The relationship between interest rates on the number of large and small business failures.

Campbell, Steven V. ; Choudhury, Askar H.

ABSTRACT

This paper presents evidence suggesting interest rates have dissimilar effects on the large firm and small business failures. We examine monthly time-series data for the period 1984-1998 and find the interest rate is positively associated with the number of large business failures and negatively associated with the number of small business failures. We also find interest rates exhibit a long memory. For small businesses the negative impact of the interest rate on the number of failures is immediate and the lagged interest rate continues to be significant and strong and for over four years; for large firms the positive impact of the interest rate on the number of failures is delayed several months before gaining strength. Using maximum likelihood estimation to relate the number of large and small business failures to the interest rate, we find the interest rate is a statistically significant determinant of small business failure and the sign of the coefficient is negative. We do not find the interest rate a statistically significant determinant of large business failure. These results suggest the interest rate is more influential in the small business failure process.

INTRODUCTION

In this paper we analyze the business failure process for large and small firms in the context of changing interest rates. Anecdotal evidence suggests interest rates and business failures are positively associated; however, empirical evidence of a positive association is weak. Most of the prior empirical work tests large firm samples and, due to research design limitations, correlated predictor variables and nonstationarity over time make interpretation of individual predictors speculative. The present study focuses exclusively on the association between interest rates and the number of large firm and small firm failures over the period 1984-1998.

Although macroeconomic factors are commonly viewed as important causes of business failure, they have received sparse attention in the literature (Everett and Watson, 1998). This is unusual given the potential benefit of understanding the external causes of business failure. For example, the forecasting accuracy of bankruptcy prediction models could be enhanced by the incorporation of macroeconomic variables. This would assist lenders in assessing the risk of default, auditors in assessing the failure risk of their clients, and management in assessing the merits of restructuring. Also, understanding the external causes of business failure would allow public policymakers to better serve the business sector. Once the effects of the key macroeconomic determinants are understood, government policy could influence the failure rate by changing the economic environment in which businesses operate.

This is the first study to report differential effects for interest rates in the large firm versus small firm failure processes. Specifically, using correlation analysis, we find the relationship between interest rates and the number of large firm failures is positive (as interest rates increase, large firm failures increase), while the relationship between interest rates and the number of small firm failures is negative (as interest rates increase, small business failures decrease). Interest rates also exhibit long-term statistical dependence; however, we find the magnitude and nature of the dependence differs between large and small firms. We find the negative association between interest rates and small business failure strong and immediate and it continues to persist for over four years. In contrast, we find the positive association between interest rates and large business failure weak initially, but after a four month lag it becomes significant and continues strong for over four years. In addition to correlation analysis, we perform regression analysis to assess concurrent interest rates as a predictor of the number of firm failures. We find a statistically significant association for small firms and the coefficient is negative; we do not find a statistically significant association for large firms. These results suggest the impact of interest rates on the small firm failure process is different both in direction and magnitude from the impact on the large firm failure process.

A brief review of previous studies is presented in the following section. A description of the research design, the results, and conclusions are presented in the succeeding sections.

LITERATURE REVIEW AND HYPOTHESIS DEVELOPMENT

Empirical evidence suggests business failure is often caused by a complex combination of endogenous factors (Altman, 1968; Olson, 1980; Hambrick and Crozier, 1985; Duchesneau and Gartner, 1990; Lussier, 1996; Perry, 2001; Carland et al., 2001) and exogenous factors (Altman, 1971; Carroll and Delacroix, 1982; Rose et al., 1982; Everett and Watson, 1998; Yrle et al., 2001). Empirical evidence also suggests heterogeneous failure processes for large and small firms. Large firm failure is generally a long downward spiral (Hambrick and D'Aveni, 1988), while small firm failure is generally catastrophic and abrupt (Venkataraman et al., 1990).

The primary causes of small business failure appear to be the lack of appropriate management skills, inadequate capital, and fraud (Carland, 2001). However, a number of small business studies also document the relevance of exogenous factors, such as interest rates. Peterson et al. (1983) found, although endogenous factors were the main cause of failure, exogenous factors had a significant effect in approximately one-third of small business failures. Birley and Niktari (1995) report the economy ranked third as the primary cause of failure for 486 independent owner-managed businesses as described by their accountant or bank manager. Everett and Watson (1998) suggest economic factors are associated with between 30% and 50% of small business failures, depending on the definition of failure used.

Large firm studies generally find a positive relationship between interest rates and the number of business failures (e.g. Rose et al., 1982; Wadhwani, 1986; Hudson 1989). Rose et al. (1982) performed a stepwise regression on thirteen macroeconomic factors using various lead-lag relationships. They found the most promising model had six factors two of which were interest rates, the prime rate and the ninety-day treasury bill rate, both lagged four quarters. In their regression results, the lagged ninety-day treasury rate had a positive sign and was significant at the .0001 level, while the lagged prime rate had a negative sign and was significant at the .01 level. These results illustrate the correlation among variables problem existing in most multivariate models containing several macroeconomic factors.

Studies examining the macroeconomic determinants of small business failure also tend to find a positive relationship between interest rates and firm failure. Hall and Young (1991) found directors, in stating reasons for the failure of their businesses, rated high interest rates as ranking eighth in importance. Using regression analysis, Yrle et al. (2001) found small business failure rates are positively associated with interest rates. Everett and Watson (1998) found a significant positive association between business failures and interest rates when "failure" was defined as bankruptcy, but when "failure" was defined as discontinuance of ownership, the unemployment rate replaced the interest rate as a significant predictor.

Conventional theory holds in a period of high interest rates or credit unavailability, failure may be induced by raising borrowing costs in excess of profit margins (Mensah, 1984). Many small businesses carry relatively heavy loads of short-term debt and are particularly sensitive to debt carrying costs (Hall, 1992). Additionally, in times of high interest rates, consumer discretionary income is reduced which impacts the revenues of many small businesses. Conventional theory thus argues for a positive association between interest rates and business failure.

Recent literature suggests a more complex theoretical relationship between interest rates and business failures. Campbell and Choudhury (2002) view business failure as a process in which individual firm failures are interconnected through layers of contractual relationships. The length of the collaboration period can affect the failure rate by mitigating the disruptive impact of contractual disengagement on other marginally viable firms. A longer collaboration period causes less contractual disruption, thereby mitigating contagion effects and slowing business failure momentum (Campbell and Choudhury, 2002). But, the effect of interest rates on the collaboration period is uncertain. Levy (2001, p1) presents a model highlighting the, "nexus of interactions among financial, industrial and macroeconomic factors determining the Pareto optimal date on which the firm's claimants stop collaborating and force the firm into liquidation". On the one hand a high interest rate will discourage the equity holder since it increases the firm's liability accumulation rate. On the other hand, it enhances the attraction of the firm's debt to the creditor relative to alternative financial transactions and thereby reduces the compensation payment required for the creditor's collaboration (Levy, 2001, p.8). High interest rates certainly increase borrowing costs which could induce some firms to fail; however, by extending the collaboration period, higher interest rates could slow business failure momentum and thereby save other marginally viable firms. The net effect of high interest rates on business failure is therefore uncertain under the Levy model.

In summary, the empirical evidence suggests a positive association between interest rates and firm failures for both large and small firms, however, the anecdotal evidence is weak and the multivariate studies have collinearity problems. Using the research design discussed in the following section, the present study attempts to isolate the association between interest rates and the number of large firm and small firm failures.

RESEARCH DESIGN

Our sample is a time series of monthly business failure and interest rate data beginning January 1984 and ending November 1998. Limiting the sample period to these months, avoids certain shortcomings in the business failure data. In January 1984 Dun and Bradstreet, Inc. (D&B) made significant changes in its data collection procedures, D&B is the primary source of data on the number of business failures and the business failure rate. It increased its coverage of the service sector, included three new sectors (agriculture, forestry, and fishing; finance, insurance, and real estate; and transportation and public utilities), and moved some industries from the manufacturing and services sector to other sectors (Lane and Scary, 1991). A footnote to the D&B business failure data warns users of the potential non-comparability in the pre-and post-1984 data (Dunn and Bradstreet's measures of failures, 1955-1998) and Lane and Scary (1991) find the 1984 data change, "seriously affects the comparability of the pre-and post-1984 data on business failures" [p.96]. To avoid this non-comparability problem, we begin the time series in January 1984 and end the time series in November 1998, at this time D&B reorganized its internal operations and ceased reporting business failure statistics.

D&B defines a business failure 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, 1998). All industrial and commercial enterprises petitioned into the Federal Bankruptcy Courts are included in this definition. Also included are: 1) concerns forced out of business through actions in the state courts such 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. D&B defines a small business as a concern having less than $100,000 in current liabilities and a large business as a concern having more than $100,000 in current liabilities. Current liabilities include all accounts and notes payable, whether secured or unsecured, known to be held by banks, officers, affiliated companies, suppliers, or government. Not included are long-term publicly held obligations (Dun and Bradstreet, 1998).

Table 1 shows the distributions of small and large business failures for the sample period. Small firm failures exceeded large firm failures by a little less than a 2:1 margin. Also, the number of small firm failures per month shows more variance than the number of large firm failures. Table 1 also presents the summary statistics for the prime bank interest rate over the sample period. The interest rate data were obtained from the Conference Board. The prime interest rate was relatively stable over the sample period, ranging from six to thirteen percent.

To test the relationship between interest rates and the number of business failures we perform two separate analyses. First, we use correlation analysis to examine the direction of the association and whether interest rates exhibit a long memory, a term used to refer to long-term statistical dependence in time series data. Second, we regress the number of small firm and large firm business failures on the prime interest rate (INTEREST RATE) and a control for business failure momentum (MOMENTUM). INTEREST RATE is the bank prime rate stated as a percentage; MOMENTUM is a constant growth series beginning at 1 and growing by the constant amount B=1 each month. The control variable, MOMENTUM, is a proxy for market expansion and systemic growth.

In the regression analysis, the Durbin-Watson statistic on ordinary least squares (OLS) estimates indicated the presence of positive autocorrelation even after controlling for systemic growth. One major consequence of autocorrelated errors (or residuals) when applying ordinary least squares is the formula variance [[[sigma].sup.2] [(X' X).sup.-1]] of the OLS estimator is seriously underestimated where X represents the matrix of independent variables and [[sigma].sup.2] is the error variance (Choudhury, 1994). We evaluated the autocorrelation function and partial autocorrelation function of the OLS regression residuals using SAS procedure PROC ARIMA (see SAS/ETS User's Guide, 1993). This was necessary because the Durbin-Watson statistic is not valid for error processes other than first order (see Harvey 1981, pp. 209-210). This allowed observance of the degree of autocorrelation and identification of the order of the model sufficiently describing the autocorrelation. After evaluating the autocorrelation function and partial autocorrelation function, the residuals model was identified as second order autoregressive model (1 - [[phi].sub.1] B - [[phi].sub.2] [B.sup.2]) [v.sub.t] = [[epsilon].sub.t] (see Box, Jenkins, & Reinsel, 1994). The final specification of the regression model is of the following form for large and small firm failures:

[LGFAIL.sub.t] = [[beta].sub.0] + [[beta].sub.1] [MOMENTUM.sub.t] + [[beta].sub.2] INTEREST_[RATE.sub.t] + [v.sub.t] and [v.sub.t] = [[phi].sub.1-] [v.sub.t-1] + [[phi].sub.2] [v.sub.t-2] + [[epsilon].sub.t] (1),

[SMFAIL.sub.t] = [[beta].sub.0] + [[beta].sub.1] [MOMENTUM.sub.t] + [[beta].sub.2] INTEREST_[RATE.sub.t] + [v.sub.t] and [v.sub.t] = [[phi].sub.1] [v.sub.t-1] + [[phi].sub.2][v.sub.t-2] + [[epsilon].sub.t] + [[epsilon].sub.t] (2),

Where:

MOMENTUM = a series starting at 1 and growing at a constant amount B=1 each month; INTEREST RATE = the average prime rate charged by banks.

We use the maximum likelihood technique to estimate the regression parameters. Maximum likelihood estimation is preferred over two step generalized least squares because it can estimate both regression parameters and autoregressive parameters simultaneously. In addition, maximum likelihood estimation accounts for the determinant of the variance-covariance matrix in its objective function (likelihood function). In general, the likelihood function of a regression model with autocorrelated errors has the following form:

L([beta], [theta], [[sigma].sup.2]) = - n/2 ln ([[sigma].sup.2]) 1/2 ln [absolute value of ([OMEGA])] - (Y - X [beta])' [[OMEGA].sup.-1] (Y - X [beta]) / 2[[sigma].sup.2],

where

Y--vector of response variable (number of failures),

X--matrix of independent variables (MOMENTUM, NEWBUS, and Intercept),

[beta]--vector of regression parameters,

[theta]--vector of autoregressive parameters,

[[sigma].sup.2]--error variance,

[OMEGA]--variance-covariance matrix of autocorrelated regression errors.

For further discussion on different estimation methods and the likelihood function, see Choudhury et al. (1999); also see SAS/ETS User's Guide, 1993 for expressions of the likelihood function.

RESULTS

In this section we report the results of tests investigating the association between interest rates and the number of large and small business failures. Table 2 presents correlation statistics for business failures and interest rates, and lagged interest rates for the period January 1984--November 1998. Strong correlations are observed in opposite directions for large and small firms.

In Table 2 the large firm time series exhibits a weak positive correlation between interest rates and the number of large firm failures initially; however, interest rates exhibit a long memory. The impact of interest rates becomes significant at four months and remains strong for over four years. This finding is consistent with prior empirical evidence suggesting large firm failure is a protracted downward spiral (Hambrick and D'Aveni, 1988). The concept of long memory is used to indicate a statistical dependence in which in a time series the autocorrelation function decays at a much slower rate than in the case of short-term statistical dependence. Long-term dependence has only begun to be addressed in macroeconomic and financial time series data (Abderrezak, 1998).

The third and sixth columns in Table 2 report the correlation statistics for small firm failures. Contrary to the large firm results, the correlation between interest rates and the number of small firm failures is negative and immediate. The immediate impact is consistent with prior empirical evidence suggesting small firm failure, particularly new small firm failure, is often abrupt and catastrophic (Venkataraman et al., 1990), but the negative correlation was unexpected. The lagged interest rate correlations are also negative and exhibit a long memory.

The regression results reported in Table 3 provide confirming evidence of the contrasting effects of interest rates on large firm and small firm failures.

The interest rate variable is not a statistically significant predictor of large firm failures; however, for small firms failures the interest rate variable is significant and the coefficient is negative. These results suggest, if the prime interest rate increases by one percent, small business failures decrease by approximately 270 firms per month. The estimated coefficient for business failure momentum (MOMENTUM) is also statistically significant for small business failures. These results suggest, if time advances by one month, the number of small business failures increase by approximately 11 firms over the prior month. After being adjusted for autocorrelation, the Durbin-Watson test-statistic indicates the errors are not correlated. Also, the R-squared statistic for the small firm model is high at .86, versus .62 for large firm failures. This result further suggests interest rates are more determinative of small business failure.

CONCLUSION

This paper makes a number of significant contributions to the literature. It provides additional evidence of differences in the small business and large business failure processes. Interest rates were found to be a key determinant of small business failure, but not large business failure. It also provides evidence suggesting interest rates exhibit a long memory. These results while important were not unexpected given the prior work done in this area. The unexpected finding was the negative association between interest rates and the number of small business failures. This result contradicts other small firm studies examining the macroeconomic determinants of business failure; however, unlike the present study, these prior studies did not control for systemic growth, nor did they address the autocorrelation and collinearity issues.

Considering interest rates separately from other macroeconomic factors illustrates how state policy makers can benefit from using the results of this study. It is well known high interest rates impede small business formation. These results add another dimension to the debate concerning the effects of changing interest rates. Regarding small business failures, changing interest rates involves a policy choice of either helping marginally viable existing small businesses survive (a high interest rate environment) or helping new small businesses form (a low interest rate environment). Additional theory development is needed, particularly with regard the importance of the collaboration period in the small business failure process.

The sample period is a limitation of this study. To determine whether the negative association between interest rates and small business failure is stationary, future research could examine interest rates and business failures over different time periods and in different economies. Also, future research concerning the macroeconomic determinants of business failure should consider whether more useful results could be obtained by explicitly addressing multicollinearity and autocorrelation in the research design. Isolating the effect of specific macroeconomic determinants may be more informative than multivariate models with greater explanatory power.

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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 Periods January 1984 - November 1998 (Monthly Data).

 Monthly Standard
Variables (b) Means Deviations Minimums Maximums

SMFAIL 3763.00 1202.00 1230.00 6365.00
LGFAIL 2027.00 511.84 1223.00 4145.00
INTEREST RATE 8.70 1.63 6.00 13.00

(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;

INTEREST RATE = average prime rate charged by banks,
stated as a percentage.

Table 2: Correlations between Number of Failures, Interest
Rate, and Lagged Interest Rate for the Periods
January 1984-November 1998.

Monthly Large Firm Small Firm
Lags (a) Failures (b) Failures (b)

INTEREST 0.06456 -0.77135
RATE LAG0 (0.3905) (<.0001)

RATE LAG1 0.0779 -0.76215
 (0.3000) (<.0001)

RATE LAG2 0.09258 -0.75384
 (0.2177) (<.0001)

RATE LAG3 0.12374 -0.73810
 (0.0989) (<.0001)

RATE LAG4 0.15973 -0.72331
 (0.0327) (<.0001)

RATE LAG5 0.19998 -0.70803
 (0.0073) (<.0001)

RATE LAG6 0.24166 -0.68991
 (0.0011) (<.0001)

RATE LAG7 0.27786 -0.67374
 (0.0002) (<.0001)

RATE LAG8 0.3101 -0.65273
 (<.0001) (<.0001)

RATE LAG9 0.33816 -0.62985
 (<.0001) (<.0001)

RATE LAG10 0.3659 -0.60411
 (<.0001) (<.0001)

RATE LAG11 0.3822 -0.58176
 (<.0001) (<.0001)

RATE LAG12 0.39348 -0.55911
 (<.0001) (<.0001)

RATE LAG13 0.40935 -0.53279
 (<.0001) (<.0001)

RATE LAG14 0.4163 -0.50647
 (<.0001) (<.0001)

RATE LAG15 0.43179 -0.47767
 (<.0001) (<.0001)

RATE LAG16 0.44502 -0.45676
 (<.0001) (<.0001)

RATE LAG17 0.45763 -0.4385
 (<.0001) (<.0001)

RATE LAG18 0.47734 -0.42417
 (<.0001) (<.0001)

RATE LAG19 0.49121 -0.41501
 (<.0001) (<.0001)

RATE LAG20 0.51164 -0.40557
 (<.0001) (<.0001)

RATE LAG21 0.52333 -0.3984
 (<.0001) (<.0001)

RATE LAG22 0.52956 -0.39509
 (<.0001) (<.0001)

RATE LAG23 0.53878 -0.39678
 (<.0001) (<.0001)

RATE LAG24 0.53811 -0.39989
 (<.0001) (<.0001)

Monthly Large Firm Small Firm
Lags (a) Failures (b) Failures (b)

INTEREST
RATE LAG0

RATE LAG25 0.53808 -0.40337
 (<.0001) (<.0001)

RATE LAG26 0.52880 -0.41202
 (<.0001) (<.0001)

RATE LAG27 0.52879 -0.41761
 (<.0001) (<.0001)

RATE LAG28 0.53150 -0.42731
 (<.0001) (<.0001)

RATE LAG29 0.53792 -0.43827
 (<.0001) (<.0001)

RATE LAG30 0.55111 -0.45553
 (<.0001) (<.0001)

RATE LAG31 0.56267 -0.47297
 (<.0001) (<.0001)

RATE LAG32 0.57631 -0.49083
 (<.0001) (<.0001)

RATE LAG33 0.58200 -0.50864
 (<.0001) (<.0001)

RATE LAG34 0.58878 -0.5282
 (<.0001) (<.0001)

RATE LAG35 0.57716 -0.54882
 (<.0001) (<.0001)

RATE LAG36 0.56716 -0.56809
 (<.0001) (<.0001)

RATE LAG37 0.56207 -0.58248
 (<.0001) (<.0001)

RATE LAG38 0.53461 -0.59443
 (<.0001) (<.0001)

RATE LAG39 0.51875 -0.59917
 (<.0001) (<.0001)

RATE LAG40 0.48838 -0.60252
 (<.0001) (<.0001)

RATE LAG41 0.46729 -0.60173
 (<.0001) (<.0001)

RATE LAG42 0.45652 -0.60174
 (<.0001) (<.0001)

RATE LAG43 0.43372 -0.60598
 (<.0001) (<.0001)

RATE LAG44 0.43324 -0.60957
 (<.0001) (<.0001)

RATE LAG45 0.42167 -0.61636
 (<.0001) (<.0001)

RATE LAG46 0.41563 -0.62099
 (<.0001) (<.0001)

RATE LAG47 0.40197 -0.63103
 (<.0001) (<.0001)

RATE LAG48 0.38682 -0.6437
 (<.0001) (<.0001)

( ) p-values

(a) Variable Definitions: RATE LAG(J) = bank prime interest
rate lagged J months back in time.

(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.

Table 3: Regression Results for Number of Large and Small Firm
Failures for the Period January 1984-November 1998 (Monthly
Data)a : Maximum Likelihood Estimates.

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

Intercept 3621.00 (C) (2.66) *** 1848.00 (0.97)
MOMENTUM -3.44 (1.30) 10.75 (2.93) ***
INTEREST RATE -25.49 (-0.40) -269.89 (-2.96) ***
R-Squared 0.62 0.86
Durbin-Watson 2.06 2.08

(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:

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

INTEREST RATE = average prime rate charged by banks;

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

(d) The regression residuals model was identified as,
(1 - [[phi].sub.1]B - [[phi].sub.2][B.sup.2])[v.sub.t] =
[[epsilon].sub.t] and the estimated first and second order
autoregressive (AR) parameters from SAS were, (1 + 0.44 B + 0.40
[B.sup.2])[v/sib/t] [[epsilon].sub.t] (6.26) *** (5.26) ***

Where t-statistics for autoregressive parameters are reported in
parentheses and they are both significant at the one (***) percent
level.

(e) The regression residuals model was identified as,
(1 - [[phi].sub.1]B - [[phi].sub.2][B.sup.2])[v.sub.t] =
[[epsilon].sub.t] and the estimated first and second order
autoregressive (AR) parameters from SAS were (1 + 0.46 B + 0.37
[B.sup.2])[v.sub.t] = [[epsilon].sub.t] (6.37) *** (5.00) ***

Where t-statistics for autoregressive parameters are reported in
parentheses and they are both significant at the one (***) percent
level.