Consumer Bankruptcies and the Bankruptcy

Consumer Bankruptcies and the Bankruptcy Reform

Act: A Time-Series Intervention Analysis, 1960±1997

JON P. NELSON

Department of Economics, Pennsylvania State University, University Park, PA

Abstract

The Bankruptcy Reform Act of 1978, effective on October 1, 1979, signi®cantly altered the basic rules by which consumers ®le for bankruptcy. Between 1979 and 1997, the number of nonbusiness bankruptcies ®led annually rose from 200,000 to 1.35 million, and the rate of bankruptcies per 100,000 adults increased from 129 to 715. A controversial aspect of bankruptcy is how much of this increase can be attributed to the 1978 act. Early empirical studies provide estimates ranging from a low of 6% to a high of 75% for the immediate post-act period. However, two recent studies using longer data series report that none of the increase was due to the act. Previous studies suffer from several econometric problems, including inadequate attention to stochastic properties and stationarity of the data series, as well as data errors due to reporting changes. This paper uses an ARIMA intervention analysis to estimate the impact of the 1978 act. Using adjusted quarterly data for 1960:3 to 1995:4, the data ®rst are examined for unit roots. The tests reject the presence of seasonal unit roots but con®rm the presence of a nonseasonal unit root. The empirical analysis therefore is based on logged ®rst differences of bankruptcy ®lings and ®ling rates per capita. An ARIMA model is estimated using the preintervention data for 1960:3 to 1979:3. This model is re-estimated for 1960:3 to 1995:4 with the intervention terms included. The intervention model estimates indicate that the 1978 act increased consumer bankruptcies by 36% in the post-act period relative to the pre-act period, or about 72,400 additional bankruptcies per year. Overall, the net impact of the 1978 act was modest compared to the substantial rise in bankruptcies that has occurred since 1979.

Key words: bankruptcy, ARIMA models, seasonal unit roots

1. Introduction

By some accounts, these changes were responsible for a signi®cant increase in consumer bankruptcy ®lings and rates. As displayed in ®gure 1, bankruptcy ®lings and rates were relatively stable during the 1970s but rose sharply in 1980±1981 and thereafter. The surge in bankruptcy ®lings renewed the congressional debate and prompted several empirical studies of the impact of the code on consumer bankruptcies. For instance, a report to Congress by the U.S. General Accounting Of®ce (U.S. GAO, 1983) found that the code increased the total number of ®lings in ®scal 1981±1982 by only 6%, but a time-series study by Kowalewski (1982) found an impact of 30%. However, two recent studies using longer data series (reviewed later) found no effect of the new code on consumer bankruptcy. Previous empirical studies have attempted to measure the code's impact using structural econometric time-series models incorporating macroeconomic data on business cycle conditions such as lagged unemployment rates and social indicators such as divorce

rates. The theoretical models underlying these studies often are incomplete and few studies pay suf®cient attention to the stochastic properties of the time-series data in question. Further, the net effect of the 1978 act may have been altered by other legal changes, including changes in reporting methods for joint petitions and several amendments to the act. As a consequence, there is great uncertainty regarding the impact of the 1978 act on consumer ®lings, despite continued pressure for more reform. The importance of this issue is highlighted by the magnitude of creditors' losses, which are estimated at $32 billion total and $10 billion for the bankcard industry alone (VISA, 1998).

This paper investigates the net impact of the 1978 act, using interrupted time-series, or intervention, analysis. This technique is an extension of the autoregressive integrated moving average (ARIMA) methods introduced by Box and Tiao (1975) and Box and Jenkins (1976) to measure the effect of a policy change or event (intervention) on the outcome variable. Deterministic dummy variables and Koyck-type distributed lags are included in a conventional ARIMA model of the stochastic process underlying the outcome. Because the effects of an intervention may be clouded by gradual responses and other underlying patterns in the data, such as trends, drift, and seasonal variation, ARIMA analysis provides a means of measuring the impact of an intervention in the presence of these complications. Recent studies using this technique include assessments of international terrorism controls (Cauley and Im, 1988), poverty reduction programs (Fomby and Hayes, 1990), antidumping actions (Lloyd, Morrissey, and Reed, 1998), and political tax cycles (Yoo, 1998). Financial studies that employ intervention analysis include analyzes of credit availability (Van Fenstermaker and Filer, 1986), interest rate regulations (Edmister and Merriken, 1989), the stock market crash of 1987 (Blackley, 1992), and an S&L insurance crisis (Cooperman, Lee, and Wolfe, 1992).

This study uses quarterly data on consumer bankruptcy ®lings and rates for the time period 1960:3 to 1997:4, where the outcome variable is the number of bankruptcy ®lings (or per capita rate), adjusted for joint petitions by married couples. First, the data are examined for seasonal and nonseasonal unit roots. Second, using various model selection criteria and logged ®rst differences of the data, an ARIMA model is estimated for the 77 quarters prior to the effective date of the act. Third, the intervention model is estimated for the period 1960:3 to 1995:4, with the interval 1996:1 to 1997:4 used for forecasting. The methods used in this paper have a number of advantages over the methods used in previous studies, including greater attention to the stochastic properties of the data, removal of autocorrelation, use of more recent data, and application of an exhaustive set of model diagnostics, including forecasting tests. ARIMA models also have the advantage of allowing for changes in parameter values in pre-event and postevent periods. In contrast to two recent structural econometric studies, this paper ®nds that the Bankruptcy Reform Act had a signi®cant and substantial impact on bankruptcy outcomes relative to the immediate pre-act period. However, given the substantial rise in bankruptcies since 1979, the long-term effect of the 1978 act was modest.

tests for temporary effects of the act. Section 6 contains the results of the intervention analysis and forecasts for 1996±1997. Section 7 contains the conclusions.

2. Background

2.1. Historical perspective

The federal government derives its powers with respect to bankruptcy from Article 1 of the Constitution. Beginning in 1800, several temporary bankruptcy laws were enacted, but state insolvency laws were the primary means for resolution of debtor-creditor problems. Following the Panic of 1893, Congress enacted the Bankruptcy Act of 1898. Although amended numerous times, most radically in 1938, this act served the nation for 80 years (Tabb, 1995). However, beginning in the mid-1960s, there was growing dissatisfaction, including a concern that impersonal forms of consumer installment credit were causing an increase in nonbusiness bankruptcies (Stanley and Girth, 1971). In 1970, Congress created the Commission on the Bankruptcy Laws to study and report on the existing law. The commission ®led its two-part report in 1973. Five years later, after a decade of study and debate, Congress enacted the Bankruptcy Reform Act of 1978, including the new federal Bankruptcy Code. The new code became effective on October 1, 1979.

The principal objective of debtors who ®le for bankruptcy is to discharge as much of their unsecured debt as possible. The basic choice faced by consumers is between ®ling under chapter 7 or chapter 13. Chapter 7 is a straight liquidation bankruptcy, meaning that debtors need not give up any future income but may have to relinquish some current assets. About 70±75% of debtors choose to ®le under chapter 7. To encourage a ®nancial ``fresh-start,'' chapter 7 allows debtors to retain certain exempt assets (the ``grubstake''), including prescribed or reasonably necessary amounts of equity in household and personal goods, tools of trade, automobiles; and homesteads. Prior to 1978, exemptions were controlled entirely by state law. The new code provided for federal exemptions totaling about $13,600, including $7,500 for equity in residential property, $1,200 for motor vehicles, $750 for professional tools, $500 for jewelry, $200 per item for household furnishings and goods, and a ``wildcard'' exemption equal to $400 plus any unused portion of the homestead exemption. However, a last-minute compromise in 1978 allowed individual states to substitute their own statutory exemptions (Posner, 1997). By 1983, all states had opted out of the federal exemptions, although 16 states presently allow debtors to choose between the state and federal exemptions. Some states have responded with generous exemptions, especially the homestead exemption, while other states have chosen relatively modest exemption levels. Recent analysis indicates that the level of the homestead exemption matters for state-by-state bankruptcy ®lings (Nelson, 1999).

because the code provides that the amount repaid to unsecured creditors under chapter 13 must be at least as great as the creditors would have received under chapter 7. Among the interest groups involved in bankruptcy, the bankcard industry has argued for greater use of chapter 13, and the Bankruptcy Amendments and Federal Judgeship Act of 1984 was a partial attempt to encourage this outcome.2

In the face of rising consumer ®lings in 1980±1981, the new code was immediately the subject of much debate and many calls for revision. The attempted revisions were further complicated when the Supreme Court in 1982 held that the jurisdictional provisions of the 1978 act were unconstitutional. A new and highly complicated jurisdictional structure was provided by the 1984 amendments, effective in October 1984. Additional amendments were enacted in 1986, which established chapter 12 for family farm reorganizations and made permanent the previously experimental U.S. trustee program. Finally, the Bankruptcy Reform Act of 1994 doubled the federal exemption for chapter 7 and tied it to the consumer price index (effective April 1, 1998). Congress also established a new National Bankruptcy Review Commission and mandated it to make recommendations for updating and improving the code (U.S. NBRC, 1997; see also www.nbrc.gov).

2.2. Early empirical evidence

®ling data were adjusted for changes in joint petitions under the new code and seasonal dummies variables were included for the ®rst and second quarter of each year. A large number of possible explanatory variables (22 in all) were examined, but only 3 variables (debt-income ratio, interest payment burden, socioeconomic index) were included in the ®nal model. Although the regression was adjusted for ®rst-order autocorrelation, the two reported Durbin-Watson statistics were still low (1.45 and 1.57). A dummy variable for the new law change indicated ``that the Code may have contributed no more than an estimated 6 to 7% of the total adjusted ®lings and 12 to 14% of the total number of debtors for ®scal years 1980, 1981, and 1982'' (U.S. GAO, 1983, p. 19).

In contrast to these studies, Boyes and Faith (1986) used an ARIMA intervention model to study monthly bankruptcy petitions in the U.S. District Court located in Phoenix, Arizona. The study period was January 1976 through December 1981, and the estimates indicated that the permanent effect of the code was about 43 more bankruptcies per month or an increase of 21.6% over the trend. The authors conclude ``that the effect of the implementation of the BRA was to increase substantially the number of bankruptcies'' (Boyes and Faith, 1986, p. 147).

2.3. Recent empirical studies

The preceding studies examined the impact of the code in the ®rst few years of its implementation, and none extended the data past 1982. It is not clear from this work whether the impact of the 1978 act was temporary or permanent. For example, it may be that many attorneys delayed the ®ling of new petitions in early 1979 to take advantage of higher exemptions available after October 1979. This would show up as a temporary decrease in ®lings in 1979, followed by a temporary increase in 1980±1981. Further, with the exception of the GAO study, none of the studies pays heed to the change in joint ®ling procedures under the new code. Two recent empirical studies examined the impact of the new code over longer time periods. A study by Bhandari and Weiss (1993) examined consumer bankruptcy rates using annual data for the period 1947±1987. The bankruptcy rate is regressed on the debt-income ratio, unemployment rate, divorce rate, and a dummy variable for the new code. The estimates are corrected for autocorrelation, but Durbin-Watson statistics are not reported. The code dummy is statistically insigni®cant, leading them to conclude that ``the enactment of the Bankruptcy Code in 1978 did not have an appreciable impact on the number of consumer bankruptcy cases ®led'' (Bhandari and Weiss, 1993, p. 8). However, they failed to adjust the data for reporting changes due to joint petitions and did not test for stationarity of the data series.

(Domowitz and Eovaldi, 1993, p. 822). Therefore, in contrast to earlier studies, Domowitz and Eovaldi concluded that the new code had no impact on consumer bankruptcies. Rather, their study suggests that economic and social conditions after 1980±1981 were responsible for a continued rise in bankruptcy ®lings and rates or that any effects of the new code were temporary in nature. However, less than half of the explanatory variables were statistically signi®cant, and they did not examine the data for stationarity.

With the exception of the study by Boyes and Faith, all previous researchers relied on structural econometric models to estimate the impact of the 1978 act. Various combinations of variables were tried with differing degrees of success. Simple dummy variables were used to represent possibly complex effects of the new act. While all studies attempted to correct the estimates for ®rst-order autocorrelation, insuf®cient attention is paid to the stochastic properties of the data and seasonality in quarterly data series. None of the studies using quarterly data conducted tests for unit roots or fourth-order autocorrelation. Except for the GAO study and Domowitz and Eovaldi, no attention was paid to the effect of joint petitions on bankruptcy data series. Further, none of the previous studies directly tested for temporary versus permanent effects of the act. The remainder of this paper examines the data on quarterly consumer ®lings and rates using an ARIMA intervention model. First, the paper develops a formal model of a policy intervention. Following Domowitz and Eovaldi, the data are adjusted for joint petitions. Tests are conducted for seasonal and nonseasonal unit roots. Empirical results are presented ®rst for the preintervention period, and these estimates are used for short- and long-term forecasting for the period after 1979:3. A substantial change in the model structure is indicated by the forecasts. The ARIMA model then is expanded to include intervention terms, and the model is re-estimated using the sample period 1960:3 to 1995:4. Tests are conducted for both temporary and permanent effects of the act. The ®nal model is used to measure the net impact of the 1978 act relative to the pre-act period.

3. ARIMA intervention model

Consider the following dynamic regression model involving time-series data on a realization, or outcome, in level form denoted byYt:

YtˆC‡n…B†It‡Nt tˆ1;. . .;T …1†

whereCis a constant term,n…B†is a lag polynomial of possibly in®nite order, Bis the backshift operator,I_t is a deterministic binary indicator (dummy) variable, andN_t is the stochastic disturbance, which is assumed to be autocorrelated.3The speci®cation ofNis discussed ®rst, followed by I, and ®nally n…B†. To model the disturbance term, let Dd

represent the d-order difference operator, where Ddˆ …1ÿB†d and Bd_Y

tˆYtÿd. Let

y_tˆ …1ÿB†d…1ÿBs_†D

Y_tˆDdD_sDY_trepresent a data series that has been differencedd -times nonseasonally andD-times seasonally. Letf…B†represent ap-order autoregressive process, or AR…p†, such that f…B† ˆ …1ÿf₁Bÿf₂B2_{ÿ ÿf}

pBp†. Finally,

y…B† ˆ …1ÿy1Bÿy2B2ÿ ÿyqBq†represents aq-order moving average process, or

N_tˆ y…B†y…B s_†

f…B†f…Bs_†Dd_D sD

a_t …2†

wherea_t is a white-noise error term, which is independently and identically distributed with 0 mean and constant variance,a_t*NID…0;s2

0†, and is independent of It (Box and

Jenkins, 1976, p. 305; Enders, 1995, p. 113). The error term represents the random shock component ofN_tthat cannot be predicted from the ARIMA process.

The dummy variable in (1) can be used to represent two basic forms of intervention. First, a pulse or temporary intervention lasting for only one period can be represented by a one-time dummy variable (e.g.,tˆ1979:4):

I_tˆ0 t6ˆi …3†

ˆ1 tˆi

As discussed already, temporary effects of a legal intervention might occur in the preintervention period if there was anticipation of the change. Second, the dummy can represent a step or permanent intervention, beginning at observationt(e.g.,t1979:4):

I_tˆ0 t5i …4†

ˆ1 ti

As analyzed empirically next, the effects of the 1978 act could be temporary or permanent or some combination of temporary and permanent interventions. Further, the lag polynomialn…B†, or impulse-response transfer function, allowsIto in¯uenceYvia a distributed lag. The approach followed in intervention-transfer function modeling is to writen…B†as a rational distributed lag, orn…B† ˆo…B†=d…B†, where the numerator and denominator polynomials, respectively, are de®ned by

o…B† ˆo₀ÿo₁Bÿ ÿo_kBh …5†

d…B† ˆ1ÿd1Bÿ ÿdrBr …6†

where all the roots ofo…B†andd…B†are assumed to be less that unity. In (5), the purpose of theh-order polynomial inI_tis to capture patterned steps or pulses due to the intervention, while in (6) ther-order polynomial inY_tcaptures decay-adjustment patterns.

Substituting for eqs. (2), (5), and (6) in eq. (1) and rearranging terms yields

DdDD_sY_tˆC₀‡o…B†

d…B†D d

DD_sI_t‡ y…B†y…B s_†

f…B†f…Bs_†at …7†

DdDD_sY_tˆC₁‡ o0B b

…1ÿd1B†

DdDD_sI_t‡ y…B†y…B s_†

f…B†f…Bs_†at …8†

whereC1is a constant that captures any deterministic trend in the data,o0is the impact or

level-change parameter,d1is the slope or rate-of-adjustment parameter, andBbcaptures a

delay or ``dead time'' ofbperiods before the intervention begins to affectYt.

In summary, intervention models generalize the univariate Box-Jenkins methodology by allowing the time path of the dependent variable to be in¯uenced by the time path of the intervention variables (Enders, 1995). In contrast to the simple dummy variables used in previous studies, the policy intervention need not occur as a pure jump or step; rather, there can be a gradual adjustment to the change. If It represents a permanent step

intervention, theno₀40 andd₁ˆ0. If there is decay or adjustment to the intervention, stability requires that 05 d₁ 1, which is the Koyck distributed-lag model. In this context, o₀ captures the initial impact of the intervention and the long-run asymptotic change is given by o₀…1ÿd₁B†. Similar interpretations are possible for pulse-type interventions, except that the long-run change is expected to be 0. Tests of permanent versus temporary interventions are possible, by using alternative forms of I_t and signi®cance tests ono₀andd₁. Also, by interacting the distributed lag term with a dummy, it can be restricted to affect the outcome only in the postintervention period. This paper tests for temporary interventions for each quarter during 1979:1 to 1980:4 and for permanent changes beginning in the quarter 1980:1 or, alternatively, the quarter 1985:1.

4. Data, variables, and unit root tests

4.1. Quarterly bankruptcy data

Quarterly data on bankruptcy petitions are collected by the Administrative Of®ce of the U.S. Courts (AOC) and published in table F-2 in the AOC'sBankruptcy Statistical Tables

because the analysis that follows uses logged ®rst-differences (quarterly growth rates), a constant adjustment of 14% affects the differenced value ofonlythe ®rst quarter of ®lings under the new code; that is, 1979:4. The results reported have are not affected in any important way by the data adjustment procedure employed in this study, and the model estimates using a 20% adjustment yielded similar results.

4.2. Variables and descriptive statistics

Let the log level of the number of bankruptcies be denoted by BANK and let the log of the per capita rate be denoted by RATE, where time subscripts are deleted for simplicity. The ®rst-differenced versions of these series are given byD(BANK) and D(RATE). Also, let

DdDD_s (BANK) andDdDD_s (RATE) represent the logged data that have been differencedd

-Table 1. Descriptive statistics

Series/Time Period Mean Std. Deviation Maximum Minimum

Total bankruptcies

1960:3±1995:4 95,255 72,987 266,729 29,373

Period 1 43,306 6,681 61,260 29,373

Period 2 156,794* 67,752 266,729 56,148

Per capita rate

1960:3±1995:4 59.155 36.300 147.095 26.426

Period 1 33.697 4.027 43.868 26.426

Period 2 89.312* 34.357 147.095 36.706

BANK

1960:3±1995:4 11.213 0.684 12.494 10.287

Period 1 10.664 0.155 11.023 10.287

Period 2 11.863* 0.459 12.494 10.936

RATE

1960:3±1995:4 3.924 0.535 4.991 3.274

Period 1 3.510 0.118 3.781 3.274

Period 2 4.414* 0.404 4.991 3.603

D(BANK)

1960:3±1995:4 0.016 0.065 0.213 ÿ0.156

Period 1 0.009 0.071 0.181 ÿ0.156

Period 2 0.023 0.058 0.213 ÿ0.085

D(RATE)

1960:3±1995:4 0.012 0.065 0.208 ÿ0.161

Period 1 0.005 0.071 0.178 ÿ0.161

Period 2 0.020 0.057 0.208 ÿ0.089

times nonseasonally andD-times seasonally. Figure 1 shows the level and log-level data for the number of bankruptcies and the ®ling rate per capita for the period 1960:3 to 1997:4. These graphs indicate that the trends for the number of petitions and per capita rates are similar. The data were ®rst-differenced in log form to obtain a data series that might be stationary in mean and variance. The differenced data in the bottom panels indicate several outliers or pulses at various points in time, and it is not obvious from these data whether the effect of the new code was a temporary or permanent increase in the number of petitions and ®ling rates. It is possible that the effect of the new code was temporary, with an initial negative pulse during early 1979 as attorneys anticipated the new law, then positive pulses after 1979:3 as they took advantage of the code. Table 1 shows descriptive statistics for the data broken into two subperiods, before and after 1979:4, with tests for statistical differences between the means. These preliminary tests suggest a structural change after 1979:4 in the levels and log-levels data, since the period 1 means are smaller than period 2 means. However, the mean differences for the data in logged®rst-differences, while substantial, are not statistically signi®cant.

4.3. Unit root tests

The data series are ®rst tested for stationarity; that is, do the data series contain one or more unit roots? It generally is inappropriate to apply classical regression procedures to data series that contain one or more unit roots, but no previous time series study of bankruptcy rates has considered this issue. To distinguish between seasonal and nonseasonal unit roots, the augmented Dickey-Fuller (ADF) test must be modi®ed. For seasonal unit roots, the HEGY test was used (Hylleberg et al., 1990). Following a ``test-down'' procedure, the HEGY regression model was estimated with a constant term, time trend, and three quarterly seasonal dummies (Enders, 1995, p. 227). To ensure that the residuals are white noise, lagged dependent variables also were included, starting with eight lags. The model then was simpli®ed to re¯ect the statistical signi®cance of these various terms. Table 2 displays the results of the HEGY test. The results reject the presence of seasonal unit roots at any frequency and uniformly indicate the presence of a 0-frequency, or nonseasonal, unit root. Table 3 displays the results of the standard ADF tests on the data in log levels and

Table 2. HEGY seasonal unit root test results, 1960:3±1995:4

Dependent Test p1ˆ0 p2ˆ0 p3ˆp4ˆ0 Q(12)-Statistic

Variable Version Lags t-Statistic t-Statistic F-Statistic (p-Value)

D1_s(BANK) C, T, D 1 ÿ2.658 4.101* 22.904* 7.576

(0.817)

D1s(RATE) C, T, D 1 ÿ2.518 4.108* 23.050* 7.903

(0.793)

Notes:HEGY Test: Nonseasonal unit root,p1ˆ0, semiannual unit root,p2ˆ0, and annual (i.e., quarterly) unit

root,p3ˆp4ˆ0 Notation: Cˆconstant; Tˆtime trend; Dˆseasonal dummies. Asterisk indicates statistically

the ®rst-difference of these data. The ADF test results indicate that the logged data series are I(1) and the logged ®rst-differences are I(0).4 Hence, the empirical analysis that follows is carried out using the logged ®rst-differences of the data.

5. Preintervention ARIMA analysis

5.1. Model identi®cation

Prior to estimation of the intervention model, I identi®ed and estimated an ARIMA model without the intervention term. This step is necessary, because the basic model structure is assumed to be invariant to the intervention. In general, identi®cation should be carried out using stationary data for the preintervention period, provided this is the longest data interval (Enders, 1995, p. 274). This study includes 77 preintervention observations and 65 postintervention observations, so the former period is employed. Inspection of the sample autocorrelation (AC) and partial autocorrelation (PAC) functions revealed a strong seasonal pattern. The AC correlogram for D(BANK) had prominent spikes at quarterly intervals, beginning at the fourth lag…ACˆ0:494†. The PAC at the fourth lag also was large (0.479). This pattern suggests a fourth-order seasonal autoregressive process. The ACs for the ®rst and ®fth lags were both smaller (ÿ0.025 and ÿ0.179) and the second and sixth lags were larger (ÿ0.162 and ÿ0.306). The third and seventh lags were smaller (ÿ0.073 and ÿ0.160). This AC pattern repeats itself, with damping. The PAC values tend to mirror the AC values (e.g., PACˆ ÿ0:025, ÿ0.163, and ÿ0.084 for the ®rst three lags). This dual pattern suggests a mixed stochastic, or ARMA, process, possibly involving second-order terms. The AC and PAC correlograms for theD(RATE) series are very similar to those forD(BANK).

5.2. Estimation

Based on these AC and PAC patterns, three tentative ARIMA models were estimated. Table 4 shows the empirical results, where the coef®cient values are reported using computer notation; hence, AR(1) is a ®rst-order nonseasonal autoregressive term, MA(1) is a ®rst-order nonseasonal moving average term, SAR(4) is a ®rst-order multiplicative seasonal autoregressive term, and so forth. For model selection, the Akaike information

Table 3. ADF unit root test results, 1960:3±1995:4

Dependent Variable Test Version Lags t-Statistic ADF 1% Critical Value

BANK C, T 6 ÿ1.750 ÿ4.028

D(BANK) C 5 ÿ4.688* ÿ3.480

BANK C, T 6 ÿ1.651 ÿ4.028

D(BANK) C 5 ÿ4.655* ÿ3.480

criterion (AIC) is employed and smaller values are better. For model evaluation, diagnostics are reported for (1) Ljung-BoxQ-statistic at 24 lags for the null hypothesis of no autocorrelation, (2) Jarque-Bera (J-B)w2_{-statistic for normally distributed residuals, (3)}

Breusch-Godfrey (B-G) F-statistic for no autocorrelation, and (4) Engles's ARCH F -statistic for autoregressive conditional homoscedasticity. Thep-values for the diagnostics are reported in parentheses (lowp-values imply rejection of the null), and the B-G and ARCH tests are conducted using four- and one-®tted terms, respectively. Also reported are the residual standard deviation (SEE), and the maximum absolute residual autocorrelation (max AC), and its critical value. In all cases, the estimated models satisfy the stability conditions of stationarity for the autoregressive coef®cients and invertibility for the moving average coef®cients. The results in table 4 indicate that the best model by most

Table 4. Preintervention ARIMA estimates, 1960:3±1979:3

D(BANK) D(RATE)

(1) (2) (3) (4) (5) (6)

AR(1) ÿ0.454 Ð Ð ÿ0.435 Ð Ð

(1.830) (0.838)

AR(2) 0.557 0.295 Ð 0.458 0.294 Ð

(2.405) (2.321) (0.973) (2.321)

MA(1) 0.694 0.038 Ð 0.568 0.034 Ð

(2.631) (0.311) (1.025) (0.276)

MA(2) ÿ0.418 Ð 0.362 ÿ0.309 Ð 0.364

(1.316) (3.463) (0.612) (3.511)

SAR(4) 0.496 0.919 0.917 0.548 0.918 0.916

(5.750) (29.823) (36.902) (5.049) (29.439) (36.874)

SMA(4) Ð ÿ0.636 ÿ0.542 Ð ÿ0.633 ÿ0.542

(4.978) (4.549) (4.925) (4.556)

SMA(8) Ð ÿ0.281 ÿ0.365 Ð ÿ0.284 ÿ0.366

(2.310) (3.418) (2.333) (3.429)

AIC ÿ2.867 ÿ2.944 ÿ2.994 ÿ2.743 ÿ2.946 ÿ2.992

SEE 0.056 0.054 0.053 0.059 0.054 0.053

AC max.a _{0.220 0.187 0.198 0.215 0.185 0.199}

Q(24) 25.783 18.464 18.143 22.898 18.331 18.206

(0.136) (0.492) (0.578) (0.242) (0.500) (0.574)

J-B 0.796 1.685 0.940 5.655 1.713 0.851

(0.672) (0.431) (0.625) (0.059) (0.425) (0.653)

B-G 2.814 0.103 0.163 0.568 0.092 0.166

(0.033) (0.981) (0.956) (0.687) (0.985) (0.955)

ARCH 0.848 0.114 0.001 1.263 0.119 0.002

(0.360) (0.737) (0.996) (0.265) (0.731) (0.969)

Notes: T-statistics in parentheses for coef®cients andp-values for diagnostics; adjusted sample sizeˆ70 or 72.

a_{Largest absolute residual autocorrelation, with a critical value of 0.234 for signi®cance at the 0.05 level.}

AICˆAkaike information criterion for goodness of ®t; SEEˆstandard error of estimate; Q(24)ˆLjunq-Box Q-statistic for autocorrelation with 24 lags; J-BˆJarque-Beraw2_{-statistic for normally distributed residuals;}

evaluation criteria is an ARIMA…0;1;2†6…1;0;2†process, which are regressions (3) and (6). The residuals are of high quality using any of the diagnostics. The constant term never was signi®cant and has been excluded from the model.

5.3. Tests for temporary effects and forecasts

Next, the preintervention model was re-estimated for each of the quarters from 1979:1 to 1979:3, incorporating individual pulse dummies. This procedure is a test of anticipation by attorneys and debtors of the advantages of the new code, which took effect in October 1979. The expected coef®cient signs are negative, but none of the estimated coef®cients was statistically signi®cant and only one had the expected sign. This result also is consistent with the residual pattern for this time interval. As a second test, the preintervention model was used to forecast the values for BANK for 1979:4 to 1981:4. The preintervention model underpredicted the immediate postintervention data, and the mean absolute percent error (MAPE) was 11%. This result also suggests a change in the underlying relationship. Last, I used the preintervention model to forecast the values for BANK for 1979:4 to 1995:4 (results available on request). Using dynamic forecasts, the model underpredicted total bankruptcies by 19% in 1985:4, 62% in 1990:4, and 67% in 1995:4. These estimates strongly indicate a change in the coef®cient values or model structure after 1979:4.

6. Intervention analysis of the Bankruptcy Reform Act

6.1. Model estimates

The ARIMA intervention model given by eq. (8) was estimated for the period 1960:3 to 1995:4. Table 5 shows the results forD(BANK) andD(RATE). First, regressions (1) and (4) test for temporary interventions in 1979:4 and 1980:1, respectively, by using two pulse dummies, D794 and D801.5 Both the coef®cients are statistically signi®cant, but the negative signs are contrary to expectations. Second, the pulse dummies are replaced by a permanent step-type dummy, D80, beginning in 1980:1 and extending through the remainder of the sample period. This allows for one quarter of dead time, based on the results for D794. The results for this intervention are shown by regressions (2) and (5) in table 5. These results indicate that the new code had a permanent positive impact on the number of petitions and the per capita rate.

indicate high-quality residuals. As an additional speci®cation test, Harvey (1993, p. 163) stresses that attention must be paid to the residuals immediately after the intervention and, for this purpose, Harvey and Durbin (1986) suggest a Chow-type speci®cation test based on the sum of squares of the generalized recursive residuals. Their test was applied by ®rst ®tting the ARIMA model to the sample 1960:3 to 1980:4, with and without the intervention terms. Forecasts were prepared for the immediate postintervention data for the 4-, 8-, 12-, and 16-quarters after 1980:1, both with and without updating of the model parameter estimates. The tests indicated that the model without the intervention terms was misspeci®ed for 1980:1 to 1980:4, but the intervention model was never misspeci®ed. Hence, regressions (3) and (6) in table 5 are the ®nal model estimates.

Table 5. ARIMA intervention estimates, 1960:3±1995:4

D(BANK) D(RATE)

(1) (2) (3) (4) (5) (6)

MA(2) 0.361 0.227 0.190 0.358 0.225 0.191

(4.302) (2.600) (2.151) (4.269) (2.580) (2.155)

SAR(4) 0.941 0.935 0.943 0.940 0.933 0.942

(45.834) (34.461) (37.722) (45.466) (33.893) (37.160)

SMA(4) ÿ0.505 ÿ0.578 ÿ0.650 ÿ0.506 ÿ0.578 ÿ0.649

(5.508) (6.181) (6.969) (5.527) (6.178) (6.947)

SMA(8) ÿ0.294 ÿ0.187 ÿ0.129 ÿ0.295 ÿ0.188 ÿ0.130

(3.451) (2.137) (1.474) (3.454) (2.145) (1.486)

D(D794) ÿ0.158 Ð Ð ÿ0.158 Ð Ð

(4.712) (4.711)

D(D801) ÿ0.071 Ð Ð ÿ0.071 Ð Ð

(2.105) (2.107)

D(D80) Ð 0.161 0.187 Ð 0.160 0.186

(3.419) (3.968) (3.410) (3.952)

D…BANK…ÿ1††D80 Ð Ð 0.395 Ð Ð Ð

(3.441)

D…RATE…ÿ1††D80 Ð Ð Ð Ð Ð 0.391

(3.412)

AIC ÿ3.163 ÿ3.113 ÿ3.183 ÿ3.165 ÿ3.114 ÿ3.183

SEE 0.049 0.050 0.048 0.049 0.050 0.048

AC max.a _{0.188 0.178 0.163 0.189 0.205 0.162}

Q(24) 38.029 30.696 22.322 38.028 30.679 22.250

(0.009) (0.059) (0.323) (0.009) (0.060) (0.327)

J-B 1.825 9.574 4.773 1.841 9.506 4.784

(0.402) (0.008) (0.091) (0.398) (0.009) (0.091)

B-G 1.874 1.659 1.078 1.843 1.637 1.086

(0.119) (0.164) (0.370) (0.125) (0.169) (0.366)

ARCH 0.066 0.049 0.227 0.051 0.074 0.187

(0.798) (0.825) (0.634) (0.821) (0.786) (0.666)

6.2. Interpretation of the results

The estimated coef®cient for D80,o0, is the change in the log level in 1980:1. The antilog

transformation ofo0is the ratio of the postintervention series level to the preintervention

series level (McCleary and Hay, 1980, p. 174). This ratio can be expressed as the percent change in the expected value due to the intervention, which is given by…^eo0ÿ1†6100.

The asymptotic change in the log level is given by o₀=…1ÿd₁†, which also can be transformed to a ratio and expressed as a percent change. Using regression (3) from table 5, the intervention impact is a log change of 0.187, or an increase of 20.6% in the number of bankruptcies. The asymptotic change is 0.309, or an increase of 36.2%.6For per capita rates, the impact and asymptotic increases are 20.4 and 35.7%, respectively. These values donot mean that bankruptcies are 36% higher each year after 1979 or that 36% of all bankruptcies are due to the 1978 act. Rather, to evaluate the asymptotic change, it must be compared to an actual value during the preintervention period (McCleary and Hay, 1980, p. 185). For this purpose, I use the number of bankruptcies and per capita rate for the year 1979, which were approximately 200,000 and 129, respectively. Hence, the isolated or partial effect of the 1978 act was an increase of about 72,400 bankruptcies per year and a rate increase of 46 per 100,000 adults. These changes are greater than 0, but they account for only a modest portion of the total change that have occurred since 1979. For example, during the period 1979±1995, the number of bankruptcies rose from 200,000 per year to 875,000 per year, or a change of 675,000. During the same period, the rate of bankruptcy rose from about 129 to 467, or a change of 338. Expressed in percentages, the 1978 act accounts for 10.7% of the change in petitions over this period and 13.6% of the per capita rate increase.

6.3. Postsample forecasts

As a ®nal test of the intervention model, regression (3) in table 5 was used to forecast the number of bankruptcies for two periods: ®rst, the early intervention period of 1979:4 to 1981:4 and, second, the postsample period of 1996:1 to 1997:4. Using both dynamic and static forecasts, the results are presented in table 6. Based on the MAPE values, the intervention model forecasts are superior to those prepared using the preintervention model (discussed earlier). The MAPE is 5.8% compared to 11.0% for the former model. For the period 1996:1 to 1997:4, the intervention model always underpredicts using dynamic forecasts and the MAPE is 10.3%. However, this result also is superior to an ARIMA model that omits the intervention terms. The static (one-period) forecast has a MAPE of 2.5% and generally underpredicts the actual values.

7. Summary and conclusions

are estimated to be 36% higher relative to the levels experienced in 1979. This estimate improves on recent studies by Bhandari and Weiss (1993) and Domowitz and Eovaldi (1993), which reported that the 1978 act has no effect on consumer bankruptcies. In contrast to these studies, my estimates are based on an ARIMA model that accounts for the stochastic process generating the data and was estimated using a stationary data series. Further, extensive regression diagnostics are obtained for the ARIMA models. Unlike recent studies, statistical tests were conducted for both temporary and permanent effects of the act and, since bankruptcy planning takes time, my estimates allowed for a gradual adjustment to the law. Also, I accounted for the change in joint petitions permitted by the new Bankruptcy Code, and the model estimates were used to obtain forecasts of recent bankruptcy ®lings. Last, based on several changes in the model speci®cation, the intervention estimates were robust.

Several caveats are in order for the results in this paper and related empirical studies. First, bankruptcy laws are complex. The Bankruptcy Reform Act and amendments made numerous changes that both encouraged and discouraged bankruptcy ®lings. The results

Table 6. Forecast evaluation of the ARIMA model: Total bankruptcies

Dynamic Static

Table 5. Reg. 3 Table 5. Reg. 3

Quarter Actual Forecast Error Forecast Error

1979:4 49,253 52,604 3,351 52,604 3,351

1980:1 59,638 63,855 4,217 59,787 149

1980:2 73,819 73,249 ÿ570 67,559 ÿ6,260

1980:3 76,612 78,662 2,050 79,235 2,623

1980:4 77,526 81,079 3,553 78,774 1,248

1981:1 77,931 82,088 4,157 77,932 1

1981:2 80,846 86,208 5,362 83,432 2,586

1981:3 79,505 85,572 6,067 79,449 ÿ56

1981:4 77,578 86,102 8,524 78,770 1,192

1996:1 252,761 242,035 ÿ10,726 242,035 ÿ10,726

1996:2 283,170 263,244 ÿ19,926 274,910 ÿ8,260

1996:3 290,111 265,092 ÿ25,019 287,523 ÿ2,588

1996:4 298,244 273,259 ÿ24,985 300,740 2,496

1997:1 321,242 281,987 ÿ39,255 312,239 ÿ9,003

1997:2 353,177 300,844 ÿ52,333 345,162 ÿ8,015

1997:3 340,059 301,671 ÿ38,388 357,872 17,813

1997:4 347,685 301,373 ÿ46,312 349,942 2,257

MAE

reported here show only the net impact of these changes, but it is important to examine the separate effects of particular provisions of the law. Cross-sectional studies are of considerable value in this respect (see White, 1987±1988; Buckley and Brinig, 1998; Nelson, 1999). Second, legal changes alter economic incentives in many ways. For example, advertising by bankruptcy lawyers has increased in recent years, and this also may have affected the level and trend of bankruptcy petitions. However, the results in this study suggest that the impact of the 1978 act was concentrated in 1980±1981; that is, the 1980:1 impact was 20.6% and the asymptotic change of 36.2%. This result is consistent with several early studies. It seems unlikely that attorney advertising would have such a large impact in 1980:1 or shortly thereafter. Further, the constant term always was insigni®cant, indicating the absence of deterministic trends as might be caused by attorney advertising. Third, the rate of bankruptcies increased from about 200,000 in 1979 to 875,000 in 1995, a change of 675,000 or an increase of 338%. However, the 1978 act accounts for only 10.7% of this change. This suggests that other economic, ®nancial, legal, and social factors played an important role in the total rise of the number of bankruptcies. However, the estimates presented here are conservative in that induced changes from the act are re¯ected in changes in the coef®cient values, given the basic stochastic structure of the data.

Acknowledgments

I thank Ed Coulson, Norm Swanson, and two anonymous referees for helpful comments on earlier drafts. The usual caveats apply.

Notes

1. Four distinct issues are contained in the empirical literature on nonbusiness bankruptcies: ®rst, the general impact of the 1978 act, which is the subject of the paper, using both pre- and post-act data; second, given post-act data on petitions, the cross-state determinates of bankruptcy rates as examined empirically in White (1987±1988), Buckley and Brinig (1998), and Nelson (1999); third, the ability-to-pay issue (that is, whether bankrupts could repay a greater portion of their debts), as analyzed in Sullivan, Warren and Westbrook, (1989); Barron and Staten, 1997; and U.S. GAO, 1998); and fourth, the impact of bankruptcies on credit markets, see Gropp, Scholz, and White (1997).

2. The 1984 amendments discouraged the courts from approving token repayments plans under chapter 13. For contrasting views on bankruptcy policy and the bankcard industry, see Black and Herbert (1985), Ausubel (1997), and Posner (1997).

3. In addition to the seminal work of Box and Jenkins (1976, Chs. 10±11), intervention-transfer function analysis is discussed in Mills (1990), Pankratz (1991), Pindyck and Rubinfeld (1991), and Enders (1995). For discussion of the constant term, see Vandaele (1983). For an economic interpretation of mixed ARIMA models, see Granger and Newbold (1986).

4. This result was con®rmed by the Philips-Perron unit root test. I also applied the HEGY and standard ADF tests to the two subperiods for each of the data series. Qualitatively, the results of these tests are the same as for the entire sample, except for weak evidence of a semiannual unit root during 1960:3 to 1979:3. Given the low power of unit root tests, the results for the full sample are preferred.

1980:2 to 1980:4 were insigni®cant. Tests for a permanent intervention beginning in 1985:1 were insigni®cant. All the ®nal AR terms in tables 4 and 5 are signi®cantly less than 1.

6. For alternative speci®cations, the model was over®tted by second-differencing the data and estimating an ARIMA…0;2;1†6…1;0;1†model. The results were an initial impact of 25.0% and an asymptotic change of 49.3%. Also, the data were fourth-differenced and an ARIMA…0;1;2†6…1;1;1†model was estimated. The results were an initial impact of 20.8% and an asymptotic change of 32.2%. While the results in table 6 are preferred, these alternative estimates provide additional support for the measured impact of the new code.

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