Data and Summary Statistics

In our empirical test, equity prices are collected from CRSP (the Center for Research in Security Prices) and the financial statement information is retrieved from Compustat. The sampling period of the firms is from January 1986 to December 2005, while the quarterly accounting information is from 1984 to 2005 since some firms under financial distress stop filing financial reports a long time before they are delisted from the stock exchanges. The accounting information we use in our study is quarterly reports from CRSP/Compustat Merged (CCM) Database. This is to obtain the most updated debt levels and payout information, especially for those defaulted firms. In our empirical test, we consider only ordinary common shares (first digit of CRSP share type code 1) and exclude certificates, American trust components, and ADRs. Our final sample covers a 20-year period from 1986 to 2005 and includes 15,607 companies.

In our empirical test, we adopt two different definitions of default:

Definition I The broad definition of bankruptcy by Brockman and Turtle (2003), which includes firms that are delisted because of bankruptcy, liquidation, or poor performance. A firm is considered performance delisted, named by Brockman and Turtle, if it is given a CRSP delisting code of 400, or 550 to 585. Note that there are still other delisted firms due to mergers, exchanges, or being dropped by the exchange for other reasons, and they are considered as survival firms.

Definition II This definition of bankruptcy is similar to that adopted by Chen, Hu, and Pan (2006). Default firms are collected from the BankruptcyData.com database, which includes over 2,500 public and major company filings dating back to 1986. We next match the performance delisted firms with those samples collected from BankruptcyData.com, and add back the liquidated firms (with delisting code 400), to be our default group. All remaining firms are classified as survival firms. Note that one difference between our classification and Chen, Hu, and Pan (2006) is that some of the companies that filed bankruptcy petitions but were later acquired by (merged with) other companies (Delisting code: 200) are classified into survival group.

Table 3 Summary of Model Key Features

Model Asset Value Distribution Barrier Interest Rate Recovery Bankruptcy Cost

Merton Log-normal None Constant Random No

Brockman and Turtle (Flat Barrier) Log-normal Flat Constant Random No Black and Cox Log-normal Exponential Constant Random No

Leland Log-normal Flat* Constant Fixed Yes

* The character of endogenous flat barrier is different from the exogenously flat barrier. The endogenous barrier is derived endogenously from the optimal leverage decision, and its flat feature results from the stationary debt structure.

Table 4 Summary of Model Parameters

Model Asset Value Process Barrier

Related Bankruptcy

Cost Related Tax Shield

Related Other Parameters

Merton θ_V ={µ_V,g,σ_V}^# r,F

Brockman and Turtle (Flat Barrier) θ_V ={µ_V,g,σ_V}^# H r , F Black and Cox θ_V ={µ_V,g,σ_V} H(C),γ r,F Leland θ_V ={µ_V,g,σ_V}^# α _{T , C C} r

# The original Merton, Brockman and Turtle, and Leland models do not assume the asset payout, but they can be easily added into the models.

Before proceeding to the summary statistics of our final sampling firms, we first describe our sample selection criteria. First, companies with more than one share classes are excluded in our test. Second, since we also need accounting information in order to empirically test these models, firms without accounting information within two quarters going backward from the end of the estimation period are excluded. Thirdly, active firms (delisting code 100) during our sampling period while being delisted in 2006 are excluded. This is to ensure survival firms with delisting code 100 are financially healthy companies. Finally, to ensure adequate sample size for the MLE approach, we consider only those companies with over 252 days common share prices available.

Next, we report in Table 5 the main firm characteristics of our default samples in terms of market equity value, book leverage (total liabilities divided by asset value), and market leverage (total liabilities divided by market value of the firm). We can find that on average firms in default group are smaller and tend to have higher book and market leverage. In addition, the mean and median of book and market leverage of default group of default Definition II are higher than those of Definition I. This is because firms that delisted without filing Chapter 11 are considered as default firms in default Definition I, and as survival firms in Default definition II; such firms may not have debt levels as high as companies which filed Chapter 11. Finally, in Table 6, a summary of the default firms by industry and year is presented.

In the end of this section, we present our key inputs for the structural models. Determining the amount of debt for our empirical study is not an obvious matter. As opposed to the simplest approach, for example, by Brockman and Turtle (2003), to set the face value of debt equal to the total liabilities, we adopt the rough formula provided by Moody’s KMV — the value of current liabilities including short-term debt, plus half of the long-term debt. This formula is also adopted by some researchers such as Vassalou and Xing (2004).^xi

Secondly, the payout rategcaptures the payouts in the form of dividends, share repurchase, and bond coupons to stock holders and bondholders. To estimate the payout rate, we adopt the weighted average method similar to those by Eom, Helwege, and Huang (2004) and Ericsson, Reneby, and Wang (2006) as

) 1

( ) (

)

(Interest Expenses Total Liabilities ×Leverage+ Equity Payout ratio × −Leverage whereLeverage=Total Liabilities (Total Liabilities+Market EquityValue)

For the market value of equity, we chose the number of shares outstanding times market price per share on the day closest to the financial statement date. The equity payout rate is estimated as the total equity payout, which is the sum of cash dividends, preferred dividends, and purchase of common and preferred stock, divided by the total equity payout plus market value of equity.

Table 5 Summary Statistics of Sampling Firms Default Definition I

Group Number of firms Mean Median Maximum Minimum

Market Equity Value Survival 10729 1770.7762 173.0430 367495.1442 0.3016

Default 4878 58.1062 8.7146 36633.7544 0.0271

Book Leverage Survival 10729 0.5541 0.5500 4.0093 0.0008

Default 4878 0.7628 0.6880 203.0000 0.0003

Market Leverage Survival 10729 0.4321 0.3932 0.9961 0.0007

Default 4878 0.5188 0.5387 0.9997 0.0001

Default Definition II

Group Number of firms Mean Median Maximum Minimum

Market Equity Value Survival 14244 1340.6120 81.9271 367495.1442 0.0271

Default 1363 136.7769 23.4698 36633.7544 0.3356

Book Leverage Survival 14244 0.5996 0.5666 203.0000 0.0003

Default 1363 0.8253 0.7888 12.5273 0.0025

Market Leverage Survival 14244 0.4389 0.4058 0.9997 0.0001

Default 1363 0.6718 0.7577 0.9995 0.0024

Table 6 Number of the Default Firms by Industry and Year Default Definition I

SIC Code

Year Missing 0 1 2 3 4 5 6 7 8 9 Total

1986 4 1 62 21 73 8 27 11 27 9 0 243

1987 0 5 23 16 44 9 31 10 18 4 0 160

1988 0 1 26 22 53 11 31 10 40 13 0 207

1989 1 4 23 30 63 14 29 17 30 6 0 217

1990 0 1 19 22 86 16 33 21 29 10 0 237

1991 0 2 28 33 85 10 31 24 39 13 0 265

1992 0 2 53 26 84 16 45 31 38 22 0 317

1993 0 2 15 15 52 8 11 13 15 9 0 140

1994 0 0 20 13 52 12 20 19 25 8 2 171

1995 0 1 19 21 50 12 38 21 39 16 1 218

1996 0 0 7 20 42 10 33 12 17 11 2 154

1997 0 0 16 25 52 17 44 15 36 17 0 222

1998 0 2 36 45 97 25 61 35 64 32 2 399

1999 0 4 48 53 87 22 43 28 50 34 0 369

2000 0 0 10 34 71 26 50 28 53 26 0 298

2001 0 2 15 42 87 44 58 23 131 24 1 427

2002 0 0 14 31 87 45 23 31 94 17 0 342

2003 0 1 9 20 75 20 34 16 54 18 0 247

2004 0 0 3 13 23 7 16 20 20 4 0 106

2005 0 0 5 20 43 14 8 17 25 7 0 139

Total 5 28 451 522 1306 346 666 402 844 300 8 4878

SIC Code: 0: Agriculture, Forestry, and Fishing; 1: Mining and Construction; 2 and 3: Manufacturing; 4: Transportation, Communications, Electric, Gas, and Sanitary Service; 5: Wholesale Trade, and Retail Trade; 6: Finance, Insurance, and Real Estate; 7 and 8: Service; 9: Public Administration

Table 6 Number of the Default Firms by Industry and Year (Cont.) Default Definition II

SIC Code

Year Missing 0 1 2 3 4 5 6 7 8 9 Total

1986 1 0 5 3 11 3 4 2 3 1 0 33

1987 0 2 3 1 4 0 3 0 2 1 0 16

1988 0 0 3 1 4 6 7 1 0 0 0 22

1989 0 0 4 7 6 4 11 6 5 0 0 43

1990 0 0 3 3 12 4 8 7 2 1 0 40

1991 0 2 2 3 21 3 7 7 7 2 0 54

1992 0 1 5 2 10 6 13 7 3 5 0 52

1993 0 0 4 4 11 0 6 4 2 0 0 31

1994 0 0 2 4 14 3 5 3 4 2 2 39

1995 0 0 2 5 8 6 16 8 6 4 0 55

1996 0 0 5 6 7 3 16 2 2 0 0 41

1997 0 1 5 5 12 7 13 4 7 5 0 59

1998 0 1 6 13 28 7 20 12 13 11 1 112

1999 0 0 13 14 21 14 18 8 8 13 0 109

2000 0 0 6 17 28 15 30 12 21 13 0 142

2001 0 0 3 15 41 31 28 10 49 10 0 187

2002 0 0 6 9 33 27 11 12 23 8 0 129

2003 0 0 1 11 33 12 16 3 14 5 0 95

2004 0 0 2 7 7 3 8 5 7 0 0 39

2005 0 0 3 5 22 13 8 3 5 6 0 65

Total 1 7 83 135 333 167 248 116 183 87 3 1363

SIC Code: 0: Agriculture, Forestry, and Fishing; 1: Mining and Construction; 2 and 3: Manufacturing; 4: Transportation, Communications, Electric, Gas, and Sanitary Service; 5: Wholesale Trade, and Retail Trade; 6: Finance, Insurance, and Real Estate; 7 and 8: Service; 9: Public Administration

Thirdly, since the models in our study assume constant interest rate, one needs to feed in the appropriate interest rate for model estimation. The three month T-bill rate from the Federal Reserve website is chosen as the risk-free rate. However, the three month T-bill rate

fluctuated heavily; from a high of 9.45% in March 1989, it dropped to a low of 0.81% in June 2003, and then went back to 4.08% in the end of December 2005. Therefore, to assure the proper discount rate for each firm across a 20-year sampling period, interest rates are estimated as the average of 252 daily 3-month Constant Maturity Treasury (CMT) rates for each firm during the sampling period.

Finally, the Leland model needs debt coupons and we follow Ericsson, Reneby and Wang (2006) to set the average coupon as risk-free rate times total liabilities:

Rate Riskfree s

Liabilitie Total

Coupon= × . In addition, the Leland model considers tax deductibility as well as bankruptcy cost. We follow Eom, Helwege, and Huang (2004) and set the tax rate to 35% and financial distress cost as 51.31%. Furthermore, we also follow Leland (1998) and Ericsson, Reneby and Wang (2006) and set the tax rate to 20% as an alternative setting. This is to reflect personal tax advantages to equity returns which reduce the advantage of debt.