- Email: [email protected]
Costs of short-term credit for small and large firms
The Quarterly Review of Economics and Finance 50 (2010) 485–491
Contents lists available at ScienceDirect
The Quarterly Review of Economics and Finance journal homepage: www.elsevier.com/locate/qref
Costs of short-term credit for small and large firms David A. Walker ∗ John A. Largay Professor, McDonough School of Business, Georgetown University, Washington, DC 20057, United States
a r t i c l e
i n f o
Article history: Received 20 May 2010 Accepted 7 June 2010 Available online 15 June 2010 JEL classification: D22 M21 C32
a b s t r a c t Changes in costs of credit for small and large firms respond differently to economic conditions and the markets are segmented. Costs for small firms are less responsive to changing economic conditions. Small firms borrow via credit card loans and from banks. Dynamic models prove the costs of funds are negative functions of quantities borrowed and positive functions of the Fed funds rate. During recessions, the decline in funds’ prices to large firms is greater than the reductions to small firms. Large firms benefit to a greater extent than small firms when prices of credit are changing. © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
Keywords: Small business credit Segmented markets
1. Introduction Small businesses employ 51 percent of the domestic work force and produce the same percentage of the non-farm private gross product (U.S. Small Business Administration, 2007). In the past 15 years, 64 percent of new American jobs were created by small firms (Gramigna, 2009, page 9). Thus, any disruption in credit markets or sources of small business credit has significant, negative consequences for U.S. employment and the economy. Costs or prices of credit to small firms are virtually always higher than prices paid by larger firms. This is especially true during a credit crunch, and the current deep recession is no exception. Ninety-two percent of small firms rely on credit card loans, and they often pay more than twice the interest rate that large firms pay when they borrow at or near the prime rate. In November 2009, the prime rate was 3.25 percent, and credit card rates exceeded 13 percent (Federal Reserve Statistical Release G19, www.federalreserve.gov). Some qualifying small businesses paid as little as 6.0 percent for short-term loans from banks (Dunkelberg & Wade, November, 2009). Many small firms already have too much debt or are considered too risky to qualify for this “low” credit card rate or other short-term credit. From October 2008 to October 2009, the prime rate fell by 1.75 percent, the bank rate paid by qualifying small firms declined by only 0.60 percent
∗ Tel.: +1 2026874582. E-mail address: [email protected].
(Dunkelberg & Wade, November, 2009), and the credit card rate increased 1.0 percent. The 2009 credit crisis has been especially difficult for small firms. The 2008 federal stimulus package, as well as the initial commitments from the Obama package, hardly benefited small firms until quite recently. The stimulus package included a small business-lending program that took effect on February 17, 2009. Disagreement between reports concerning the support by the U.S. Small Business Administration during the current recession may be the result of the slow pace with which the SBA has provided support. Spector (2009, page C5) reports “The U.S. Small Business Administration approved 36% fewer government-guaranteed loans in its fiscal year 2009. That loan volume dropped to $9.3 billion, falling short of the previous year’s mark by $3.4 billion.” The U.S. Small Business Administration (2009) claims, that as of November 6, 2009 it supported $14.3 billion in small business lending through the American Recovery and Reinvestment Act, with 73 percent in loans since February 17, 2009 (American Banker, 2009). Traditional SBA programs have required tremendous amounts of paperwork and time lags that discouraged many small firms and financial institutions from participating in SBA programs. This paper focuses on the differences in the change in prices represented by the costs of credit to small and large firms over the past 15 years and how these costs respond to changing economic conditions. The primary hypothesis is that prices of credit for large firms respond more favorably and more directly to changing economic conditions, and changes in costs to small firms are smaller, and usually less favorable. When economic conditions improve, small firms face significant time lags for price reductions and delays to
1062-9769/$ – see front matter © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.qref.2010.06.002
486
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491
obtain additional credit. The models allow tests of the impacts of recessionary periods, including the current one. Section 2 provides the hypotheses and the literature on which the hypotheses are based. The measurements and data are delineated in Section 3. The dynamic methodology and analysis are the subjects of Section 4: unit root tests, Johansen tests for cointegration, and vector autoregressive models, with or without error corrections. Rates on credit card loans and institutions’ short-term business loans are contrasted with the prime rate. The results provide equilibrium impact multipliers for significant variables in Sections 5 and 6 shows the price effect during recession periods defined by the National Bureau of Economic Research (National Bureau of Economic Research, 2009). The conclusions follow in Section 7. 2. Literature and hypotheses 2.1. Literature The foundation for this study stems from concerns about the availability of credit for small firms in the current recession and several theoretical studies published approximately a decade ago. Three of the most important ones emphasized different issues concerning the potential availability of credit during recessions. Bernanke, Gertler, and Gilchrist (1996) discuss the flight to quality and the amplification of shocks when the supply of credit declines and the economy deteriorates. Initial shocks are amplified by a financial accelerator. The authors show how borrowers who face agency costs – as small firms surely do – incur the worst effects of an economic downturn. The empirical results at the end of this paper support that hypothesis. Kiyotaki and Moore (1997) present a dynamic credit cycle model that delineates the differences between secured borrowers, whose lenders can control credit limits, and borrowers with unsecured debt that lenders do not control. Small firms, with little collateral or that borrow on unsecured credit cards with previously contracted limits, are examples of the firms that Kiyotaki and Moore argue pay higher interest rates and are credit constrained. The authors maintain “persistence and amplification reinforce each other” (1997, page 213). As net worth declines in their dynamic models, which it does during recessions, and debt capacity deteriorates, as Shleifer and Vishny (1992) argue, the supply of debt to small firms is reduced dramatically. The results provided in Table 7 of this study are consistent with this view. Holmstrom and Tirole (1998) show the necessity for the public sector to supply and manage liquidity when credit is tight. This is the role the US Small Business Administration is attempting to play during the current recession. This is especially important since the November bankruptcy of CIT, a major U.S. private small business lender. The authors argue that often private intermediaries will be unable to provide liquidity to firms in difficult times and that firms with little collateral (smaller firms) will require the most public sector support. 2.2. Hypotheses These studies are some of the basis for hypotheses and models for this paper. Costs and prices of funds are contrasted for large and small firms across business cycles. The primary model is a simple one. The prices of funds for large (PL) and small (PS) firms are assumed to be functions of the quantities borrowed (QL and QS) and elements of X, that represent the economic environment in which funds are borrowed: PL = f (QL, QS, X)
(1)
and PS = g(QL, QS, X)
(2)
Of particular interest will be: ∂PL/∂QS, ∂PS/∂QL, and how PL and/or PS change in response to economic conditions. If, for example, ∂PL/∂QS = 0 and ∂PS/∂QL = 0, the funds markets for large and small firms are segmented. 3. Measurement and data 3.1. Measurement Large and small firms costs of credit are often not directly observable, and when the data are available, they are often not with sufficient frequency for in depth analysis. Proxies that are highly correlated and monotonically increasing with the costs of credit for large and small firms are employed to represent PL and PS, respectively. PL will be represented by the prime rate, RPRIME that the largest, most credit worthy firms pay for funds. Market rates small firms pay, PS, are a combination of (1) the interest rate small firms pay on short-term loans from institutions, RIPSM (surveyed monthly by the National Federation of Independent Business) and (2) the rate of interest on credit card loans, RCARDQ (surveyed quarterly by the Federal Reserve). An NFIB survey of small firms found that 92 percent have 1, 2, or 3 credit cards and that 96 percent use the services of a local or regional bank (NFIB Research Foundation, 2008, page 24). This study examines what dynamic factors determine rate changes, PL and PS, monthly and quarterly. For the prime rates, PL = RPRIM monthly and RPRIQ quarterly; PS = RIPSM monthly and RCARDQ quarterly. 3.2. Data RIPSM is the “actual interest paid on short-term loans” by NFIB borrowers (Dunkelberg and Wade, monthly issues). Observations are available from January 1996 through October 2008. For RCARDQ the Federal Reserve (statistical release G19) provides only quarterly data – February, May, August, and November for 1995 – 2009, third quarter. Thus, RPRIM and RIPSM can be contrasted monthly, but RPRIQ and RCARDQ must be contrasted quarterly. RPRIM and RPRIQ represent the monthly and quarterly prime rate (Federal Reserve releases H15 and G19). Economics and financial data are matched with the rates for the closest possible dates. Much small firm borrowing is supported by credit cards, but not collateralized, by a business or entrepreneur’s personal assets plus small business loans from a variety of sources. An NFIB survey reports that more than 92 percent of small business respondents use at least 1 credit card (NFIB Research Foundation, 2008, p. 24). 3.3. Costs of credit for large and small firms Differences between the costs of credit for large and small US firms are reflected by the monthly difference between the prime rate and the rate paid by independent businesses and the quarterly difference between the prime rate and the rate of interest on credit card balances. When interest rates are declining, the prime rate usually declines more rapidly than the cost of credit to small firms. For 2000–2002, credit card rates declined by 1.52 (from 14.30 to 12.78 percent), bank rates paid by NFIB small business survey respondents declined 3.20 (from 9.70 to 6.50 percent), while the prime rate dropped 4.24 (from 8.69 to 4.45 percent). Contrasting the fourth quarter of 2007 and the third quarter of 2009 shows
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491 Table 1B Unit root tests Zt = ˇ0 + Zt−1 + ˇ1 Zt−1 + ˇ2 Zt−2 + ˇ3 t + εt RPRIM and RIPSM.
Table 1A Unit root tests Zt = ˇ0 + Zt−1 + ˇ1 Zt−1 + ˇ2 Zt−2 + ˇ3 t + εt RPRIQ and RCARDQ. Variable
ˇ2 = 0 1 period lag
ˇ2 = / 0 2 period lag
Assumptions
Variable
RPRIQ RCARDQ
−1.71 −1.96
−1.93 −1.35
ˇ0 = / 0 ˇ3 = 0 / 0 ˇ3 = 0 ˇ0 =
RPRIQ RPRIQ RCARDQ
−2.73 −2.65 −6.74
−2.19 −2.12 −4.86
/ 0 ˇ3 = 0 ˇ0 = ˇ0 = 0 ˇ3 = 0 ˇ0 = / 0 ˇ3 = / 0
RPRIM RPRIM RIPSM RIPSM
5% rejection region t < −2.92 10% rejection region t < −1.95.
that interest rate declines were from 8.03 to 3.25 (−5.78) for the prime rate and 9.10 to 6.00 (−3.10) for the rate NFIB respondent small firms paid to banks. Credit card rates rose from 14.34 to 14.90 (+0.56) over the same period. March 2001 through November 2001 and since December 2007 are the only periods since 1995 that the National Bureau of Economic Research identifies as a recession periods. 4. Methodology and analysis Analyses of quarterly contrasts for RPRIQ and RCARDQ or monthly contrasts for RPRIM and RIPSM are developed by estimating vector autoregressive (VAR) models with or without error corrections. The dynamic analysis requires a three stage process: (1) unit root tests, (2) tests for cointegration, and (3) VAR parameter estimates, with or without error corrections. Whether error corrections are appropriate depends on the results of the unit root and Johansen cointegration tests. The empirical VAR and VAREC models can be applied to determine equilibrium price impact multipliers. The time series analyses for the prime and either card rates or bank rates paid by independent businesses examine two hypotheses, H1A and H1B or H2A and H2B, respectively: H1A. RPRIQ and RCARDQ are non-stationary with one unit root, or integrated of order one, I(1) H1B.
RPRIQ and RCARDQ are cointegrated and
H2A. RPRIM and RIPSM are non-stationary with one unit root, or integrated of order one, I(1) H2B.
RPRIM and RIPSM are cointegrated.
4.1. Unit root tests
RPRIM RPRIM RIPSM RIPSM
1 Period lag
2 Period lag
Assumptions
5% Reject region
−0.89 −1.48 −0.97 −1.24
−1.18 −1.73 −0.88 −1.12
ˇ0 ˇ0 ˇ0 ˇ0
= / = / = / = /
0 ˇ3 = 0 0 ˇ3 = / 0 0 ˇ3 = 0 0 ˇ3 = / 0
−2.88 −3.44 −2.88 −3.44
−3.85 −3.90 −10.99 −10.95
−3.10 −3.15 −7.19 −7.16
ˇ0 ˇ0 ˇ0 ˇ0
= / = / = / = /
0 ˇ3 = 0 0 ˇ3 = / 0 0 ˇ3 = 0 0 ˇ3 = / 0
−2.88 −3.44 −2.88 −3.44
With a one period lag (ˇ2 = 0), the t-statistics are −1.71 for RPRIQ and −1.96 for RCARDQ, respectively. Neither is significant at the 10 percent level (t < −2.92), so = 1 cannot be rejected. The level of each interest rate series is concluded to have a unit root. Allowing two period lags (ˇ2 = / 0), the t-statistics are −1.93 and −1.35, neither of which is in the rejection region for RPRIQ or RCARDQ, respectively (Table 1A, top panel). To test first differences, Zt is replaced by Zt as the dependent variable in Eq. (3). RCARDQ has t-statistics of −6.74 and −4.86 for one and two period lags, respectively, which are both in the rejection region and < 1 is accepted. For RPRIQ the necessary assumptions to reject a unit root are ˇ3 = 0 and a 10 percent rejection criterion; the t-statistics for one or two period lags are −2.73 / 0 or −2.63 and −2.12 for ˇ0 = 0 (Table 1A, botand −2.19 for ˇ0 = tom panel). A unit root for RPRIQ and RCARDQ can be rejected with a 10 percent criterion. 4.3. Unit root test results for RPRIM with RIPSM (Table 1B) Whether ˇ0 or ˇ3 is constrained to zero and for a one or two period lag, the hypotheses that RPRIM and RIPSM each have a unit root = 1 cannot be rejected (Table 1B, top panel). When Zt is replaced by Zt as the dependent variable for monthly rates in Eq. (3), a unit root can be rejected for the change in each monthly rate. RIPSM has t-statistics below −7.0 for both one and two period lags, and = 1 is rejected. A unit root can also be rejected for RPRIM; each t-statistic for RPRIM is below −3.0 (Table 1B, bottom panel). The hypotheses that RPRIM and RIPSM do not have unit roots are accepted. 4.4. Cointegration tests
Augmented Dickey–Fuller (ADF) tests (Dickey & Fuller, 1979) examine unit roots. Letting Z represent RPRIQ and then RCARDQ, H1A and H2A are tested estimating: Zt = ˇ0 + Zt−1 + ˇ1 Zt−1 + ˇ2 Zt−2 + ˇ3 t + εt
487
(3)
A rate and then the change in a rate are tested with Eq. (3), letting the dependent variable, Zt , represent the rate and then the change in the rate. The null and alternative hypotheses for the unit root tests are: H0 : = 1 and HA : < 1. A one tailed test is appropriate because ≥ 1 implies non-stationary. The alternative tests for each of the four rates, estimating Eq. (3), are to examine the cases whether ˇ0 , ˇ2 , and ˇ3 equal 0 or not. ˇ0 allows a constant, ˇ2 allows a second time lag, and ˇ3 allows a trend in Zt . 4.2. Unit root test results for RPRIQ with RCARDQ (Table 1A) The ADF test provides t-statistics for the coefficients in Eq. (3). The emphasis is on . The results are provided in Tables 1A and 1B.
Johansen’s test (Johansen, 1991) determines whether a pair of time series is cointegrated, given that each of the series possesses a unit root. Under the conditions described above neither RPRIQ and RCARDQ quarterly nor RPRIM and RIPSM monthly have unit roots. The five cases for the cointegrating equation (CE) are: (1) no deterministic trend in the data: no intercept and no trend in the CE; (2) no deterministic trend in the data; an intercept but no trend in the CE; (3) linear trend in the data; an intercept but no trend in the CE; (4) linear trend in the data; both an intercept and trend in the CE; (5) quadratic trend in the data; both an intercept and trend in the CE. The most appropriate assumption appears to be case (3) where series may have intercepts and linear trends, but the cointegrating equation has only an intercept. The cointegration tests are summarized in Tables 2A and 2B. The trace test at the 5 percent level
488
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491 Table 3 VAR model (t-statistics in parentheses, quarterly data).
Table 2A Johansen cointegration tests for RPRIQ and RCARDQ (N = 56). Hypothesized cointegrations (RPRIQ and RCARDQ)a
Trace statistic
5% Critical value
Probability
None At most 1 trace test indicates 2 cointegrating equations at 5% level
54.2914 6.3028
15.49 3.84
0.0000 0.0120
a
No deterministic trend because of first differences.
indicates two cointegrating equations for RPRIQ and RCARDQ (N = 56 quarters) and one cointegrating equation for RPRIM and RIPSM (N = 156 months), determining the autoregressive framework. 4.5. Vector autoregressive framework The results of the unit root and Johansen cointegration tests determine whether vector autoregressive models without (VAR) or with error corrections (VAREC) should be estimated jointly for RPRIQ and RCARDQ and jointly for RPRIM and RIPSM. Advantages of estimating VAR or VAREC models for a pair of rates are (1) the potential impact of each exogenous variable is tested for each rate and (2) simultaneous equilibrium impact multipliers can be determined. Exogenous factors may influence the costs of credit to large and small firms, but a particular factor will not necessarily influence each of the rates to the same extent. Since RPRIQ and RCARDQ do not have a single cointegrating equation and a unit root for RCARDQ can only be rejected at the 10 percent level, VAR rather than VAREC models are estimated for RPRIQ and RCARDQ. Since RPRIM and RIPSM have a single cointegrating equation and a unit root is rejected for each of them, VAREC models are estimated for these rates. A vector autoregressive model with an error correction term (VAREC) accommodates the cointegration (Engle & Granger, 1987). The general model for RPRIM and RIPSM is
RPRIMt RIPSMt
=
ˇ0P
ˇ0S
+
+
+
ˇ2PP ˇ2SP P S
ˇ1PP
ˇ1PS
ˇ1SP
ˇ1SS
ˇ2PS ˇ2SS
RPRIMt−1
RPRIMt−2
εPt
RPRIQt
Constant 0.0088 (0.32) RPRIQt−1 0.1968 (4.64) −0.0778 (−1.92) RPRIQt−2 −0.0350 (−0.99) RCARDQt−1 RCARDQt−2 −0.0161 (−0.46) RETMFGQt −0.0103 (−1.73) QCARDQt −0.0001 (−0.14) 0.8763 (25.33) FFQt R-square 0.96 Akaike goodness of fit statistic = −0.40
RCARDQt 0.1710 (1.64) 0.3199 (2.00) −0.1275 (−0.84) −0.1941 (−1.46) −0.3016 (−2.26) 0.0064 (0.28) −0.0065 (−1.84) 0.2921 (2.24) 0.35
4.6. Autoregressive econometric models VAR and VAREC models are estimated including two-quarter autoregressive relationships and first differences of exogenous variables. Variables are included to represent the quantities of funds borrowed at prime and credit card rates for VAR models and the quantities of funds borrowed at the prime and the rate paid by small firms to institutions on short-term loans for the VAREC model. Numerous models have been estimated, including exogenous variables to represent small and large firm demand for funds, financing experience, represented by interest rates, and macroeconomic conditions. The variables that appear in the estimated models, along with their sources, are listed in Appendix A. 4.7. RPRIQ–RCARDQ VAR quarterly model (Table 3) The quantity of funds borrowed on credit cards (QCARDQ) is the sum of the quantity of revolving and non-revolving credit. A direct measure of the quantity of funds borrowed at the prime rate is not available on a frequent basis; the change in the level of retail plus manufacturing sales (RETMFGQ) is a proxy for the quantity of funds borrowed at prime. Retail sales represent a broad measure of aggregate consumer purchasing and manufacturing sales represent business sales and production of goods and services. The most effective VAR model for RPRIQ and RCARDQ is given in Table 3. The results in Table 3 can be summarized as follows:
RIPSMt−1
RIPSMt−2
ECt−1 +
Variable
+
ˇ3P ˇ3S
Xt
εSt
The error correction term is ECt = RPRIMt + ˛0 + ˛1 RIPSMt The estimated models may include exogenous variables, included in Xt in Eqs. (1) and (2). The VAR model for RPRIQ and RCARDQ takes the same form, but ECt = 0, RCARDQ replaces RIPSM, and RPRIQ replaces RPRIM.
1. RPRIQ has a significant positive autoregressive relationship at lag 1 and a negative relationship at lag 2. 2. RCARDQ has a significant negative autoregressive relationship at lag 2 and a significant positive relationship with RPRIQ at lag 1. 3. RPRIQ and RCARDQ have significant negative relationships with their own funds borrowed proxy – RETMFGQ and QCARDQ, respectively. 4. RPRIQ and RCARDQ both have significant positive relationships with the change in the Fed Funds rate (FFQ). At the 10 percent level of significance, both the prime and the card rates decrease with increases in their own quantity proxies indicating downward sloping demands for funds. Neither quantity proxy has a significant coefficient in the equation for the
Table 2B Johansen cointegration tests for RPRIM and RIPSM (N = 156). Hypothesized cointegrations (RPRIM and RIPSM)a
Trace statistic
5% Critical value
Probability
None At most 1 trace test indicates 1 cointegrating equation at 5% level
69.5369 6.9475
25.87 12.52
0.0000 0.3500
a
No deterministic trend because of first differences.
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491 Table 5 Statistically significant coefficients of quantities of funds borrowed.
Table 4 VAREC model (t-statistics in parentheses, monthly data). Variable
RPRIMt
Constant 0.0236 (4.25) −0.0710 (−1.74) RPRIMt−1 −0.0328 (−0.85) RPRIMt−2 0.0998 (6.87) RIPSMt−1 0.0210 (1.54) RIPSMt−2 ECt−1 −0.6395 (−18.61) −0.0019 (−0.90) RETMFGMt −0.0023 (−1.13) QBORSMt 0.7465 (21.78) FFMt R-square 0.80 Akaike goodness of fit statistic = −1.69 EC = RPRIM + 0.0367 + 0.2560 RIPSM
489
RIPSMt
(Table 3)
(Table 4)
0.0152 (0.52) 0.3257 (1.52) 0.3971 (1.96) −0.9033 (−11.86) −0.4845 (−6.77) −0.3713 (−2.06) −0.0190 (−1.68) 0.0175 (1.64) 0.4468 (2.48) 0.59
QL = RETMFGQ QS = QCARDQ =0 <0 <0 =0
QL = RETMFGM QS = QBORSM =0 >0 =0 <0
∂PL/∂QS ∂PS/∂QS ∂PL/∂QL ∂PS/∂QL
Bold, italicized 0s show market segmentation, except ∂PS/∂QL from Table 4.
Table 6 Impact multipliers.
(4.33)
RPRIQt
Variable
RCARDQt
Case A. VAR quarterly impact multipliers
other funds price, indicating segmentation of the loan markets. The changes in the prime and the credit card rates respond significantly to changes in the Fed funds rate in the same direction; the response and the coefficient for FFQ is considerably larger in the RPRIQ relationship. The VAR model in Table 3 has the strongest econometric characteristics of the models tested. This model has the highest R-square values for the two relationships, and the minimum value of the Akaike information criterion (−0.40), which measures goodness of fit and is a basis for VAR model selection (see Akaike, 1974; Burnham & Anderson, 2002). 4.8. RPRIM–RIPSM VAREC model (Table 4) The quantity of funds borrowed from institutions by small firms is measured as the percentage of small firms that borrow regularly within a 3-month period (QBORSM), reported in the Dunkelberg and Wade NFIB monthly survey. RETMFGM is employed as a proxy for the quantity of funds borrowed by large firms at the prime rate. The most effective VAREC model for RPRIM–RIPSM is provided in Table 4. The variables with the most significant coefficients in the VAREC models represent the analogous factors to those in the VAR models. The results in Table 4 can be summarized as follows: 1. RPRIM and RIPSM both have significant negative autoregressive relationships with its own rate at lag 1. 2. RPRIM has a significant positive autoregressive relationship with RIPSM at lag 1. 3. At lag 2, RIPSM has a significant negative autoregressive relationship with its own rate and a significant positive autoregressive relationship with RPRIM. 4. RIPSM has a significant positive relationship with the quantity of small business loans and negative relationship with the quantity of funds borrowed at the prime rate. RPRIM does not have a significant relationship with either quantity of borrowed funds. 5. The coefficient of FFM is positive and significant in each relationship. The coefficient of FFM in the RPRIM model is 160 percent of its coefficient in the RIPSM model.
RETMFGQt QCARDQt FFQt Variable
−0.0119 0.0001 0.9761
0.0028 −0.0043 0.3208
RPRIMt
RIPSMt
Case B. VAREC monthly impact multipliers RETMFGMt QBORSMt FFMt
−0.0027 −0.0013 0.7207
−0.0088 0.0069 0.4053
4.9. Model conclusions The dynamic VAR quarterly and VAREC monthly models show that the changes in interest rates incurred by large and small firms (funds’ prices) can be represented by changes in their lagged rates, the quantities of funds borrowed or their proxies, and the Fed funds rate. When funds’ market prices change, represented by FF, the effects on small firms are smaller than effects on large firms. This is particularly true when the prices (rates) are declining. Coefficients of ∂PL/∂QS and ∂PS/∂QL are never statistically significant at a meaningful level, except for ∂PS/∂QL in the VAREC Model (at the 10 percent level). Table 5 summarizes the signs of the statistically significant coefficients of QCARDQ and QBORSM, quarterly and monthly small business funds quantities, respectively. Bold, italicized cases that equal 0, except for ∂PS/∂QL from Table 4, show large and small firms’ funds markets are segmented. The aggregate test statistics are strong for each model. Additional factors that have been tested do not have significant coefficients at the 10 percent probability level. The models in Tables 3 and 4 are the basis for developing long-run equilibrium impact multipliers. 5. Impact multipliers and equilibrium conditions Long-run simultaneous solutions to the models in Tables 3 and 4, respectively, provide “equilibrium” impact multipliers. Long-run quarterly multipliers can be determined for RPRIQt and RCARDQ from Table 3, when RPRIQt = RPRIQt−1 = RPRIQt−2 and RCARDQt
When the Federal Reserve changes it target Fed funds rate, the prime rate changes in the same direction by 75 percent of the change, and the rate small firms pay to institutions changes by 45 percent of the change. The VAREC model captures more of the variation in the prime rate (RPRIM) and than the variation in the small business-borrowing rate (RIPSM), according to the R-square values. The Akaike value is highly negative.
= RCARDQt−1 = RCARDQt−2 , Long-run monthly multipliers for RPRIMt and RIPSM can be determined from Table 4 when RPRIMt = RPRIMt−1 = RPRIMt−2 and RPRIMt = RIPSMt−1 = RIPSMt−2
490
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491
Table 7 t-Statistics for recession binary models. Variable
Intercept
Card rate equation
Prime rate equation
RPRIQ
RCARDQ
RPRIQ
RCARDQ
(−1.66)* (−2.26)* (−1.06) (−1.19)
(0.51) (0.62) (1.84)* (1.83)*
(0.10) (−0.23)
(−1.90)* (−1.83)*
RPRIQ
RCARDQ
(−2.53)**
(0.54)
**
(0.30)
Case A. quarterly models B B* RETMFGQ B* QCARDQ B* both Variable
Intercept
Card rate equation
(−2.51)
Prime rate equation
RPRIM
RIPSM
RPRIM
RIPSM
(0.47) (0.49) (0.30) (0.32)
(−0.40) (−0.43) (−0.28) (−0.33)
(−0.87) (−0.83)
(−1.37) (−1.45)
RPRIM
RIPSM
(−0.22)
(0.75)
(−0.17)
(0.88)
Case B. monthly models B B* RETMFGM B* QBORSM B* both
B = 1, March–November 2001, December 2007–present, and 0 otherwise. * Statistically significant at the 10 percent level. ** Statistically significant at the 1 percent level.
Impact multipliers for the VAR model reflect what is expected (Table 6, Case A). The impacts for the proxy for the quantity of funds borrowed by large firms (RETMFGQ) and small firms (QCARDQ) are that prices are lower for larger quantities of funds borrowed in each market. The price for large firms is more sensitive (−0.0119 versus −0.0043). The cross elasticity quantity coefficients in the quarterly model are positive as expected (+0.0001 and +0.0028). The impact multipliers from the monthly VAREC model (Table 6, Case B) show that banks charge large firms lower prices for larger quantities of funds (−0.0027), but that smaller firms are paying higher prices for larger quantities of funds (+0.0069). This is a difference between small firms borrowing on credit cards (Table 6, Case A) and their borrowing from banks (Table 6, Case B). Small firms borrowing on credit cards usually occur when more attractive sources of credit have been exhausted. Large and small firms appear to be direct competitors for bank funds. The monthly impacts of changes in the Fed funds rate are similar to the impacts in the quarterly model.
6. Effects of recessions As Bernanke et al. (1996), Kiyotaki and Moore (1997), and Holmstrom and Tirole (1998) all suggest, the impacts of recessions and tight credit card markets are more severe for firms that have the least financial market power in lending markets. The National Bureau of Economic Research defines March through November 2001 and December 2007 through the present as the recession periods during the period for this study. Let B = 1 for these recession months and B = 0 otherwise. Table 7 shows the t-statistics for four tests of the recession effects on the prices of credit: (1) only an intercept shift (B); (2) recession effect solely on quantity of funds borrowed by large firms (B*RETMFG) and intercept; (3) recession effect solely on quantity of funds borrowed by small firms (B*QCARDQ or B*QBORSM) and intercept; (4) recession joint effect on quantity of funds borrowed by large and small firms (B*RETMFG and B*QBORSM or B*QCARDQ and B) and intercept.
For the quarterly models, whenever there is a statistically significant recession (B = / 0), the credit prices are, of course, lower during the recession. In the quarterly credit card models, RCARDQ, declining rates are shown by the significant, negative t-statistics, −1.90 and −1.83. In the quarterly prime rate models, RPRIQ, declining rates are shown by the significant, negative t-statistics, −2.53 and −2.51. The small business price changes are only significant at the 10 percent level, while the large business price changes are significant at the 1 percent level. For the monthly models, none of the recession coefficients is statistically significant at the 10 percent level or better (Table 7, Case B). Evidently a month is too short for the benefit from significant price reductions to be reflected. 7. Conclusions Short-term costs of credit for large and small firms respond to common factors. Small firms borrow in the forms of credit card loans and other short-term credit from institutions. Large and small firms do not appear to be direct competitors for funds; these markets are at least somewhat segmented. The changes in the costs of funds for large and small firms are functions of the proxies for quantities of funds borrowed and changes in the Fed funds rate. The dynamic VAR prime-credit card model and VAREC prime-short-term credit model have high R-squares and significant t-statistics. Quarterly funds’ prices are more sensitive than monthly prices to quantity changes. Moreover, during recessions, the decline in prices of funds to large firms is more significant than the declines to small firms. Large and small firms face differences in quarterly and monthly markets for funds. Tables 3, 4, 6 and 7 of this study show that large firms benefit more quickly and to a greater extent than small firms when prices of credit are changing. These results support the theoretical bases in Walker and David (1989) and Walker (2008). Acknowledgements The author would like to thank Thomas Durkin and Keith Ord for helpful suggestions and guidance for this paper. Holly Wade, Giuseppa Gramigna, and Charles Ou advised the author on data sources and interpretations.
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491
Appendix A. Variables and sources Variable
Definition
Source
RPRIME
Prime Interest Rate
RPRIQ RPRIM RPRIQ RPRIM RIPSM
RPRIME quarterly RPRIME monthly RPRIQt –RPRIQt−1 RPRIMt –RPRIMt−1 Cost of loans to independent businesses
Federal Reserve release H15, monthly, 1996–2009 (Federal Reserve, 2008) Feb., May, Aug., Nov.
RIPSM RCARDQ
RIPSMt –RIPSMt−1 Bank credit card quarterly Federal Reserve release interest rate G19 Feb., May, Aug., Nov. RCARDQt –RCARDt−1 Percentage of small firms borrowing regularly within 3 months (Dunkelberg and Wade, NFIB) Credit card borrowing = QNONREV + QREVOLV QNONREV – quantity non-revolving credit (FRB statistical release G19) QREVOLV – quantity of revolving credit (FRB statistical release G19) Fed funds rate quarterly (FRB release H15) Fed funds rate monthly (FRB release H15) Business borrowing index monthly = MANUFACT + RETAIL MANUFACT − business manufacturing index (St. Louis Federal Reserve Fred2) RETAIL − retail sales index (St. Louis Federal Reserve Fred2, www.research.stlouisfed.org) Business borrowing index quarterly = MANUFACT + RETAIL Recession binary variable – NBER identification of 2001 and December 2007 onward in “Business Cycle Expansions and Contractions”
RCARDQ QBORSM QCARDQ
FFQ FFM RETMFGM
RETMFGQ B
National Federation of Independent Business, monthly, 1996–2009
References Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6) American Banker (2009). In cards, a complex dance on rates, March 10, page 1.
491
Bernanke, B., Gertler, M., & Gilchrist, S. (1996). The financial accelerator and the flight to quality. The Review of Economics and Statistics,. February. Burnham, K. P., & Anderson, D. R. (2002). Model selection and multi-model inference: A practical-theoretical approach (2nd ed.). Springer-Verlag. Dickey, D. A., & Fuller, W. A. (1979). Distribution of estimators for autoregressive time series with a unit root. Journal of the American Statistical Association. Dunkelberg, W. C., & Wade, H. (2009). NFIB small business economic trends. Washington, DC: NFIB Research Foundation. November, various issues through. Engle, Robert F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica. Federal Reserve. (2008). Highlights of proposed rules regarding credit card and overdraft services. Washington, DC: Board of Governors of the Federal Reserve. May 2. Gramigna, G. (2009). Current economic challenges, the small business economy, and federal government interventions. Washington, DC: U.S. Small Business Administration. March 30. Holmstrom, Bengt, & Tirole, Jean. (1998). Private and public supply of liquidity. Journal of Political Economy, 1. Johansen, Soren. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica. Kiyotaki, N., & Moore, J. (1997). Credit cycles. Journal of Political Economy, (2). National Bureau of Economic Research (2009). “Business Cycle Expansions and Contractions,” November 23 (http://www.nber.org.cycles.html). NFIB Research Foundation (2008). “Small business poll: Access to credit,” Washington, DC, vol. 8, 7. Shleifer, Andrei, & Vishny, Robert W. (1992). Liquidation values and debt capacity: A market equilibrium approach. Journal of Finance, XLVII(September (4)) Spector, Mike. (2009). Small businesses turn to Goldman. Wall Street Journal, (November 19), C5. U.S. Small Business Administration. (2007). The small business economy 2008. Washington, DC: U.S. Government Printing Office. December. U.S. Small Business Administration (2009). “SBA’s Economic Recovery Efforts and Impact,” Washington, DC, November 9. Walker, D. A. (2008). Credit card financing, consumer credit, and mortgage credit. In Testimony on the role of credit cards in small business financing. Washington, DC,: Hearings before the U.S. House of Representatives Committee on Small Business. April 3. Walker, D. A. (1989). Financing the small firm. Small Business Economics, (Fall).
Contents lists available at ScienceDirect
The Quarterly Review of Economics and Finance journal homepage: www.elsevier.com/locate/qref
Costs of short-term credit for small and large firms David A. Walker ∗ John A. Largay Professor, McDonough School of Business, Georgetown University, Washington, DC 20057, United States
a r t i c l e
i n f o
Article history: Received 20 May 2010 Accepted 7 June 2010 Available online 15 June 2010 JEL classification: D22 M21 C32
a b s t r a c t Changes in costs of credit for small and large firms respond differently to economic conditions and the markets are segmented. Costs for small firms are less responsive to changing economic conditions. Small firms borrow via credit card loans and from banks. Dynamic models prove the costs of funds are negative functions of quantities borrowed and positive functions of the Fed funds rate. During recessions, the decline in funds’ prices to large firms is greater than the reductions to small firms. Large firms benefit to a greater extent than small firms when prices of credit are changing. © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
Keywords: Small business credit Segmented markets
1. Introduction Small businesses employ 51 percent of the domestic work force and produce the same percentage of the non-farm private gross product (U.S. Small Business Administration, 2007). In the past 15 years, 64 percent of new American jobs were created by small firms (Gramigna, 2009, page 9). Thus, any disruption in credit markets or sources of small business credit has significant, negative consequences for U.S. employment and the economy. Costs or prices of credit to small firms are virtually always higher than prices paid by larger firms. This is especially true during a credit crunch, and the current deep recession is no exception. Ninety-two percent of small firms rely on credit card loans, and they often pay more than twice the interest rate that large firms pay when they borrow at or near the prime rate. In November 2009, the prime rate was 3.25 percent, and credit card rates exceeded 13 percent (Federal Reserve Statistical Release G19, www.federalreserve.gov). Some qualifying small businesses paid as little as 6.0 percent for short-term loans from banks (Dunkelberg & Wade, November, 2009). Many small firms already have too much debt or are considered too risky to qualify for this “low” credit card rate or other short-term credit. From October 2008 to October 2009, the prime rate fell by 1.75 percent, the bank rate paid by qualifying small firms declined by only 0.60 percent
∗ Tel.: +1 2026874582. E-mail address: [email protected].
(Dunkelberg & Wade, November, 2009), and the credit card rate increased 1.0 percent. The 2009 credit crisis has been especially difficult for small firms. The 2008 federal stimulus package, as well as the initial commitments from the Obama package, hardly benefited small firms until quite recently. The stimulus package included a small business-lending program that took effect on February 17, 2009. Disagreement between reports concerning the support by the U.S. Small Business Administration during the current recession may be the result of the slow pace with which the SBA has provided support. Spector (2009, page C5) reports “The U.S. Small Business Administration approved 36% fewer government-guaranteed loans in its fiscal year 2009. That loan volume dropped to $9.3 billion, falling short of the previous year’s mark by $3.4 billion.” The U.S. Small Business Administration (2009) claims, that as of November 6, 2009 it supported $14.3 billion in small business lending through the American Recovery and Reinvestment Act, with 73 percent in loans since February 17, 2009 (American Banker, 2009). Traditional SBA programs have required tremendous amounts of paperwork and time lags that discouraged many small firms and financial institutions from participating in SBA programs. This paper focuses on the differences in the change in prices represented by the costs of credit to small and large firms over the past 15 years and how these costs respond to changing economic conditions. The primary hypothesis is that prices of credit for large firms respond more favorably and more directly to changing economic conditions, and changes in costs to small firms are smaller, and usually less favorable. When economic conditions improve, small firms face significant time lags for price reductions and delays to
1062-9769/$ – see front matter © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.qref.2010.06.002
486
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491
obtain additional credit. The models allow tests of the impacts of recessionary periods, including the current one. Section 2 provides the hypotheses and the literature on which the hypotheses are based. The measurements and data are delineated in Section 3. The dynamic methodology and analysis are the subjects of Section 4: unit root tests, Johansen tests for cointegration, and vector autoregressive models, with or without error corrections. Rates on credit card loans and institutions’ short-term business loans are contrasted with the prime rate. The results provide equilibrium impact multipliers for significant variables in Sections 5 and 6 shows the price effect during recession periods defined by the National Bureau of Economic Research (National Bureau of Economic Research, 2009). The conclusions follow in Section 7. 2. Literature and hypotheses 2.1. Literature The foundation for this study stems from concerns about the availability of credit for small firms in the current recession and several theoretical studies published approximately a decade ago. Three of the most important ones emphasized different issues concerning the potential availability of credit during recessions. Bernanke, Gertler, and Gilchrist (1996) discuss the flight to quality and the amplification of shocks when the supply of credit declines and the economy deteriorates. Initial shocks are amplified by a financial accelerator. The authors show how borrowers who face agency costs – as small firms surely do – incur the worst effects of an economic downturn. The empirical results at the end of this paper support that hypothesis. Kiyotaki and Moore (1997) present a dynamic credit cycle model that delineates the differences between secured borrowers, whose lenders can control credit limits, and borrowers with unsecured debt that lenders do not control. Small firms, with little collateral or that borrow on unsecured credit cards with previously contracted limits, are examples of the firms that Kiyotaki and Moore argue pay higher interest rates and are credit constrained. The authors maintain “persistence and amplification reinforce each other” (1997, page 213). As net worth declines in their dynamic models, which it does during recessions, and debt capacity deteriorates, as Shleifer and Vishny (1992) argue, the supply of debt to small firms is reduced dramatically. The results provided in Table 7 of this study are consistent with this view. Holmstrom and Tirole (1998) show the necessity for the public sector to supply and manage liquidity when credit is tight. This is the role the US Small Business Administration is attempting to play during the current recession. This is especially important since the November bankruptcy of CIT, a major U.S. private small business lender. The authors argue that often private intermediaries will be unable to provide liquidity to firms in difficult times and that firms with little collateral (smaller firms) will require the most public sector support. 2.2. Hypotheses These studies are some of the basis for hypotheses and models for this paper. Costs and prices of funds are contrasted for large and small firms across business cycles. The primary model is a simple one. The prices of funds for large (PL) and small (PS) firms are assumed to be functions of the quantities borrowed (QL and QS) and elements of X, that represent the economic environment in which funds are borrowed: PL = f (QL, QS, X)
(1)
and PS = g(QL, QS, X)
(2)
Of particular interest will be: ∂PL/∂QS, ∂PS/∂QL, and how PL and/or PS change in response to economic conditions. If, for example, ∂PL/∂QS = 0 and ∂PS/∂QL = 0, the funds markets for large and small firms are segmented. 3. Measurement and data 3.1. Measurement Large and small firms costs of credit are often not directly observable, and when the data are available, they are often not with sufficient frequency for in depth analysis. Proxies that are highly correlated and monotonically increasing with the costs of credit for large and small firms are employed to represent PL and PS, respectively. PL will be represented by the prime rate, RPRIME that the largest, most credit worthy firms pay for funds. Market rates small firms pay, PS, are a combination of (1) the interest rate small firms pay on short-term loans from institutions, RIPSM (surveyed monthly by the National Federation of Independent Business) and (2) the rate of interest on credit card loans, RCARDQ (surveyed quarterly by the Federal Reserve). An NFIB survey of small firms found that 92 percent have 1, 2, or 3 credit cards and that 96 percent use the services of a local or regional bank (NFIB Research Foundation, 2008, page 24). This study examines what dynamic factors determine rate changes, PL and PS, monthly and quarterly. For the prime rates, PL = RPRIM monthly and RPRIQ quarterly; PS = RIPSM monthly and RCARDQ quarterly. 3.2. Data RIPSM is the “actual interest paid on short-term loans” by NFIB borrowers (Dunkelberg and Wade, monthly issues). Observations are available from January 1996 through October 2008. For RCARDQ the Federal Reserve (statistical release G19) provides only quarterly data – February, May, August, and November for 1995 – 2009, third quarter. Thus, RPRIM and RIPSM can be contrasted monthly, but RPRIQ and RCARDQ must be contrasted quarterly. RPRIM and RPRIQ represent the monthly and quarterly prime rate (Federal Reserve releases H15 and G19). Economics and financial data are matched with the rates for the closest possible dates. Much small firm borrowing is supported by credit cards, but not collateralized, by a business or entrepreneur’s personal assets plus small business loans from a variety of sources. An NFIB survey reports that more than 92 percent of small business respondents use at least 1 credit card (NFIB Research Foundation, 2008, p. 24). 3.3. Costs of credit for large and small firms Differences between the costs of credit for large and small US firms are reflected by the monthly difference between the prime rate and the rate paid by independent businesses and the quarterly difference between the prime rate and the rate of interest on credit card balances. When interest rates are declining, the prime rate usually declines more rapidly than the cost of credit to small firms. For 2000–2002, credit card rates declined by 1.52 (from 14.30 to 12.78 percent), bank rates paid by NFIB small business survey respondents declined 3.20 (from 9.70 to 6.50 percent), while the prime rate dropped 4.24 (from 8.69 to 4.45 percent). Contrasting the fourth quarter of 2007 and the third quarter of 2009 shows
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491 Table 1B Unit root tests Zt = ˇ0 + Zt−1 + ˇ1 Zt−1 + ˇ2 Zt−2 + ˇ3 t + εt RPRIM and RIPSM.
Table 1A Unit root tests Zt = ˇ0 + Zt−1 + ˇ1 Zt−1 + ˇ2 Zt−2 + ˇ3 t + εt RPRIQ and RCARDQ. Variable
ˇ2 = 0 1 period lag
ˇ2 = / 0 2 period lag
Assumptions
Variable
RPRIQ RCARDQ
−1.71 −1.96
−1.93 −1.35
ˇ0 = / 0 ˇ3 = 0 / 0 ˇ3 = 0 ˇ0 =
RPRIQ RPRIQ RCARDQ
−2.73 −2.65 −6.74
−2.19 −2.12 −4.86
/ 0 ˇ3 = 0 ˇ0 = ˇ0 = 0 ˇ3 = 0 ˇ0 = / 0 ˇ3 = / 0
RPRIM RPRIM RIPSM RIPSM
5% rejection region t < −2.92 10% rejection region t < −1.95.
that interest rate declines were from 8.03 to 3.25 (−5.78) for the prime rate and 9.10 to 6.00 (−3.10) for the rate NFIB respondent small firms paid to banks. Credit card rates rose from 14.34 to 14.90 (+0.56) over the same period. March 2001 through November 2001 and since December 2007 are the only periods since 1995 that the National Bureau of Economic Research identifies as a recession periods. 4. Methodology and analysis Analyses of quarterly contrasts for RPRIQ and RCARDQ or monthly contrasts for RPRIM and RIPSM are developed by estimating vector autoregressive (VAR) models with or without error corrections. The dynamic analysis requires a three stage process: (1) unit root tests, (2) tests for cointegration, and (3) VAR parameter estimates, with or without error corrections. Whether error corrections are appropriate depends on the results of the unit root and Johansen cointegration tests. The empirical VAR and VAREC models can be applied to determine equilibrium price impact multipliers. The time series analyses for the prime and either card rates or bank rates paid by independent businesses examine two hypotheses, H1A and H1B or H2A and H2B, respectively: H1A. RPRIQ and RCARDQ are non-stationary with one unit root, or integrated of order one, I(1) H1B.
RPRIQ and RCARDQ are cointegrated and
H2A. RPRIM and RIPSM are non-stationary with one unit root, or integrated of order one, I(1) H2B.
RPRIM and RIPSM are cointegrated.
4.1. Unit root tests
RPRIM RPRIM RIPSM RIPSM
1 Period lag
2 Period lag
Assumptions
5% Reject region
−0.89 −1.48 −0.97 −1.24
−1.18 −1.73 −0.88 −1.12
ˇ0 ˇ0 ˇ0 ˇ0
= / = / = / = /
0 ˇ3 = 0 0 ˇ3 = / 0 0 ˇ3 = 0 0 ˇ3 = / 0
−2.88 −3.44 −2.88 −3.44
−3.85 −3.90 −10.99 −10.95
−3.10 −3.15 −7.19 −7.16
ˇ0 ˇ0 ˇ0 ˇ0
= / = / = / = /
0 ˇ3 = 0 0 ˇ3 = / 0 0 ˇ3 = 0 0 ˇ3 = / 0
−2.88 −3.44 −2.88 −3.44
With a one period lag (ˇ2 = 0), the t-statistics are −1.71 for RPRIQ and −1.96 for RCARDQ, respectively. Neither is significant at the 10 percent level (t < −2.92), so = 1 cannot be rejected. The level of each interest rate series is concluded to have a unit root. Allowing two period lags (ˇ2 = / 0), the t-statistics are −1.93 and −1.35, neither of which is in the rejection region for RPRIQ or RCARDQ, respectively (Table 1A, top panel). To test first differences, Zt is replaced by Zt as the dependent variable in Eq. (3). RCARDQ has t-statistics of −6.74 and −4.86 for one and two period lags, respectively, which are both in the rejection region and < 1 is accepted. For RPRIQ the necessary assumptions to reject a unit root are ˇ3 = 0 and a 10 percent rejection criterion; the t-statistics for one or two period lags are −2.73 / 0 or −2.63 and −2.12 for ˇ0 = 0 (Table 1A, botand −2.19 for ˇ0 = tom panel). A unit root for RPRIQ and RCARDQ can be rejected with a 10 percent criterion. 4.3. Unit root test results for RPRIM with RIPSM (Table 1B) Whether ˇ0 or ˇ3 is constrained to zero and for a one or two period lag, the hypotheses that RPRIM and RIPSM each have a unit root = 1 cannot be rejected (Table 1B, top panel). When Zt is replaced by Zt as the dependent variable for monthly rates in Eq. (3), a unit root can be rejected for the change in each monthly rate. RIPSM has t-statistics below −7.0 for both one and two period lags, and = 1 is rejected. A unit root can also be rejected for RPRIM; each t-statistic for RPRIM is below −3.0 (Table 1B, bottom panel). The hypotheses that RPRIM and RIPSM do not have unit roots are accepted. 4.4. Cointegration tests
Augmented Dickey–Fuller (ADF) tests (Dickey & Fuller, 1979) examine unit roots. Letting Z represent RPRIQ and then RCARDQ, H1A and H2A are tested estimating: Zt = ˇ0 + Zt−1 + ˇ1 Zt−1 + ˇ2 Zt−2 + ˇ3 t + εt
487
(3)
A rate and then the change in a rate are tested with Eq. (3), letting the dependent variable, Zt , represent the rate and then the change in the rate. The null and alternative hypotheses for the unit root tests are: H0 : = 1 and HA : < 1. A one tailed test is appropriate because ≥ 1 implies non-stationary. The alternative tests for each of the four rates, estimating Eq. (3), are to examine the cases whether ˇ0 , ˇ2 , and ˇ3 equal 0 or not. ˇ0 allows a constant, ˇ2 allows a second time lag, and ˇ3 allows a trend in Zt . 4.2. Unit root test results for RPRIQ with RCARDQ (Table 1A) The ADF test provides t-statistics for the coefficients in Eq. (3). The emphasis is on . The results are provided in Tables 1A and 1B.
Johansen’s test (Johansen, 1991) determines whether a pair of time series is cointegrated, given that each of the series possesses a unit root. Under the conditions described above neither RPRIQ and RCARDQ quarterly nor RPRIM and RIPSM monthly have unit roots. The five cases for the cointegrating equation (CE) are: (1) no deterministic trend in the data: no intercept and no trend in the CE; (2) no deterministic trend in the data; an intercept but no trend in the CE; (3) linear trend in the data; an intercept but no trend in the CE; (4) linear trend in the data; both an intercept and trend in the CE; (5) quadratic trend in the data; both an intercept and trend in the CE. The most appropriate assumption appears to be case (3) where series may have intercepts and linear trends, but the cointegrating equation has only an intercept. The cointegration tests are summarized in Tables 2A and 2B. The trace test at the 5 percent level
488
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491 Table 3 VAR model (t-statistics in parentheses, quarterly data).
Table 2A Johansen cointegration tests for RPRIQ and RCARDQ (N = 56). Hypothesized cointegrations (RPRIQ and RCARDQ)a
Trace statistic
5% Critical value
Probability
None At most 1 trace test indicates 2 cointegrating equations at 5% level
54.2914 6.3028
15.49 3.84
0.0000 0.0120
a
No deterministic trend because of first differences.
indicates two cointegrating equations for RPRIQ and RCARDQ (N = 56 quarters) and one cointegrating equation for RPRIM and RIPSM (N = 156 months), determining the autoregressive framework. 4.5. Vector autoregressive framework The results of the unit root and Johansen cointegration tests determine whether vector autoregressive models without (VAR) or with error corrections (VAREC) should be estimated jointly for RPRIQ and RCARDQ and jointly for RPRIM and RIPSM. Advantages of estimating VAR or VAREC models for a pair of rates are (1) the potential impact of each exogenous variable is tested for each rate and (2) simultaneous equilibrium impact multipliers can be determined. Exogenous factors may influence the costs of credit to large and small firms, but a particular factor will not necessarily influence each of the rates to the same extent. Since RPRIQ and RCARDQ do not have a single cointegrating equation and a unit root for RCARDQ can only be rejected at the 10 percent level, VAR rather than VAREC models are estimated for RPRIQ and RCARDQ. Since RPRIM and RIPSM have a single cointegrating equation and a unit root is rejected for each of them, VAREC models are estimated for these rates. A vector autoregressive model with an error correction term (VAREC) accommodates the cointegration (Engle & Granger, 1987). The general model for RPRIM and RIPSM is
RPRIMt RIPSMt
=
ˇ0P
ˇ0S
+
+
+
ˇ2PP ˇ2SP P S
ˇ1PP
ˇ1PS
ˇ1SP
ˇ1SS
ˇ2PS ˇ2SS
RPRIMt−1
RPRIMt−2
εPt
RPRIQt
Constant 0.0088 (0.32) RPRIQt−1 0.1968 (4.64) −0.0778 (−1.92) RPRIQt−2 −0.0350 (−0.99) RCARDQt−1 RCARDQt−2 −0.0161 (−0.46) RETMFGQt −0.0103 (−1.73) QCARDQt −0.0001 (−0.14) 0.8763 (25.33) FFQt R-square 0.96 Akaike goodness of fit statistic = −0.40
RCARDQt 0.1710 (1.64) 0.3199 (2.00) −0.1275 (−0.84) −0.1941 (−1.46) −0.3016 (−2.26) 0.0064 (0.28) −0.0065 (−1.84) 0.2921 (2.24) 0.35
4.6. Autoregressive econometric models VAR and VAREC models are estimated including two-quarter autoregressive relationships and first differences of exogenous variables. Variables are included to represent the quantities of funds borrowed at prime and credit card rates for VAR models and the quantities of funds borrowed at the prime and the rate paid by small firms to institutions on short-term loans for the VAREC model. Numerous models have been estimated, including exogenous variables to represent small and large firm demand for funds, financing experience, represented by interest rates, and macroeconomic conditions. The variables that appear in the estimated models, along with their sources, are listed in Appendix A. 4.7. RPRIQ–RCARDQ VAR quarterly model (Table 3) The quantity of funds borrowed on credit cards (QCARDQ) is the sum of the quantity of revolving and non-revolving credit. A direct measure of the quantity of funds borrowed at the prime rate is not available on a frequent basis; the change in the level of retail plus manufacturing sales (RETMFGQ) is a proxy for the quantity of funds borrowed at prime. Retail sales represent a broad measure of aggregate consumer purchasing and manufacturing sales represent business sales and production of goods and services. The most effective VAR model for RPRIQ and RCARDQ is given in Table 3. The results in Table 3 can be summarized as follows:
RIPSMt−1
RIPSMt−2
ECt−1 +
Variable
+
ˇ3P ˇ3S
Xt
εSt
The error correction term is ECt = RPRIMt + ˛0 + ˛1 RIPSMt The estimated models may include exogenous variables, included in Xt in Eqs. (1) and (2). The VAR model for RPRIQ and RCARDQ takes the same form, but ECt = 0, RCARDQ replaces RIPSM, and RPRIQ replaces RPRIM.
1. RPRIQ has a significant positive autoregressive relationship at lag 1 and a negative relationship at lag 2. 2. RCARDQ has a significant negative autoregressive relationship at lag 2 and a significant positive relationship with RPRIQ at lag 1. 3. RPRIQ and RCARDQ have significant negative relationships with their own funds borrowed proxy – RETMFGQ and QCARDQ, respectively. 4. RPRIQ and RCARDQ both have significant positive relationships with the change in the Fed Funds rate (FFQ). At the 10 percent level of significance, both the prime and the card rates decrease with increases in their own quantity proxies indicating downward sloping demands for funds. Neither quantity proxy has a significant coefficient in the equation for the
Table 2B Johansen cointegration tests for RPRIM and RIPSM (N = 156). Hypothesized cointegrations (RPRIM and RIPSM)a
Trace statistic
5% Critical value
Probability
None At most 1 trace test indicates 1 cointegrating equation at 5% level
69.5369 6.9475
25.87 12.52
0.0000 0.3500
a
No deterministic trend because of first differences.
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491 Table 5 Statistically significant coefficients of quantities of funds borrowed.
Table 4 VAREC model (t-statistics in parentheses, monthly data). Variable
RPRIMt
Constant 0.0236 (4.25) −0.0710 (−1.74) RPRIMt−1 −0.0328 (−0.85) RPRIMt−2 0.0998 (6.87) RIPSMt−1 0.0210 (1.54) RIPSMt−2 ECt−1 −0.6395 (−18.61) −0.0019 (−0.90) RETMFGMt −0.0023 (−1.13) QBORSMt 0.7465 (21.78) FFMt R-square 0.80 Akaike goodness of fit statistic = −1.69 EC = RPRIM + 0.0367 + 0.2560 RIPSM
489
RIPSMt
(Table 3)
(Table 4)
0.0152 (0.52) 0.3257 (1.52) 0.3971 (1.96) −0.9033 (−11.86) −0.4845 (−6.77) −0.3713 (−2.06) −0.0190 (−1.68) 0.0175 (1.64) 0.4468 (2.48) 0.59
QL = RETMFGQ QS = QCARDQ =0 <0 <0 =0
QL = RETMFGM QS = QBORSM =0 >0 =0 <0
∂PL/∂QS ∂PS/∂QS ∂PL/∂QL ∂PS/∂QL
Bold, italicized 0s show market segmentation, except ∂PS/∂QL from Table 4.
Table 6 Impact multipliers.
(4.33)
RPRIQt
Variable
RCARDQt
Case A. VAR quarterly impact multipliers
other funds price, indicating segmentation of the loan markets. The changes in the prime and the credit card rates respond significantly to changes in the Fed funds rate in the same direction; the response and the coefficient for FFQ is considerably larger in the RPRIQ relationship. The VAR model in Table 3 has the strongest econometric characteristics of the models tested. This model has the highest R-square values for the two relationships, and the minimum value of the Akaike information criterion (−0.40), which measures goodness of fit and is a basis for VAR model selection (see Akaike, 1974; Burnham & Anderson, 2002). 4.8. RPRIM–RIPSM VAREC model (Table 4) The quantity of funds borrowed from institutions by small firms is measured as the percentage of small firms that borrow regularly within a 3-month period (QBORSM), reported in the Dunkelberg and Wade NFIB monthly survey. RETMFGM is employed as a proxy for the quantity of funds borrowed by large firms at the prime rate. The most effective VAREC model for RPRIM–RIPSM is provided in Table 4. The variables with the most significant coefficients in the VAREC models represent the analogous factors to those in the VAR models. The results in Table 4 can be summarized as follows: 1. RPRIM and RIPSM both have significant negative autoregressive relationships with its own rate at lag 1. 2. RPRIM has a significant positive autoregressive relationship with RIPSM at lag 1. 3. At lag 2, RIPSM has a significant negative autoregressive relationship with its own rate and a significant positive autoregressive relationship with RPRIM. 4. RIPSM has a significant positive relationship with the quantity of small business loans and negative relationship with the quantity of funds borrowed at the prime rate. RPRIM does not have a significant relationship with either quantity of borrowed funds. 5. The coefficient of FFM is positive and significant in each relationship. The coefficient of FFM in the RPRIM model is 160 percent of its coefficient in the RIPSM model.
RETMFGQt QCARDQt FFQt Variable
−0.0119 0.0001 0.9761
0.0028 −0.0043 0.3208
RPRIMt
RIPSMt
Case B. VAREC monthly impact multipliers RETMFGMt QBORSMt FFMt
−0.0027 −0.0013 0.7207
−0.0088 0.0069 0.4053
4.9. Model conclusions The dynamic VAR quarterly and VAREC monthly models show that the changes in interest rates incurred by large and small firms (funds’ prices) can be represented by changes in their lagged rates, the quantities of funds borrowed or their proxies, and the Fed funds rate. When funds’ market prices change, represented by FF, the effects on small firms are smaller than effects on large firms. This is particularly true when the prices (rates) are declining. Coefficients of ∂PL/∂QS and ∂PS/∂QL are never statistically significant at a meaningful level, except for ∂PS/∂QL in the VAREC Model (at the 10 percent level). Table 5 summarizes the signs of the statistically significant coefficients of QCARDQ and QBORSM, quarterly and monthly small business funds quantities, respectively. Bold, italicized cases that equal 0, except for ∂PS/∂QL from Table 4, show large and small firms’ funds markets are segmented. The aggregate test statistics are strong for each model. Additional factors that have been tested do not have significant coefficients at the 10 percent probability level. The models in Tables 3 and 4 are the basis for developing long-run equilibrium impact multipliers. 5. Impact multipliers and equilibrium conditions Long-run simultaneous solutions to the models in Tables 3 and 4, respectively, provide “equilibrium” impact multipliers. Long-run quarterly multipliers can be determined for RPRIQt and RCARDQ from Table 3, when RPRIQt = RPRIQt−1 = RPRIQt−2 and RCARDQt
When the Federal Reserve changes it target Fed funds rate, the prime rate changes in the same direction by 75 percent of the change, and the rate small firms pay to institutions changes by 45 percent of the change. The VAREC model captures more of the variation in the prime rate (RPRIM) and than the variation in the small business-borrowing rate (RIPSM), according to the R-square values. The Akaike value is highly negative.
= RCARDQt−1 = RCARDQt−2 , Long-run monthly multipliers for RPRIMt and RIPSM can be determined from Table 4 when RPRIMt = RPRIMt−1 = RPRIMt−2 and RPRIMt = RIPSMt−1 = RIPSMt−2
490
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491
Table 7 t-Statistics for recession binary models. Variable
Intercept
Card rate equation
Prime rate equation
RPRIQ
RCARDQ
RPRIQ
RCARDQ
(−1.66)* (−2.26)* (−1.06) (−1.19)
(0.51) (0.62) (1.84)* (1.83)*
(0.10) (−0.23)
(−1.90)* (−1.83)*
RPRIQ
RCARDQ
(−2.53)**
(0.54)
**
(0.30)
Case A. quarterly models B B* RETMFGQ B* QCARDQ B* both Variable
Intercept
Card rate equation
(−2.51)
Prime rate equation
RPRIM
RIPSM
RPRIM
RIPSM
(0.47) (0.49) (0.30) (0.32)
(−0.40) (−0.43) (−0.28) (−0.33)
(−0.87) (−0.83)
(−1.37) (−1.45)
RPRIM
RIPSM
(−0.22)
(0.75)
(−0.17)
(0.88)
Case B. monthly models B B* RETMFGM B* QBORSM B* both
B = 1, March–November 2001, December 2007–present, and 0 otherwise. * Statistically significant at the 10 percent level. ** Statistically significant at the 1 percent level.
Impact multipliers for the VAR model reflect what is expected (Table 6, Case A). The impacts for the proxy for the quantity of funds borrowed by large firms (RETMFGQ) and small firms (QCARDQ) are that prices are lower for larger quantities of funds borrowed in each market. The price for large firms is more sensitive (−0.0119 versus −0.0043). The cross elasticity quantity coefficients in the quarterly model are positive as expected (+0.0001 and +0.0028). The impact multipliers from the monthly VAREC model (Table 6, Case B) show that banks charge large firms lower prices for larger quantities of funds (−0.0027), but that smaller firms are paying higher prices for larger quantities of funds (+0.0069). This is a difference between small firms borrowing on credit cards (Table 6, Case A) and their borrowing from banks (Table 6, Case B). Small firms borrowing on credit cards usually occur when more attractive sources of credit have been exhausted. Large and small firms appear to be direct competitors for bank funds. The monthly impacts of changes in the Fed funds rate are similar to the impacts in the quarterly model.
6. Effects of recessions As Bernanke et al. (1996), Kiyotaki and Moore (1997), and Holmstrom and Tirole (1998) all suggest, the impacts of recessions and tight credit card markets are more severe for firms that have the least financial market power in lending markets. The National Bureau of Economic Research defines March through November 2001 and December 2007 through the present as the recession periods during the period for this study. Let B = 1 for these recession months and B = 0 otherwise. Table 7 shows the t-statistics for four tests of the recession effects on the prices of credit: (1) only an intercept shift (B); (2) recession effect solely on quantity of funds borrowed by large firms (B*RETMFG) and intercept; (3) recession effect solely on quantity of funds borrowed by small firms (B*QCARDQ or B*QBORSM) and intercept; (4) recession joint effect on quantity of funds borrowed by large and small firms (B*RETMFG and B*QBORSM or B*QCARDQ and B) and intercept.
For the quarterly models, whenever there is a statistically significant recession (B = / 0), the credit prices are, of course, lower during the recession. In the quarterly credit card models, RCARDQ, declining rates are shown by the significant, negative t-statistics, −1.90 and −1.83. In the quarterly prime rate models, RPRIQ, declining rates are shown by the significant, negative t-statistics, −2.53 and −2.51. The small business price changes are only significant at the 10 percent level, while the large business price changes are significant at the 1 percent level. For the monthly models, none of the recession coefficients is statistically significant at the 10 percent level or better (Table 7, Case B). Evidently a month is too short for the benefit from significant price reductions to be reflected. 7. Conclusions Short-term costs of credit for large and small firms respond to common factors. Small firms borrow in the forms of credit card loans and other short-term credit from institutions. Large and small firms do not appear to be direct competitors for funds; these markets are at least somewhat segmented. The changes in the costs of funds for large and small firms are functions of the proxies for quantities of funds borrowed and changes in the Fed funds rate. The dynamic VAR prime-credit card model and VAREC prime-short-term credit model have high R-squares and significant t-statistics. Quarterly funds’ prices are more sensitive than monthly prices to quantity changes. Moreover, during recessions, the decline in prices of funds to large firms is more significant than the declines to small firms. Large and small firms face differences in quarterly and monthly markets for funds. Tables 3, 4, 6 and 7 of this study show that large firms benefit more quickly and to a greater extent than small firms when prices of credit are changing. These results support the theoretical bases in Walker and David (1989) and Walker (2008). Acknowledgements The author would like to thank Thomas Durkin and Keith Ord for helpful suggestions and guidance for this paper. Holly Wade, Giuseppa Gramigna, and Charles Ou advised the author on data sources and interpretations.
D.A. Walker / The Quarterly Review of Economics and Finance 50 (2010) 485–491
Appendix A. Variables and sources Variable
Definition
Source
RPRIME
Prime Interest Rate
RPRIQ RPRIM RPRIQ RPRIM RIPSM
RPRIME quarterly RPRIME monthly RPRIQt –RPRIQt−1 RPRIMt –RPRIMt−1 Cost of loans to independent businesses
Federal Reserve release H15, monthly, 1996–2009 (Federal Reserve, 2008) Feb., May, Aug., Nov.
RIPSM RCARDQ
RIPSMt –RIPSMt−1 Bank credit card quarterly Federal Reserve release interest rate G19 Feb., May, Aug., Nov. RCARDQt –RCARDt−1 Percentage of small firms borrowing regularly within 3 months (Dunkelberg and Wade, NFIB) Credit card borrowing = QNONREV + QREVOLV QNONREV – quantity non-revolving credit (FRB statistical release G19) QREVOLV – quantity of revolving credit (FRB statistical release G19) Fed funds rate quarterly (FRB release H15) Fed funds rate monthly (FRB release H15) Business borrowing index monthly = MANUFACT + RETAIL MANUFACT − business manufacturing index (St. Louis Federal Reserve Fred2) RETAIL − retail sales index (St. Louis Federal Reserve Fred2, www.research.stlouisfed.org) Business borrowing index quarterly = MANUFACT + RETAIL Recession binary variable – NBER identification of 2001 and December 2007 onward in “Business Cycle Expansions and Contractions”
RCARDQ QBORSM QCARDQ
FFQ FFM RETMFGM
RETMFGQ B
National Federation of Independent Business, monthly, 1996–2009
References Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6) American Banker (2009). In cards, a complex dance on rates, March 10, page 1.
491
Bernanke, B., Gertler, M., & Gilchrist, S. (1996). The financial accelerator and the flight to quality. The Review of Economics and Statistics,. February. Burnham, K. P., & Anderson, D. R. (2002). Model selection and multi-model inference: A practical-theoretical approach (2nd ed.). Springer-Verlag. Dickey, D. A., & Fuller, W. A. (1979). Distribution of estimators for autoregressive time series with a unit root. Journal of the American Statistical Association. Dunkelberg, W. C., & Wade, H. (2009). NFIB small business economic trends. Washington, DC: NFIB Research Foundation. November, various issues through. Engle, Robert F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica. Federal Reserve. (2008). Highlights of proposed rules regarding credit card and overdraft services. Washington, DC: Board of Governors of the Federal Reserve. May 2. Gramigna, G. (2009). Current economic challenges, the small business economy, and federal government interventions. Washington, DC: U.S. Small Business Administration. March 30. Holmstrom, Bengt, & Tirole, Jean. (1998). Private and public supply of liquidity. Journal of Political Economy, 1. Johansen, Soren. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica. Kiyotaki, N., & Moore, J. (1997). Credit cycles. Journal of Political Economy, (2). National Bureau of Economic Research (2009). “Business Cycle Expansions and Contractions,” November 23 (http://www.nber.org.cycles.html). NFIB Research Foundation (2008). “Small business poll: Access to credit,” Washington, DC, vol. 8, 7. Shleifer, Andrei, & Vishny, Robert W. (1992). Liquidation values and debt capacity: A market equilibrium approach. Journal of Finance, XLVII(September (4)) Spector, Mike. (2009). Small businesses turn to Goldman. Wall Street Journal, (November 19), C5. U.S. Small Business Administration. (2007). The small business economy 2008. Washington, DC: U.S. Government Printing Office. December. U.S. Small Business Administration (2009). “SBA’s Economic Recovery Efforts and Impact,” Washington, DC, November 9. Walker, D. A. (2008). Credit card financing, consumer credit, and mortgage credit. In Testimony on the role of credit cards in small business financing. Washington, DC,: Hearings before the U.S. House of Representatives Committee on Small Business. April 3. Walker, D. A. (1989). Financing the small firm. Small Business Economics, (Fall).