficient estimates for FAILLAG1, the number of large or small business failures lagged one month back in time, is statistically significant (p<.01) and positive for both large and small firms. This result provides strong support for the first hypothesis. One interpretation of this finding is that for every pair of large firms failures in a given month, one more large business will fail the following month; similarly, for every four small business failures in a given month, three small businesses will fail the following month. The number of new business formations lagged three months back in time, NEWLAG3, is statistically significant (p<.01) and negative for small firms and the number of new business formations lagged six months back in time, NEWLAG6, is statistically significant (p<.01) and negative for large firms. These results provide strong support for the second hypothesis. One interpretation of this finding is that for every 100 new business formations, three large businesses that would otherwise fail in six months will not fail and six to seven small business that would otherwise fail in three months will not fail.

Table 4 reports the regression results using monthly data and as expected the monthly results are similar to the quarterly results reported in Table 3. However, some additional detail is provided by the monthly timing relationships. The coefficient estimates for the business failures lagged variable, FAILLAG(J), gradually looses explanatory power as the monthly lag time increases. For both large and small firms, the lag effect is strongest after one month (p<.01), still strong and statistically significant after two months (p<.01), and not statistically significant after three months. These results however must be interpreted with caution due to collinearity in the monthly data. The same concern holds true regarding the coefficient estimates for the new business formations lagged variable, NEWLAG(J), reported in Table 4. Our results suggest the lag effect for new business formations is strongest for small firms at eight months and large firms at sixteen months.

SUMMARY AND CONCLUSIONS

This paper examines endogenous dependence in the business failure process for large and small businesses. After controlling for systemic growth, we use lagged business failures as an explanatory variable to explain the movement in business failures over time. We find the momentum in business failures from their cumulative lagged effect over time influences other distressed business to fail. The interdependence in the business failure process can be characterized as long memory of business failures that is present in both large and small business failures; however, the memory appears to be longer for smaller firms compared to large firms.

This paper extends Hambrick and D'Aveni's (1988) finding that large corporate bankruptcies progress as long downward spirals, by providing evidence of the final phase of organizational decline, the "death struggle". Hambrick and D'Aveni suggest this final phase occurs during the large firm's last two years of existence following a prolonged period declining performance and diminishing slack. Our results suggest a more precise empirically based timeframe for commencement of the death struggle. Specifically, for large businesses we find the counterbalancing influence of new business formations ceases to be very influential within the last sixteen months prior to failure and when new business formations can no longer stave off the forces of decline, the death struggle would appear to be at hand. For small businesses, we find the counterbalancing influence of new business formations ceases to be very influential within the last eight months prior to failure. The shorter death struggle for smaller firms is consistent with the process model for new small business failure developed by Venkataraman et al. (1990).

Once the death struggle begins for a large firm, the failure process becomes similar to catastrophic process described by Venkataraman et al. (1990) for small firms: slack is gone, working capital is depleted, and all that remains before the nails are put in the coffin is the failure of one important transaction. Our results suggest such an event can be concomitant failure of another firm with which the firm has a contractual relationship and that once a firm enters the death struggle, it must be very lucky to overcome endogenous dependence in the business failure process.

This study raises several issues for future bankruptcy research. First, our evidence indicates endogenous dependence should be included in an integrated theory of business failure for large and small firms; however, this study is only a first step in modeling functional relationships. Future research could investigate factors that systematically contaminate the model residuals' ability to capture endogenous dependence. Second, our evidence has implications for increasing the explanatory power of bankruptcy prediction models and identifying the determinants of business failure. Endogenous dependence is only one dimension of business failure. Future bankruptcy prediction models could incorporate exogenous dependence as an explanatory variable and investigate its interactions with other predictors, particularly other macroeconomic variables. Finally, although we find positive associations in the number of business failures and their monthly lags going back almost two years, it is difficult to completely rule out unknown growth factors as an alternative explanation for the results.

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Steven V. Campbell, University of Idaho Askar H. Choudhury, Illinois State University

Table 1: Summary Statistics for Large and Small Firm Failures for the
Period January 1986-September 1998 (a)

 Quarter/ Standard
Variables (b) Month Means Deviation Minimums

SMFAIL Quarterly 12175.21 2764.60 7624.00
 Monthly 4084.59 936.37 2476.00
LGFAIL Quarterly 5658.21 1003.00 3954.00
 Monthly 1898.24 351.89 1223.00
SMLIAB Quarterly 218.16 40.66 155.80
 Monthly 73.19 14.59 47.60
LGLIAB Quarterly 11626.84 7367.39 3561.20
 Monthly 3900.62 2868.98 972.90
NEW Quarterly 178005.49 13784.29 153911.00
 Monthly 59335.16 5290.19 48688.00

 Quarter/
Variables (b) Month Medians Maximums

SMFAIL Quarterly 12339.00 18102.00
 Monthly 4035.00 6365.00
LGFAIL Quarterly 5529.00 7722.00
 Monthly 1882.00 2778.00
SMLIAB Quarterly 212.80 300.10
 Monthly 72.80 108.40
LGLIAB Quarterly 9302.35 38047.20
 Monthly 2968.20 15673.90
NEW Quarterly 174196.00 205844.00
 Monthly 58253.00 73060.00

(a) Small firms have less than $100,000 in current liabilities; large
firms have more than $100,000 in current liabilities. A failure is
defined as, "a concern that is involved in a court proceeding or
voluntary action that is likely to end in a loss to creditors." Source:
Dun & Bradstreet, Inc

(b) Variable Definitions:

SMFAIL = number of small firm failures;

LGFAIL = number of large firm failures;

SMLIAB = amount of current liabilities (millions of dollars)--small
firm failures;

LGLIAB = amount of current liabilities (millions of dollars)--large
firm failures; and

NEW = number of new business incorporations.

Table 2: Correlation between Number of Failures and their Lags for
Large and Small Firms Monthly Data (a)

Variables (b) Large Firm Failures Small Firm Failures

FAILLAG1 0.73301 (<0.0001) 0.84956 (<0.0001)
FAILLAG2 0.71022 (<0.0001) 0.83607 (<0.0001)
FAILLAG3 0.63847 (<0.0001) 0.81074 (<0.0001)
FAILLAG4 0.49090 (<0.0001) 0.75318 (<0.0001)
FAILLAG5 0.54512 (<0.0001) 0.79799 (<0.0001)
FAILLAG6 0.47662 (<0.0001) 0.74497 (<0.0001)
FAILLAG7 0.44652 (<0.0001) 0.72692 (<0.0001)
FAILLAG8 0.39054 (<0.0001) 0.67578 (<0.0001)
FAILLAG9 0.42561 (<0.0001) 0.66844 (<0.0001)
FAILLAG10 0.38573 (<0.0001) 0.63894 (<0.0001)
FAILLAG11 0.36153 (<0.0001) 0.61174 (<0.0001)
FAILLAG12 0.43591 (<0.0001) 0.64860 (<0.0001)
FAILLAG13 0.27099 (0.0011) 0.52284 (<0.0001)
FAILLAG14 0.28927 (0.0005) 0.52685 (<0.0001)
FAILLAG15 0.22572 (0.0073) 0.46897 (<0.0001)
FAILLAG16 0.12568 (0.1404) 0.39555 (<0.0001)
FAILAG17 0.18943 (0.0261) 0.41332 (<0.0001)
FAILLAG18 0.04476 (0.6035) 0.29929 (0.0004)
FAILLAG19 0.01472 (0.8649) 0.28552 (0.0008)
FAILLAG20 -0.06231 (0.4728) 0.24654 (0.0039)
FAILLAG21 -0.12214 (0.1597) 0.20544 (0.0173)
FAILLAG22 -0.12372 (0.1560) 0.18292 (0.0351)
FAILAG23 -0.15721 (0.0718) 0.15188 (0.0821)
FAILLAG24 -0.14542 (0.0975) 0.14625 (0.0955)

( ) p-values

(a) Small firms have less than $100,000 in current liabilities; large
firms have more than $100,000 in current liabilities. A failure is
defined as, "a concern that is involved in a court proceeding or
voluntary action that is likely to end in a loss to creditors." Source:
Dun & Bradstreet, Inc.

(b) Variable Definitions: FAILLAG(J) = number of firm failures, large
or small, lagged J months back in time.

Table 3: Extended Regressions on Number of Large and Small Firm
Failures--Quarterly Data (a)

Independent
Variables (b) Large Firms Small Firms

Intercept 6472.0858 (c) 15788.00
 (2.95) *** (2.92) ***
TREND 25.8286 72.5149
 (2.07) ** (2.03) **
FAILLAG1 0.5711 0.6866
 (4.60) *** (5.85) ***
NEWLAG3 -- -0.0807
 (-2.69) ***
NEWLAG6 -0.0281 --
 (-2.35) **
R-Squared 0.55 0.78
Durbin-Watson 1.73 1.76
 [0.09] (f) [.10]

 Large Firms Small Firms
Independent (corrected for (corrected for
Variables (b) autocorrelation) (d) autocorrelation) (e)

Intercept 7146.00 13057.00
 (3.44) *** (2.98) ***
TREND 29.1039 57.1868
 (2.64) ** (2.14) **
FAILLAG1 0.5142 0.7302
 (4.04) *** (7.00) ***
NEWLAG3 -- -0.0652
 (-2.81) ***
NEWLAG6 -0.0307 --
 (-2.82) ***
R-Squared 0.61 0.81
Durbin-Watson 1.76 1.88
 [.10] [0.20]

(a) Small firms have less than $100,000 in current liabilities; large
firms have more than $100,000 in current liabilities. A failure is
defined as, "a concern that is involved in a court proceeding or
voluntary action that is likely to end in a loss to creditors." Source:
Dun & Bradstreet, Inc.

(b) Variable Definitions:

TREND = a series starting at 1 and growing at a constant amount B = 1
each time period;

FAILLAG1 = the number firm failures, large or small, lagged one quarter
back in time; and

NEWLAG(J) = the number of new business incorporations lagged J quarters
back in time.

(c) t-statistic reported in parenthesis are significant at ten
(*), five (**), and one (***) percent levels.

(d) The model was identified as, (1 - [[phi].sub.7] [B.sup.7])
[v.sub.t] = [[epsilon].sub.t].
Estimated ARIMA model of the regression residuals from SAS,
(1 + 0.4010 [B.sup.7]) [v.sub.t] = [[epsilon].sub.t]
(0.0386)

(e) The model was identified as, (1 - [[phi].sub.6] [B.sup.6])
[v.sub.t] = [[epsilon].sub.t].
Estimated ARIMA model of the regression residuals from SAS,
(1 + 0.4237 [B.sup.6]) [v.sub.t] = [[epsilon].sub.t]
(0.0181)

Where p-values (significance level) for autoregressive parameters are
reported in parentheses.

(f) [ ] p-values for Durbin-Watson statistic.

Table 4: Regressions on Number of Large and Small Firm
Failures--Monthly Data (a)

Independent
Variables (b) Large Firms Small Firms

Intercept 1060.4792 (c) (2.76) *** 2997.0277 (2.83) ***
TREND 1.8272 (2.45) ** 5.4242 (2.32) **
FAILLAG1 0.4645 (5.19) *** 0.3915 (4.42) ***
FAILLAG2 0.3534 (3.78) *** 0.2754 (3.01) ***
FAILLAG3 -0.0548 (-0.58) 0.1266 (1.46)
NEWLAG7 -- -0.0213 (-1.87) *
NEWLAG8 -- -0.0230 (-2.05) **
NEWLAG9 -- -0.0007 (-0.06)
NEWLAG16 -0.0175 (-2.86) *** --
NEWLAG17 0.0002 (0.04) --
NEWLAG18 0.0038 (0.64) --
R-Squared 0.66 0.79
Durbin-Watson 2.01 1.95

(a) Small firms have less than $100,000 in current liabilities; large
firms have more than $100,000 in current liabilities. A failure is
defined as, "a concern that is involved in a court proceeding or
voluntary action that is likely to end in a loss to creditors." Source:
Dun & Bradstreet, Inc.

(b) Variable Definitions:

TREND = a series starting at 1 and growing at a constant amount B = 1
each time period;

FAILLAG(J) = the number firm failures, large or small, lagged J months
back in time; and

NEWLAG(J) = the number of new business incorporations lagged J months
back in time.

(c) t-statistic reported in parenthesis are significant at ten (*),
five (**), and one (***) percent levels.