BANKRUPTCY AND MASS WITHDRAWAL 

MODELING IN PIMS 

October 1, 2019 

Advanced Analytical Consulting Group, Inc. 

Constantijn W.A. Panis, PhD 

213-784-6400 

stanpanis@aacg.com 

Karthik Padmanabhan, MS, MBA 

312-551-9001 

karpad@aacg.com 
 i 

SUMMARY 

The Pension Benefit Guaranty Corporation (PBGC) insures millions of participants in 

private defined benefit (DB) pension plans against loss of some or all benefits in case 

their plan is unable to pay benefits. The PBGC uses a stochastic modeling system, 

the Pension Insurance Modeling System (PIMS), to project its future expected claims. 

PIMS consists of a version for single-employer plans (SE-PIMS) and a version for 

multiemployer plans (ME-PIMS). 

The bankruptcy of the sponsor of a single-employer plan is an important trigger of 

plan failures, and thus of additional PBGC liabilities. Likewise, the mass withdrawal of 

all employers that participate in a multiemployer plan can cause or accelerate a 

plan’s insolvency. This report reviews bankruptcy aspects of SE-PIMS and mass 

withdrawal aspects of ME-PIMS. Our interim reports on these two components 

identified numerous topics for potential review; this report focuses on priority areas. 

For the bankruptcy aspects of SE-PIMS, we generally confirmed the PBGC’s current 

and updated models for predicting bankruptcies. We found that bankruptcy rates of 

private and public firms are roughly equal, as assumed by SE-PIMS. Some issues 

were identified with the stability of SE-PIMS’s future stochastic scenarios, but the 

distribution of bankruptcy probabilities—the key outcome—was remarkably stable. 

SE-PIMS assumes that the PBGC will recover, in bankruptcy proceedings, 5% of 

unfunded liabilities for both Chapter 11 reorganizations and Chapter 7 liquidations; 

we noted that historical recoveries tended to exceed 5% but found no compelling 

reason to adjust the recovery parameters. Finally, SE-PIMS assumes that a 

bankruptcy filing does not trigger a plan failure if the plan’s assets are 80% or more 

of its liabilities; we found little historical support for this assumption, but the 

available data were incomplete and preclude us from recommending a change. 

ME-PIMS predicts mass withdrawals through a complex set of equations involving 

numerous determinants. While the determinants plausibly relate to mass withdrawal 

decisions, we found no theoretical or empirical support for the model, except that the 

average predicted mass withdrawal rate is close to the historical rate. We analyzed 

withdrawals by individual employers, which ME-PIMS does not currently model. 

These withdrawals, which are concentrated in certain industries and poorly funded 

plans, are not insignificant and may warrant inclusion in ME-PIMS. ME-PIMS makes 

assumptions about the collectability of withdrawal liabilities; we attempted to 

validate those with historical collections, but were unable to because of data 

constraints. Finally, up until very recently, ME-PIMS simulated a subset of 

multiemployer plans; we explored potential issues with modeling the universe 

instead, and found the recent expansion of ME-PIMS to be sensible and scientifically 

sound. 
 ii 

CONTENTS 

Summary ........................................................................................................ i

1. Introduction ............................................................................................. 3

2. Bankruptcy Modeling in SE-PIMS ............................................................. 4

Overview.................................................................................................... 4

Integrity of the Bankruptcy Model Estimates ................................................... 5

The Current Model .................................................................................. 5

An Updated Model .................................................................................. 5

Bankruptcy Rates of Large Private Firms ........................................................ 7

Firms with 500 or More Employees ........................................................... 8

Firms with 5,000 or More Employees ........................................................ 9

Simulated Distributions of Key Variables ...................................................... 10

Simulated Macroeconomic Variables ....................................................... 10

Simulated Firm-Level Variables .............................................................. 13

Correlations between Macroeconomic and Firm-Level Variables .................. 21

Incomplete Stochastic Variation ............................................................. 22

Recovery Claims by Bankruptcy Type........................................................... 24

Chapter 7 versus Chapter 11 ................................................................. 24

Repeat Bankruptcies ............................................................................. 26

Assumptions Triggering Plan Termination in Bankruptcy ................................. 28

3. Mass Withdrawal Modeling in ME-PIMS .................................................. 31

Overview.................................................................................................. 31

Model Complexity ...................................................................................... 32

Withdrawals by Individual Contributing Employers ......................................... 35

Collectability of Withdrawal Liabilities ........................................................... 41

Modeling the Population Rather Than a Sample ............................................. 41

4. Conclusion .............................................................................................. 43

Disclaimer ................................................................................................... 44
 3 

1. INTRODUCTION 

In order to monitor the solvency of its insurance operations, the Policy, Research and 

Analysis Department (PRAD) of the Pension Benefit Guaranty Corporation (PBGC) 

developed a system of connected models—the Pension Insurance Modeling System 

(PIMS)—to forecast revenues, expenses, and related metrics. The PBGC contracted 

with Advanced Analytical Consulting Group, Inc. (AACG) to review bankruptcy 

aspects of the Single-Employer Pension Insurance Modeling System (SE-PIMS) and 

mass withdrawal aspects of its multiemployer counterpart, ME-PIMS. This document 

reports on our review of specific priority areas. 

In SE-PIMS, we evaluated five aspects related to the modeling of potential 

bankruptcies of defined benefit (DB) plans. They are: 

1. Review of the integrity of bankruptcy model estimates; 

2. Analysis of simulated distributions of key variables for reasonableness and 

appropriate correlations; 

3. Evaluation of whether bankruptcy rates of large private firms are similar to 

those of large public firms; 

4. Analysis of historical bankruptcy recovery rates under Chapter 7 and 11 

filings, and examine repeat bankruptcies; and 

5. Evaluation of the assumptions triggering plan termination in bankruptcy. 

In ME-PIMS, we evaluated four aspects related to the modeling of mass withdrawals 

of multiemployer plans. They are: 

1. Review of the current model for unnecessary complexity and potentially 

suggest an alternative; 

2. Investigation of whether withdrawals by individual contributing employers can 

be incorporated into ME-PIMS; 

3. Evaluation of assumptions on the collectability of withdrawal liabilities; and 

4. Identification of potential issues with modeling the entire population of 

multiemployer plans rather than a sample. 

Section 2 of this report addresses bankruptcy aspects in SE-PIMS. Section 3 

discusses mass withdrawal areas in ME-PIMS, and Section 4 concludes. 
 4 

2. BANKRUPTCY MODELING IN SE-PIMS 

Overview 

According to recent Form 5500 filings, roughly 25,000 firms sponsor a PBGC-insured 

single-employer DB plan. While the Form 5500 contains financial information about 

these DB plans, they contain very little information on financial metrics that can 

predict the risk of bankruptcy of the sponsoring firms. A small subset of sponsors—

mostly companies that have publicly traded equity or debt—publish their financial 

information in annual reports, corporate filings with the Securities and Exchange 

Commission (SEC), and other channels. Compustat culls from such sources and 

bundles financial records into a database. The PBGC merged that database with 

sources on bankruptcy filings, applied various inclusion criteria, and estimated a 

bankruptcy model. This process is reviewed below in the section on “Integrity of the 

Bankruptcy Model Estimates,” starting on page 5. 

SE-PIMS uses the bankruptcy model’s parameter estimates to simulate future 

bankruptcy probabilities. Ideally, it would simulate bankruptcy probabilities for all 

sponsors of PBGC-insured DB plans, but it lacks the required financial information on 

most plan sponsors. Instead, it uses scaled copies (“partners”) of firms for which 

financial information is available to represent firms without financial information. This 

approach implicitly assumes that small and private firms face approximately equal 

bankruptcy risks as large firms with publicly available financial records. This 

assumption is evaluated below in the section on “Bankruptcy Rates of Large Private 

Firms,” starting on page 7. 

The unit of observation in the bankruptcy component of SE-PIMS is a firm (DB plan 

sponsor). SE-PIMS simulates future values of assets, liabilities, sponsor bankruptcy 

filings, and other financial metrics for 1,434 firms (350 firms plus 1,084 partners). 

Financial metrics are a function of, among others, macroeconomic variables such as 

rates of return on stocks and bonds. SE-PIMS generates 5,000 stochastic scenarios 

for its key financial metrics—500 stochastic scenarios of macroeconomic variables, 

and 10 firm-specific scenarios for every macroeconomic scenario. The simulation 

horizon is 20 years, i.e., each scenario consists of 20 future annual values. We 

explore the simulated distributions, correlations, and time series properties in the 

section on “Simulated Distributions of Key Variables,” starting on page 10. 

For purposes of SE-PIMS, a bankruptcy is defined as the filing for protection under 

Chapter 7 or 11 of the U.S. Bankruptcy Code. By default, SE-PIMS assumes that the 

consequences for pension plans of a Chapter 7 liquidation are the same as for a 

Chapter 11 reorganization. That assumption is tested in the section on “Recovery 

Claims by Bankruptcy Type,” starting on page 24. 

Finally, the bankruptcy of a DB plan sponsor does not necessarily result in 

termination of the plan. SE-PIMS assumes that the plan will continue to fulfill its 

obligations despite a bankruptcy of its sponsor if assets cover 80% or more of 

liabilities. We evaluate that assumption in the section on “Assumptions Triggering 

Plan Termination in Bankruptcy,” starting on page 28. 
 5 

Integrity of the Bankruptcy Model Estimates 

The Current Model 

The bankruptcy model used in the current version of SE-PIMS is primarily based on 

Compustat data with annual corporate financial information, augmented with 

information on corporate bankruptcies from New Generation Research, Inc. (“New 

Generation Research”). The analysis took the following approach. 

 The sample was restricted to companies that sponsored a DB plan. 

 The analysis was restricted to bankruptcy filings in 1980 and later because 

the U.S. Bankruptcy Code underwent major changes in 1980. The most 

recent bankruptcy filings in the analysis date to 1998. 

 Companies were included only if they reported 500 or more employees in at 

least two consecutive years, and only starting with the two years in which 

they first met that criterion, even if their workforce later shrank below 500 

people. 

 The analysis does not incorporate repeat bankruptcies; records after the first 

bankruptcy since 1980 are excluded from the analysis. 

 Companies incorporated outside the United States are excluded from 

estimation. 

 Companies that are subsidiaries of other companies are excluded from the 

analysis. 

 A weighting scheme is applied to correct for the PBGC’s finding that records 

are disproportionately often missing when companies approach bankruptcy. 

 The model is a logistic regression model to explain the annual incidence of 

bankruptcies. 

AACG replicated the PBGC’s procedures and encountered a few issues, including the 

following: 

 The timing of bankruptcies was not always correct in the analysis file. For 

example, a company that (according to a manual search) filed for bankruptcy 

in 1986 was included as filing for bankruptcy in 1997. The erroneous timing 

may have affected parameter estimates because explanatory variables 

changed over time. For example, the workforce exceeded 6,000 people up to 

1984 and was reported as zero people during the 1990s. 

 The data contained gaps in companies’ time series that did not appear to be 

addressed by the weighting scheme. 

 The weighting scheme accounts for employment category, which was imputed 

if missing. Under certain circumstances, that imputation appeared to be 

incorrectly implemented. 

We did not attempt to quantify the implications of these issues. However, the next 

subsection suggests that the introduced biases was negligible. 

We confirmed that the bankruptcy model estimates were applied accurately to the 

2018 version of SE-PIMS. 

An Updated Model 

The current bankruptcy model was estimated on data from 1980 to 1998. During the 

subsequent 20 years, the average annual number of bankruptcy filings was lower 
 6 

than during the estimation period: the average annual number of corporate 

bankruptcy filings decreased from 61,640 in 1980–1998 to 36,056 in 1999–2018 

(Statistical Abstract of the United States, 1980–2011; Administrative Office of the 

U.S. Courts, 1997–2018).1

Given a potential concern that a model based on 1980–1998 data would overstate 

recent bankruptcy filings, we analyzed bankruptcy data through 2017. 

The PBGC provided us with Compustat data from 1988 through 2017, along with 

additional information on bankruptcy filings from New Generation Research, 

Research Insight, and a 2006 Corporate Tracker file. We merged the source files and 

prepared the data for estimation following the principles described in the previous 

section. The average annual bankruptcy probability, weighted to correct for nonrandom patterns of missing data, was 0.84% per year for 1988–2017, compared 

with 0.90% per year for 1980–1998 (based on the estimation sample of the current 

model). In other words, the long-term average bankruptcy rate among large DB 

sponsors has not changed much since 1980–1998, and any concern that the current 

bankruptcy model substantially overestimates bankruptcy risks appears to be 

misplaced. 

The similarity of bankruptcy rates in 1980–1998 and 1988–2017 stands in contrast 

to the steep decline in number of filings after 1998. Part of the explanation lies in the 

fact that the number of publicly listed companies has decreased markedly, from 

9,113 in 1997 to 5,734 in 2016.2 Also, the number of filings relates to all 

corporations, whereas the relevant bankruptcy rate applies to the small subset of 

firms in the bankruptcy analysis, namely large corporations that sponsor a DB plan 

and publish financial information. 

We emphasize that bankruptcy rates are volatile over time (Figure 1). The 

observation that the average 1980–1998 rate (0.90%) was close to the 1988–2017 

average (0.84%) should therefore be interpreted with caution. 

1

 Because of incomplete historical data on filings under Chapters 7 and 11, these 

numbers refer to all corporate filings, including those under Chapters 12 or 13. 

2

 “America’s Roster of Public Companies Is Shrinking Before Our Eyes,” Wall Street 

Journal, January 6, 2017. Available at https://www.wsj.com/articles/americasroster-of-public-companies-is-shrinking-before-our-eyes-1483545879. 
 7 

Figure 1. Weighted Bankruptcy Rates among Large DB Plan Sponsors, 

by Year (1988–2017) 

For comparison, the FY 2018 PBGC Projections Report (Table 4) documented an 

average bankruptcy probability of 0.5% during the simulation period. 

We estimated a logistic regression model of the probability of a bankruptcy based on 

the 1988–2017 data. The results are qualitatively similar to those estimated on 

1980–1998 data and used in the current SE-PIMS. All signs of estimates of 

parameters that the two specifications have in common are the same, and their 

statistical significance levels are very similar. Separately, we compared our estimates 

to those obtained by the PBGC, based on the same source data. The sample and 

results were very slightly different, presumably mostly because our algorithm to 

match data sources differs from the PBGC’s.3 For all practical purposes, we confirm 

the PBGC’s updated model. 

Bankruptcy Rates of Large Private Firms 

The bankruptcy model equation in SE-PIMS was estimated on data for firms (1) that 

sponsored one or more DB plans, (2) for which financial data were available, and (3) 

that employed 500 or more workers in at least two consecutive years. Large private 

firms typically lack published financial data and are thus excluded from the models 

3

 The AACG algorithm attempts to increase the match rate by using a normalized 

version of company names, in addition to the keys used by the PBGC (CUSIP, EIN, 

and Global Vantage Key). Our final sample consisted of 36,895 records, compared 

with 36,291 in the PBGC estimation sample. 

Average: 0.84%

0.0%

0.5%

1.0%

1.5%

2.0%

2.5% Rate of Bankruptcy Filing

1988 1993 1998 2003 2008 2013 2018

Year

Source: AACG calculations based on Compustat data augmented with bankruptcy information; see text.
 8 

used to estimate bankruptcy rates in SE-PIMS. We investigated whether large private 

firms have significantly different bankruptcy probabilities than public firms. 

Firms with 500 or More Employees 

First, we compared bankruptcy rates for public and private firms with 500 or more 

employees. Bankruptcy data were sourced from New Generation Research, an 

industry source on corporate bankruptcies. Around 2012, New Generation Research 

updated its data collection procedures for private companies that expanded the 

number of bankruptcies as well the amount of information recorded about the 

bankruptcy. This allowed us to estimate bankruptcy rates for large private 

companies, albeit for a recent time period only. 

In the case of a company with many subsidiaries, New Generation Research data 

contains records for the parent company and its subsidiaries. In these cases, we kept 

and used only one instance (with preference given to a public instance, if present) 

when calculating the bankruptcy rates.4 

As Figure 2 shows, the rates for large private firms are roughly in line with 

bankruptcy rates of large public firms.5

4

 For evaluation purposes, we kept and included all instances of bankruptcy records 

for a company and its subsidiaries and used it to calculate bankruptcy rates. The 

resulting bankruptcy rates were too high to be plausible. 

5

 The denominator used to calculate the private bankruptcy rate is obtained from a 

firm count maintained by the Census Bureau’s Business Dynamic Statistics. A firm is 

defined as “a business organization consisting of one or more domestic 

establishments that were specified under common ownership or control. The firm 

and the establishment are the same for single-establishment firms.” See 

https://www.census.gov/ces/dataproducts/bds/data.html. We subtracted the number 

of public companies (from Compustat) to obtain the number of private firms. 
 9 

Figure 2. Bankruptcy Rates: Private and Public Companies with 500 or More 

Employees (1981–2017) 

Firms with 5,000 or More Employees 

Next, we compared bankruptcy rates for public and private firms with 5,000 or more 

employees. As Figure 3 shows, the bankruptcy rates for very large private firms are 

very close to those for very large public firms. 

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017

Public Companies Private Companies

Sources: New Generation Research, Inc., Compustat, U.S. Census Bureau - Business Dynamics Statistics
 10 

Figure 3. Bankruptcy Rates: Private and Public Companies with 5,000 or 

More Employees (1981–2017) 

On the basis of the results discussed above, there is no need to have separate 

bankruptcy rate assumptions for plans sponsored by private employers. However, 

the available time series for private firms is short and we recommend this analysis 

be updated in a few years to ensure bankruptcy rates for large private and public 

companies do not diverge in the future. 

Simulated Distributions of Key Variables 

The unit of observation in the bankruptcy component of SE-PIMS is a firm (DB plan 

sponsor). SE-PIMS simulates future values of assets, liabilities, sponsor bankruptcy 

filings, and other financial metrics for 1,434 firms (350 firms plus 1,084 partners). 

Financial metrics are a function of, among others, macroeconomic variables such as 

rates of return on stocks and bonds. SE-PIMS generates 5,000 stochastic scenarios 

for its key financial metrics—500 stochastic scenarios of macroeconomic variables, 

and 10 firm-specific scenarios for every macroeconomic scenario. The simulation 

horizon is 20 years, i.e., each scenario consists of 20 future annual values. This 

section summarizes the distributions, correlations, and time series properties of 

simulated macroeconomic and firm-specific values. 

Simulated Macroeconomic Variables 

It is our understanding that only the 30-year Treasury yield and the rate of return on 

stocks are fully stochastic in the economic projections, and that all other values 

(such as inflation and rates of return on Treasury bonds, corporate bonds, and plan 

assets) are derived from those two variables. 

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017

Public Companies Private Companies

Sources: New Generation Research, Inc., Compustat, U.S. Census Bureau - Business Dynamics Statistics
 11 

Figure 4 shows the historical yield on 30-year Treasury bonds from 1977 through 

2018 (green line) and the distribution of projected yields through 2038 (blue lines).6

Figure 4. Historical and Distribution of Projected Yield on 

30-Year Treasury Bonds 

By construction, projected yields start close to recent historical yields and waver out 

over time, because (the natural logarithm of) the yield on 30-year government 

bonds is modeled as a difference from its previous value (SE-PIMS System 

Description, page 2-9 and footnote 1 on page 5-13): 

∆ln(i௧) = α௜ + β௜∆ln(i௧ିଵ) + ε௜,௧, 

where both α௜ = 0 and β௜ = 0 in simulations. We regressed simulated values of 

∆ln(i௧ିଵ) on ∆ln(i௧) and confirmed that neither the estimated α௜ nor β௜ is 

statistically distinguishable from zero in SE-PIMS simulations. With α௜ = β௜ = 0, the 

log-yield follows a random walk. 

6

 Historical data are monthly, projected data are annual. Percentiles of projected 

yields are calculated within each year, i.e., the depicted blue lines are not illustrative 

of any single scenario. From February 2002 through February 2006, the U.S. 

Treasury did not sell any bonds with a 30-year maturity; instead, the figure depicts 

the yield on 20-year bonds for that period. 

5th percentile

25th percentile

Median

75th percentile

95th percentile

0%

3%

6%

9%

12%

15%

1980s 1990s 2000s 2010s 2020s 2030s

Sources: Board of Governors of the Federal Reserve System (historical data), SE-PIMS (projections).

Yield on 30-year Treasury bonds (20-year bonds from Feb. 2002 to Feb. 2006).
 12 

At the time these simulations were generated, the yield on 30-year Treasury bonds 

was near historic lows. One may be concerned that yields drift even lower, into 

unchartered territory, in a sizable number of scenarios. Indeed, yields have in fact 

decreased further—for example, to 1.98% on August 15, 2019—and they are lower 

yet in some other developed economies—for example, the German government 

issued 30-year bonds at a negative yield in August 2019.7 The current generating 

equation (random walk in log-yields) does not support negative yields. 

Few investors purchase a newly issued 30-year bond and hold it until maturity. To 

represent annual bond returns, SE-PIMS converts yields into one-year returns—see 

Figure 5.8

Figure 5. Historical and Distribution of Projected Annual Returns on 30-Year 

Treasury Bonds 

Figure 5 shows the historical annual returns on 30-year Treasury bonds and the 

distribution of projections in SE-PIMS. Even at the 95th percentile, simulated rates of 

7

 “Germany for First Time Sells 30-Year Bonds Offering Negative Yields,” Wall Street 

Journal, 21 August 2019. Available at https://www.wsj.com/articles/germany-forfirst-time-sells-30-year-bonds-offering-negative-yields-11566385847. 

8

 Consider a $1 bond that was purchased at par when the yield was r0. One year 

later, the bond pays a coupon of r0 and its market value is equal to the net present 

value of 29 remaining annual coupon payments of r0 plus a $1 principal repayment 

after 29 years, all discounted at the prevailing yield r1. The rate of return is thus the 

coupon payment (r0) plus the amount by which the market value after one year 

exceeds the $1 purchase price. We confirmed that SE-PIMS correctly converted 

yields into annual returns. 

5th percentile

25th percentile

Median

75th percentile

95th percentile

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

1980s 1990s 2000s 2010s 2020s 2030s

Sources: Board of Governors of the Federal Reserve System (historical data), SE-PIMS (projections).

Return on 30-year Treasury bonds (20-year bonds from Feb. 2002 to Feb. 2006).
 13 

return frequently fall short of historical values. Rates of return on existing bonds are 

boosted when yields fall, but since current yields are already low, the potential for 

sizable yield decreases (and correspondingly high rates of return) is limited. In other 

words, we have no concern over the relatively low rates of return on bonds during 

the simulation period. 

Turning from government bonds to corporate stocks, Figure 6 shows the historical 

annual returns (including dividends) of a portfolio of stocks that mimic the Standard 

& Poor’s 500 (S&P 500) index from 1986 to 2018 (brown line), and the distribution 

of projected returns through 2038 (blue lines). 

Figure 6. Historical and Distribution of Projected Annual Returns on Stocks 

SE-PIMS models annual real returns on stocks as an autoregressive process (SEPIMS System Description, page 2-10 and footnote 1 on page 5-13): 

ln(1 + s௧) = α௦ + β௦ln(1 + s௧ିଵ) + ε௦,௧, 

where α௦ = 0.0652 and β௦ = 0. (At these values, simulated values should randomly 

fluctuate around e0.0652-1=6.7%.) We regressed simulated values of ln(1 + s௧ିଵ) on 

ln(1 + s௧) and confirmed that the estimated β௜ is not statistically significant from 

zero in SE-PIMS simulations. Our estimate of α௦ is 0.0708, and statistically different 

from 0.0652 at 5% significance level. 

Simulated Firm-Level Variables 

Bankruptcy probabilities are a function of (lagged) ratio of corporate assets over 

liabilities, ratio of cash flow (net of pension contributions) over assets, employment, 

5th percentile

25th percentile

Median

75th percentile

95th percentile

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

60%

1990s 2000s 2010s 2020s 2030s

Sources: Bloomberg, Cboe (historical data), SE-PIMS (projections).
 14 

funded ratio of the company’s DB plan(s), and indicators for activity in the financial 

or utilities sectors. The industry indicators are time-invariant; future values of the 

other explanatory variables are simulated in SE-PIMS, appropriately transformed 

(logged/lagged), multiplied by parameter estimates, and converted into bankruptcy 

probabilities. 

Table 1 shows the parameters applied to calculate bankruptcy probabilities. These 

were obtained from a logistic regression, as described on page 5.9

Table 1. Bankruptcy Probability Parameters 

Intercept -4.6623 

Log(assetst-1/liabilitiest-1) -0.9197 

Log(assetst-2/liabilitiest-2) 0.2406 

Log(employmentt-1) -0.2503 

Log(employmentt-1) x Log(assetst-1/liabilitiest-1) -0.0373 

Log(employmentt-1) – Log(employmentt-2) -0.6676 

Log(funded ratiot-1) -0.1302 

Cash flowt-1/Assetst-1 -3.8125 

Cash flowt-2/Assetst-2 -2.0676 

Financial industry -2.7136 

Utilities industry -1.6721 

For any single simulation, denote the sum of products of parameters and explanatory 

variables by β′X. The probability that a firm will file for bankruptcy in a given year is 

൫1 + exp(−β′X)൯

ିଵ

. 

Special adjustments are made to particularly high bankruptcy probability estimates 

(which are capped at 20%) and to the probabilities of 14 firms (and their partners), 

whose intercepts were modified. We replicated the bankruptcy probability 

calculations for 2021–2038 and found that the 99.6% of the results matched those in 

SE-PIMS within 0.01%.10 Almost all discrepancies of more than 0.01% were limited 

to just four firms (and their partners); a potential explanation is that their 

calculations were adjusted in a way that is unknown to us.11 The cap at 20% affected 

about 0.03% of the calculations. 

To determine whether a firm is simulated to enter bankruptcy, SE-PIMS converts 

probabilities into binary outcomes (bankruptcy or no bankruptcy). The standard way 

of doing this is by comparing the probability to a variable between 0 and 1, randomly 

drawn from a uniform distribution; if the probability exceeds the random variable, a 

9

 The SE-PIMS System Description (page 6-13) documents these parameters with 

opposite signs. As printed in Table 1, a positive (negative) parameter may be 

interpreted as increasing (decreasing) the bankruptcy probability when the 

explanatory variable increases in value. For example, the parameter on employment 

is negative, indicating that more employees translate into lower bankruptcy risks. 

10 Calculations for 2018–2020 could not be verified because the required lagged 

values were not available in our data extract. 

11 The four firms are represented by IDs 580, 816, 1076, and 1271. 
 15 

bankruptcy is simulated; otherwise, the firm continues operating. As a result, the 

average bankruptcy probability should equal the average share of firms that are 

simulated to file for bankruptcy (up to random variation). We found this to be 

approximately true for 2021 and later years, but not for 2020. Averaged over all 

1,434 firms/partners and all 5,000 scenarios, i.e., over more than 7 million outcomes 

annually, the average fraction that SE-PIMS projected to file for bankruptcy was 

0.55% in 2020, compared with an average bankruptcy probability of 0.49% (Figure 

7). It is unclear to us what may have caused this discrepancy. 

Figure 7. Average Bankruptcy Probabilities and Simulated Bankruptcy Rates 

(2018–2038) 

Figure 7 also demonstrates that the average bankruptcy probability and rate 

gradually decrease over time. This is consistent with expectations, because high-risk 

firms face elevated bankruptcy rates and disproportionately drop out of the 

simulations, leaving a mix of relatively low-risk firms in later years. 

The green line in Figure 7 shows average bankruptcy calculations for 1,434 

firms/partners and 5,000 scenarios. Consider just three out of the 1,434 

firms/partners (Figure 8). The firms differ in their 2018 credit rating, as compiled by 

Compustat. SE-PIMS simulated the highest average bankruptcy probabilities for the 

firm with the worst credit rating (BB-), followed by the firm rated at BBB, and the 

lowest probabilities for the firm with the best credit rating (AA+). This is, of course, 

consistent with expectations and suggests that the bankruptcy model responds 

appropriately to financial metrics. (The model does not control for credit rating itself; 

see Table 1). 

Average calculated

bankruptcy probability

Simulated

bankruptcy rate

0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.7%

0.8%

2018 2023 2028 2033 2038

Source: SE-PIMS for 2018, specification 127.
 16 

Figure 8. Average Bankruptcy Probabilities for Three Illustrative Firms 

(2018–2038) 

Figure 8 further demonstrates that average bankruptcy probabilities are converging 

over time. This is, again, consistent with expectations. The credit ratings are based 

on the firms’ financial status in 2018. SE-PIMS models the ratios of equity to 

liabilities and of cash flow to assets as mean reversion processes, so that financially 

weak (strong) firms become stronger (weaker) over time, leading to a convergence 

of average financial strength and bankruptcy probabilities. 

More generally, Figure 9 shows average bankruptcy probabilities of all firms with 

known credit rating, by rating category. (The vertical axis uses a logarithmic scale.) 

As expected, bankruptcy probabilities tend to correlate with credit rating, and 

converge over time. 

Firm 172 (AA+ in 2018)

Firm 866 (BBB in 2018)

Firm 1251 (BB- in 2018)

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.7%

0.8%

2018 2023 2028 2033 2038

Projection year

Source: SE-PIMS for 2018, specification 127.
 17 

Figure 9. Average Bankruptcy Probabilities, by Credit Rating (2018–2038) 

While it is expected that the average bankruptcy probability of firms with different 

initial financial strengths converge over time, microsimulation models generally aim 

to preserve distributions in their future scenarios. Figure 10 illustrates the 

distribution of simulated bankruptcy probabilities. (The vertical scale uses a 

logarithmic scale.) Apart from a decline of the 5th and 95th percentiles during the 

early part of the simulation period, the distribution of bankruptcy probabilities is 

remarkably stable. 

AAA/AA+/AA/AA-/A+

A/A-/BBB+

BBB/BBB-/BB+/BB/BBB+/B/B-/CCC+/CC

0.1%

0.2%

0.4%

1%

2%

4%

2018 2023 2028 2033 2038

Source: SE-PIMS for 2018, specification 127. Probabilities are weighted and displayed on a logarithmic scale.
 18 

Figure 10. Distribution of Simulated Bankruptcy Probabilities (2018–2038) 

The declining rates at the 5th and 95th percentile pose a puzzle. Since SE-PIMS’s 

initial conditions reflect the economy’s particular state around 2017, one may expect 

to see shifting distributions as the model evolves to stochastically cover a more 

representative set of states. However, the economy was generally robust in 2017, 

and initial bankruptcy rates may have been below their long-term average. The 

pattern in Figure 10, with declining rates at the 5th and 95th percentiles, runs counter 

to that argument. 

Similar to Figure 10’s distribution of bankruptcy probabilities, Figure 11 shows 

distributions of simulated values for other financial metrics: 

1. Ratio of corporate assets over liabilities, 

2. Employment (in 1,000 workers), 

3. Corporate equity (stock market capitalization), 

4. Pension underfunding (consolidated for firms that sponsor multiple plans), 

5. Pension plan funded ratio (consolidated), 

6. Corporate liabilities, 

7. Ratio of corporate cash flow (before pension contributions) to assets, and 

8. Ratio of pension contributions to assets. 

The vertical axes use logarithmic scales (except see below). Most panels show the 

5

th, 25th, 50th, 75th, and 95th percentiles during the simulation period (blue lines). The 

percentiles are calculated separately for each year, i.e., the lines do not represent 

specific simulated paths. 

5th percentile

25th percentile

Median

75th percentile

95th percentile

0.02%

0.05%

0.1%

0.2%

0.5%

1%

2%

2018 2023 2028 2033 2038

Projection year

Source: SE-PIMS for 2018, specification 127.
 19 

Figure 11. Distribution of Simulated Financial Metrics (2018–2038) 

5th percentile

25th percentile Median

75th percentile

95th percentile

1

2

4

8

2018 2023 2028 2033 2038

1. Corporate Assets / Liabilities

5th percentile

25th percentile Median

75th percentile

95th percentile

2

4

10

20

40

100

200

400

2018 2023 2028 2033 2038

2. Employment

5th percentile

25th percentile Median

75th percentile

95th percentile

400

1,000

2,000

4,000

10,000

20,000

40,000

100,000

200,000

400,000

1,000,000

2,000,000

2018 2023 2028 2033 2038

3. Corporate Equity

Median is $0

75th percentile (left axis)

95th percentile (left axis)

99th percentile (left axis) Fraction

non-zero

(right axis) 0%

10%

20%

30%

40%

50%

0.1

0.2

0.4

1

2

4

10

20

40

100

200

400

1,000

2,000

4,000

2018 2023 2028 2033 2038

4. Pension Underfunding

5th percentile

25th percentile Median

75th percentile

95th percentile

60%

100%

200%

500%

2018 2023 2028 2033 2038 Source: SE-PIMS for 2018, specification 127.

5. Pension Funded Ratio

5th percentile

25th percentile Median

75th percentile

95th percentile

100

200

400

1,000

2,000

4,000

10,000

20,000

2018 2023 2028 2033 2038

6. Corporate Liabilities

5th percentile

25th percentile Median

75th percentile

95th percentile

0.4%

1%

2%

4%

10%

20%

2018 2023 2028 2033 2038

7. Cash Flow / Assets

Median is 0%

75th percentile

(left axis)

95th percentile (left axis)

99th percentile (left axis)

Fraction nonzero (right axis) 0%

10%

20%

30%

40%

50%

0.02%

0.04%

0.1%

0.2%

0.4%

1%

2%

4%

2018 2023 2028 2033 2038

8. Pension Contributions / Assets

Source: SE-PIMS for 2018, specification 127.
 20 

In each year, about 7 million values of the pertinent metric enter into the calculation 

of percentiles.12 Most values of pension underfunding (panel 4) and the ratio of 

pension contributions to assets (panel 8) are zero, so the medians of their 

distributions are zero. In addition to the 75th and 95th percentiles, these two panels 

also show the 99th percentile, along with a green line that depicts the fraction of 

values that are not zero. The green lines’ scales are on the right axes; unlike all left 

axes, those scales are linear rather than logarithmic. 

Figure 11 serves to gauge the stability of each metric’s distribution over the 

simulation period. The distributions need not remain constant. For example, as time 

proceeds, weaker firms will have been removed from simulations due to a 

bankruptcy. Also, the 2018 or 2019 starting year is close to recent history, and 

recent history is not necessarily representative of longer periods. 

Most simulated values maintain their distribution quite well in the 20-year simulation 

period, with two notable issues. First, corporate equity (panel 3) generally increases, 

which may be due to the specification of its generating process (SE-PIMS System 

Documentation, pages 5-7 and 5-13): 

∆ln(E௧) = αா + βா∆ln(E௧ିଵ) + εா,௧

where αா=0.0306 and βா=0.0206. In words, the equity growth rate is weakly 

persistent over time (positive but small βா), with an upward drift in equity of about 

3% per year. That drift translates into an upward-shifting distribution of corporate 

equity over the simulation period. The upward shift may reflect general economic 

growth, though its primary driver (αா) is not correlated with macroeconomic 

variables. (The macroeconomic portion of the stochastic innovation term, εா,௧, is 

highly correlated with the residual in stock market returns, but its mean is zero.) 

Insofar we are aware, corporate equity does not play any direct role in bankruptcy 

modeling, and we did not investigate further. 

Second, the distribution of pension funded ratio (panel 5) generally deteriorates until 

2023 and improves in later years. We are unsure what drives this pattern. The early 

years may be driven by SE-PIMS’s assumption that firms make only the minimal 

required pension contribution, and that contribution is generally small in the near 

future because it is our understanding that many firms have accumulated credit 

balances in recent years. Improvements in plan funding in later years are more 

difficult to explain. By 2028, a quarter of plans are predicted to have funded ratios in 

excess of 145% (and in excess of 228% by 2038). 

We understand that the concept of funded ratio in Figure 11 differs from the metric 

used for purposes of plan termination after a sponsor bankruptcy. The latter tends to 

be lower, in part because it tends to assume a lower discount rate of future benefits. 

That said, the two metrics presumably move in tandem, and it appears worthwhile to 

explore whether the funded ratio for termination purposes is projected to follow a 

similar pattern as that for funding purposes. A generally upward trajectory may 

12 To be precise, 7,170,000 values (1,434 firms/partners times 5,000 scenarios) in 

the early years and fewer in later years because firms drop out after their path 

involves a bankruptcy filing. By 2038, 6,510,400 values remain for each metric. 
 21 

suggest that SE-PIMS understates claims due to plan terminations following 

bankruptcies. 

The pattern in funded ratios is consistent with the distribution of pension 

underfunding (panel 4); the fraction of firms with underfunding initially increases 

from 17% in 2018 to 44% in 2023 and declines thereafter. It is also consistent with 

the distribution of the ratio of pension contributions to assets (panel 8), and with the 

FY 2018 PBGC Projection Report, which anticipates a decline in new claims after 

2023.13

Correlations between Macroeconomic and Firm-Level Variables 

We calculated correlation coefficients between select pairs of macroeconomic and 

firm-level variables. 

Stock market returns and bankruptcy risks. We expect a negative correlation 

between bankruptcy risks and the rate of return on a broad basket of stocks. 

However, the contemporaneous correlation between bankruptcy risk and rate of 

return on stocks is 0.0063 in the simulation data, i.e., positive and very small.14 We 

also calculated annualized 10-year trailing average rates of return and found a 

correlation with bankruptcy risks of -0.1116; negative, as expected.15

Stock market returns and the ratio of cash flow to assets. We expect a positive 

correlation between cash flow and stock market returns. However, the 

contemporaneous correlation was -0.2090 in the simulation data, and the correlation 

with annualized 10-year trailing average rates of return on stocks was -0.1651. This 

finding goes counter to our expectations; see below. 

Rate of return on pension assets and pension funded ratio. SE-PIMS assumes that 

DB plan assets earn a rate of return that is a function of returns on bonds and 

stocks. (Ultimately, SE-PIMS exogenously generates only the yield on 30-year 

Treasury bonds and stock market returns.) We expect a positive correlation between 

the rate of return on pension assets and plans’ funded ratios. Indeed, the 

contemporaneous correlation was positive (0.1631). More importantly, the 

correlation with annualized 10-year trailing average rates of return on pension assets 

was also positive (0.4409) and stronger than the contemporaneous correlation, as 

expected. 

Rate of return on pension assets and pension underfunding. We expect a negative 

correlation between rates of returns on pension assets and plans’ underfunding. The 

13 See Figure 13 in the FY 2018 PBGC Projections Report, available at 

https://www.pbgc.gov/sites/default/files/fy-2018-projections-report.pdf. 

14 The correlation is based on 136,507,182 records (up to 20 simulation years of 

1,434 firm/partners and 5,000 scenarios). Arguably, the number of degrees of 

freedom is only one-tenth of this number, because macroeconomic variables are 

generated for only 500 scenarios and replicated 10 times. Either way, the number of 

observations is huge and all reported statistics in this section are highly statistically 

significant. 

15 Based on simulated values in 2028 and later; we used only simulated values—

which start with 2019—to calculate 10-year trailing average rates. The number of 

records (73,376,024) is again very large. 
 22 

contemporaneous correlation was -0.1290 and the correlation with annualized 10-

year trailing rates was -0.1871; negative and stronger than the contemporaneous 

correlation, as expected. 

Rate of return on pension assets and ratio of pension contributions to assets. We 

expect a negative correlation between rates of returns on pension assets and firms’ 

contributions to pensions. The contemporaneous correlation was -0.0078 (negative 

but small) and the correlation with annualized 10-year trailing rates was -0.1259; 

negative and stronger than the contemporaneous correlation, as expected. 

In sum, the correlations between macroeconomic and firm-level metrics that we 

explored are generally consistent with expectations, except for the correlation 

between stock market returns and the ratio of cash flow to assets. This exception 

may be the result of the autoregressive way in which the ratio of cash flow to assets 

is modeled (SE-PIMS System Description, page 5-7 and 5-13): 

CFA௧ = α஼ி஺ + β஼ி஺CFA௧ିଵ + γ஼ி஺F + ε஼ி ,௧

where CFA௧ represents the ratio of cash flow to assets in year t and F is an indicator 

for the financial services industry. In words, the ratio depends on the firm’s ratio in 

the prior year and on a stochastic innovation term, ε஼ி஺,௧. The macroeconomic 

portion of that term is negatively correlated with the stochastic term in stock market 

returns; the correlation coefficient is -0.76 (SE-PIMS System Description, page 5-

14). This explains the overall negative correlation, but the pattern goes counter to 

our expectations. 

Incomplete Stochastic Variation 

Finally, we observed a lack of variation among certain variables in the simulation 

data. In principle, we expect all firm-specific metrics to vary across all simulation 

scenarios. However, employment, pension underfunding, pension funded ratio, and 

corporate liabilities values appear to be constant across partners of a firm and across 

cycles within a scenario. Consider Table 1, which shows select variables of a 

randomly selected firm (51) and a randomly selected group of scenarios (212-1 

through 212-10). The firm enters both as itself (51-1) and for two partners (51-2, 

51-3). Note that all variables take on the same value for all partners and simulation 

cycles (except when a firm is simulated to have filed for bankruptcy, such as firm 51-

1 in scenario 212-5 and firm 51-2 in scenario 212-8). While only 2019 and 2020 are 

shown, this lack of variation occurs in all years. Other metrics, such as the ratio of 

corporate assets to liabilities, do vary across partners and scenarios. It is our 

understanding that this lack of stochastic variation is a design choice to speed up 

certain computation-intensive actuarial calculations in SE-PIMS. 
 23 

Table 2. Illustrative Simulation Values of Select Variables 

Firm- Scenario- Employment Underfunding Funding ratio Liabilities

Partner Cycle 2019 2020 2019 2020 2019 2020 2019 2020

51-1 212-1 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-1 212-2 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-1 212-3 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-1 212-4 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-1 212-5 52.73 . 72.29 . 0.878 . 590.33 .

51-1 212-6 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-1 212-7 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-1 212-8 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-1 212-9 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-1 212-10 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-2 212-1 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-2 212-2 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-2 212-3 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-2 212-4 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-2 212-5 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-2 212-6 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-2 212-7 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-2 212-8 52.73 . 72.29 . 0.878 . 590.33 .

51-2 212-9 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-2 212-10 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-1 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-2 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-3 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-4 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-5 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-6 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-7 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-8 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-9 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

51-3 212-10 52.73 59.35 72.29 90.79 0.878 0.845 590.33 584.04

Source: SE-PIMS for 2018, specification 127.
 24 

Recovery Claims by Bankruptcy Type 

Chapter 7 versus Chapter 11 

While SE-PIMS has the capability to model a Chapter 7 or a Chapter 11 bankruptcy 

separately, the probability of a Chapter 11 bankruptcy is set to zero in its 2018 

implementation. However, the historical number of Chapter 11 reorganizations is 

sizeable, and the fraction of total filings that were under Chapter 11 fluctuated 

between 17% and 34% (see Figure 12).16

Figure 12. Chapter 7 and Chapter 11 Bankruptcy Filings over Time 

Chapter 11 bankruptcies involve a reorganization and can have different implications 

for pension plans compared to a Chapter 7 liquidation. We analyzed differences in 

recovery rates for DB pension plans after filings under Chapter 7 and Chapter 11. 

The analysis is based primarily on two data sources. First, the PBGC provided us with 

a listing of terminated and trusteed plans, their termination date, unfunded liabilities, 

and the amounts that could be recovered in bankruptcy proceedings for “Due and 

Unpaid Employer Contribution” and unfunded “Employer Liability.” (It is our 

understanding that the latter represents an unsecured claim in bankruptcy, whereas 

16 Figure 12 is based on all corporate bankruptcies, not just bankruptcies of 

companies that sponsor a DB plan. It is our impression that DB plan sponsors tend to 

be larger than other corporations, and that Chapter 11 is more common among 

larger than among smaller companies. In other words, Chapter 11 reorganizations 

may be more common among DB plan sponsors than Figure 12 suggests. Also see 

Table 3, where we identified 62 filings under Chapter 7 and 164 under Chapter 11. 

Chapter 7 filings (left axis)

Chapter 11

Chapter 11 as a fraction of

total filings (right axis)

0%

10%

20%

30%

40% Chapter 11 as a fraction of total filings

0

10,000

20,000

30,000

40,000

50,000

60,000 Annual bankruptcy filings (trailing 12 months)

97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18

Calendar year

Source: Administrative Office of the U.S. Courts.
 25 

the former has a higher level of priority.) Second, the PBGC provided us with a 

database from New Generation Research with information on corporate bankruptcies 

(company name, EIN, year of filing, and type of filing—Chapter 7, 11, or other). To 

improve the match rate between the two data sources, we also used Form 5500 

filings, which provide a cross-walk between plan and sponsor names. 

We restricted the list of terminated plans to 622 plans that were trusteed in 2010–

2018. Of these, 62 were matched to a Chapter 7 filing and 164 to a Chapter 11 

filing. The bankruptcy filing type of the remaining 396 plans could not be determined 

because they matched to multiple bankruptcies of different filing types (11 plans) or 

did not match (385 plans). Table 3 summarizes the PBGC’s recoveries in bankruptcy 

proceedings, by bankruptcy type. 

Table 3. Recoveries in Bankruptcy Proceedings, by Type of Bankruptcy Filing 

(2010–2018) 

Both the average recovery and the average unfunded liability were smaller for plans 

whose sponsor liquidated under Chapter 7 than for plans whose sponsor reorganized 

under Chapter 11. The average recovery rate as a percentage of unfunded liability 

was also lower under Chapter 7 (6.8%) than under Chapter 11 (9.6%). However, the 

pattern reverses when weighting the recoveries by unfunded liability: 17.0% under 

Chapter 7 and 9.8% under Chapter 11. Put differently: the PBGC recovered 17.0% of 

the unfunded liabilities under Chapter 7, compared with 9.8% under Chapter 11. 

Ultimately, the weighted recovery rate is more relevant to the PBGC’s balance sheet 

than the unweighted average rate. 

The analysis is sensitive to the experiences with large plans. For example, the higher 

weighted fraction under Chapter 7 is due to a single plan whose recoveries amounted 

to 49% of that plan’s unfunded liabilities and more than doubled the weighted 

recovery rate of plans under Chapter 7. 

Median recovery rates tend to be low because the recovery was zero for many plans. 

For example, the PBGC did not recover anything from 55% of plans under Chapter 7, 

so the median recovery was 0.0%. 

The average recovery rates for all 622 terminated plans were 6.8% (unweighted) 

and 9.0% (weighted). 

In sum, while the recovery rates in Chapter 7 liquidations may differ from those in 

Chapter 11 reorganizations, our analysis presents no compelling case for changing 

Chapter 7 Chapter 11 Unknown All

Number of trusteed plans 62 164 396 622

Average recovery $0.8m $2.5m $0.3m $1.0m

Average unfunded liability $4.8m $25.6m $5.5m $10.7m

Mean recovery rate

Unweighted 6.8% 9.6% 5.7% 6.8%

Weighted by unfunded liability 17.0% 9.8% 6.2% 9.0%

Median recovery rate

Unweighted 0.0% 1.1% 0.0% 0.0%

Weighted by unfunded liability 1.5% 5.1% 0.7% 2.3%

Sources: PBGC, New Generations Research, Form 5500 filings.
 26 

SE-PIMS’s current practice of applying the same recovery rate to all plans that are 

projected to be trusteed after a bankruptcy. Separately, SE-PIMS currently assumes 

that 5% of unfunded liabilities will be recovered. This is a somewhat conservative 

estimate in light of the 9.0% average weighted recovery among all 622 trusteed 

plans. To place the difference in perspective: SE-PIMS assumes that the PBGC will 

absorb 95% of unfunded liabilities, and our findings suggest that the net claim was 

in fact 91% of unfunded liabilities in recent years. 

Repeat Bankruptcies 

Separately, AACG investigated repeat bankruptcies by the same firm. Based on 

bankruptcy data from New Generation Research, we identified 216 companies that 

filed for bankruptcy twice between 1981 and 2018 (Figure 13). 

Figure 13. Bankruptcies by Year for Companies that Filed for Bankruptcy 

Twice 

Of these companies, 184 companies were public when they first filed for bankruptcy 

and 32 were private. A vast majority (209 out of 216 companies) filed under Chapter 

11, and only two companies under Chapter 7. (Five companies filed under Chapter 

15, under which a representative of a corporate bankruptcy proceeding outside the 

United States can access the U.S. court system.) 

 -

 5

 10

 15

 20

 25

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017

First Instance Second Instance

Source: NEW GENERATION RESEARCH, INC.
 27 

Figure 14. Number of Public and Private Companies by Bankruptcy Filing 

Instance (1981–2018) 

When these same companies filed for bankruptcy again, only 138 were public and 78 

were private (Figure 14). Most repeat bankruptcies (198 out of 216) again filed 

under Chapter 11, while 13 companies filed under Chapter 7 (Figure 15). 

Figure 15. Type of Bankruptcy by Bankruptcy Filing Instance 

We identified 17 companies that filed for bankruptcy three times. All were public 

when they first filed for bankruptcy. One company was private when it refiled, and 

seven companies were private by the time they filed for the third time. All filed under 

Chapter 11 of the Bankruptcy Code in every instance. 

Ideally, the analysis would tell whether second or third bankruptcies are more or less 

likely to occur than first bankruptcies. Unfortunately, the sample is too small to 

reliably answer that question, especially since our interest is limited to companies 

184

138

32

78

0

50

100

150

200

250

First Instance Second Instance

Public Private

Source: NEW GENERATION RESEARCH, INC.

209 198

2 13

5 5

0

50

100

150

200

250

First Instance Second Instance

Chapter 11

Chapter 7

Chapter 15

Source: NEW GENERATION RESEARCH, INC.
 28 

that sponsor a DB plan. Even if SE-PIMS were to model subsequent bankruptcies, 

their contribution to the parameter estimation would be restricted further because 

their DB plan could have terminated after the first filing or because they became 

privately held, so that their financial information would no longer be public. In sum, 

we envision little benefit from expanding SE-PIMS to account for repeat 

bankruptcies. 

Assumptions Triggering Plan Termination in Bankruptcy 

When a plan sponsor enters bankruptcy in an SE-PIMS scenario, its plan(s) may or 

may not be trusteed, depending on the plans’ funded ratios (SE-PIMS System 

Description, page 4-4). If the market value of assets of all plans sponsored by the 

firm is 80% or more of the combined termination liabilities for all the plans, no claim 

is assumed. Otherwise, PBGC terminates and trustees the plans, i.e., it assumes the 

plans’ assets and liabilities. We explored to what extent the 80% rule matches recent 

experiences. 

The PBGC provided us with a list of plans that were terminated after their sponsor 

filed for bankruptcy, and another list of plans that survived their sponsor’s 

bankruptcy.17 Information on terminated plans included assets and liabilities, so their 

funded ratio was readily determined. For plans that survived a bankruptcy, unfunded 

liability was available, but not their funded ratio. 

In the context of the 80% rule, assets and liabilities are measured for termination 

purposes as opposed to for funding purposes, as reflected on Form 5500 filings. An 

important difference lies in the discount rate applied to future benefit payments. The 

discount rate for termination purposes tends to be lower than that for funding 

purposes, resulting in higher liabilities and a lower funded ratio. 

The lists with terminated and surviving plans were matched to Form 5500 filings just 

prior to the approximate date of bankruptcy. We imputed the funded ratio of 

surviving plans as follows. 

First, we assumed that the PBGC’s metric of assets for termination purposes is close 

to the market value of assets reported on Form 5500 filings (Schedule SB, line 2a). 

Since liabilities are equal to the sum of assets and unfunded liabilities, we imputed 

the funded ratio of surviving plans as assets/(assets+unfunded liabilities).18 Figure 

16 shows the distribution of funded ratio (for termination purposes) for 300 trusteed 

plans and 105 consolidated surviving plans. The boxes delimit the 25th, 50th, and 

17 More precisely: a list of companies that filed for bankruptcy and whose plans 

survived. We understand that in a small number of cases, one or more plans 

survived the bankruptcy, and one or more plans were terminated and trusteed. 

However, no information was provided on which plans survived and which did not. 

Since such mixed results are rare, we treated all plans of corporate parents on the 

list as having survived. 

18 Recall that information on unfunded liabilities for termination purposes is provided 

for corporate parents and not for their individual plans. We therefore consolidated 

assets from Form 5500 filings to the level of the sponsor, and used consolidated 

plans as the unit of observation. 
 29 

75th percentiles; the “whiskers” denote adjacent values, and the single dots reflect 

individual outlier plans.19 The red vertical line is at 80% funding. 

Figure 16. The Distribution of Funded Ratios around Bankruptcy for 

Trusteed and Surviving Plans (2009–2018); 

Imputation Based on Unfunded Liability and Form 5500 Assets 

As expected, almost all trusteed plans had a funded ratio under 80%. However, most 

plans (81%) that survived their sponsor’s bankruptcy also had an (imputed) funded 

ratio below 80%. While surviving plans were generally better funded than trusteed 

plans, most surviving plans would be misclassified based on the 80% rule. 

Second, we adopted a regression-based imputation approach. Using complete data 

for terminated plans, we estimated a linear regression model of funded ratio for 

termination purposes and applied the parameter estimates to consolidated surviving 

plans to impute their funded ratios. Explanatory variables included the “adjusted 

funding target attainment percentage” (Schedule SB, line 15), assets (Schedule SB, 

line 2a), total funding target (Schedule SB, line 3d(3)), and unfunded liabilities for 

termination purposes (from the PBGC); all monetary figures were converted into per 

participant amounts. (Several alternative model specifications gave very similar 

results.) See Figure 17. 

19 Adjacent values are the most extreme values within 150% of the interquartile 

range from the nearer quartile. Tukey’s Rule, a commonly used guideline in 

statistical analysis, states that statistical outliers are values outside the adjacent 

values. (John W. Tukey, 1977. Exploratory Data Analysis. Addison-Wesley.) 

0% 20% 40% 60% 80% 100%

Funded Ratio (for termination purposes)

Survived

Trusteed

Source: PBGC, Form 5500 filings.
 30 

Figure 17. The Distribution of Funded Ratios around Bankruptcy for 

Trusteed and Surviving Plans (2009–2018); Imputation Based on 

Regression Model 

The regression-based imputation also resulted in funded ratios among consolidated 

surviving plans that rarely exceed 80%, suggesting that the decision to terminate 

and trustee a plan is more complex than a simple rule based on an 80% funded ratio 

threshold. 

Separately, we were surprised to find that the funded ratios of surviving plans were 

generally low. Of course, neither imputation approach discussed above is perfect. It 

may be worthwhile for the PBGC to revisit the issue based on non-imputed data. 

Finally, we explored whether other metrics better distinguish trusteed and surviving 

plans, but found that both adjusted funding target attainment percentage (from 

Schedule SB, line 15) and per participant unfunded liability (from the PBGC) have 

distributions that overlap in a manner similar to that depicted in Figure 16. 

0% 20% 40% 60% 80% 100%

Funded Ratio (for termination purposes)

Survived

Trusteed

Source: PBGC, Form 5500 filings.
 31 

3. MASS WITHDRAWAL MODELING IN ME-PIMS 

Overview 

At a very high level, ME-PIMS incorporates mass withdrawals as follows. 

 Plans may require financial assistance from the PBGC when they become 

insolvent. A plan is considered insolvent when its assets are depleted and it 

can no longer make benefit payments. 

 Mass withdrawals may trigger or accelerate insolvency. A mass withdrawal 

occurs when all participating employers stop participating in the plan at the 

same time. 

 ME-PIMS “books” a financial responsibility within 10 years before it is 

expected to become insolvent for an ongoing plan or within 20 years for a 

plan in mass withdrawal. 

 For each plan, ME-PIMS calculates a probability of mass withdrawal based on 

six factors that relate to the size and financial status of the plan. 

 Once a plan is flagged as facing a mass withdrawal, the plan is frozen—no 

further accruals due to service or increases in benefits units, no new entrants, 

and a roll-back of benefits. The roll-back affects active, retired and termvested participants. The plan will be owed withdrawal liability payments from 

formerly participating employers, but some of those payments may not be 

collectable. 

 The PBGC books a financial responsibility within 10 or 20 years before an 

expected insolvency, but provides financial assistance only upon insolvency. It 

is possible that the plan’s finances improve (in reality or in simulation), in 

which case the claim will be unbooked. 

This section reviews several areas related to mass withdrawal modeling in ME-PIMS. 

First, the mathematical formula that ME-PIMS uses to predict mass withdrawals is 

complex and not based on a statistical model of historical mass withdrawals. We 

discuss the model and suggest an alternative in the section “Model Complexity,” 

starting on page 32. 

Second, ME-PIMS currently models mass withdrawals, but not withdrawals by 

individual employers. We analyzed individual withdrawals in historical data; see the 

section on “Withdrawals by Individual Contributing Employers,” starting on page 35. 

(Separately, our companion report on potential contagion effects of mass 

withdrawals discusses factors that employers may consider when deciding whether to 

withdraw from a plan.) 

Third, employer withdrawals generally trigger a withdrawal liability, which is payable 

in installments. ME-PIMS makes certain assumptions about the collectability of 

withdrawal liability payments. We attempted to validate these assumptions in the 

section on “Collectability of Withdrawal Liabilities,” starting on page 41. 

Finally, ME-PIMS simulates a sample of multiemployer plans, rather than the 

universe. We identified potential issues and obstacles to incorporating all plans in the 

section on “Modeling the Population Rather Than a Sample,” starting on page 41. 
 32 

Model Complexity 

ME-PIMS calculates mass withdrawal probabilities based on six metrics that relate to 

plan size and financial status: 

S1.Plan size (tied to the number of active and total participants), 

S2.Ratio of active to inactive participants, 

S3.Ratio of assets to benefit payments and expenses, 

S4.Ratio of the market value of assets to vested liabilities, 

S5.Ratio of current year to previous year contributions, and 

S6.Ratio of credit balance to employer contributions. 

Those metrics are time-varying and must themselves be forecast in order to predict 

mass withdrawals. An algorithm transforms the six metrics into mass withdrawal 

probabilities such that those probabilities, on average, mimic historical mass 

withdrawal rates. (For purposes of this section, ignore the possibility that future 

rates may differ from historical rates.) Smaller plans and plans in weaker financial 

health are projected to experience a mass withdrawal at higher rates than larger 

plans on solid footing. 

Like SE-PIMS, ME-PIMS is a system to forecast, ultimately, liabilities on the PBGC’s 

balance sheet. Its accuracy is enhanced if it can pinpoint the plans that will 

experience a mass withdrawal. However, it makes little difference whether ME-PIMS 

misidentifies plan A for mass withdrawal when really plan B will experience it; what 

matters is the size of the liability that mass withdrawals create for the PBGC. Some 

of the six metrics that are used to calculate a mass withdrawal probability relate to 

that liability, but none capture it directly or fully. For example, one of the metrics is 

the year-over-year percentage increase in contributions to the plan, which seems to 

bear no relationship to the financial assistance that the plan may require. 

Potential financial assistance is perhaps best measured by a plan’s total unfunded 

vested liability. That metric is not used to calculate mass withdrawals, possibly 

because its predictive ability is low. This raises the question whether the modeling 

system gains much from calculating mass withdrawal probabilities based on factors 

that may have little correlation with potential financial assistance. 

We do not know how well the six factors correlate with total unfunded vested 

liability. If they correlate poorly, perhaps the model may be simplified into a uniform 

probability of mass withdrawal that is applied to all plans. Or perhaps the sole factor 

determining that probability should be a plan’s total unfunded vested liability. 

A similar issue exists in the context of bankruptcies in SE-PIMS. In that model, 

several explanatory variables are based on Compustat data, which are available for 

only a subset of plan sponsors. Simplification of the bankruptcy model in SE-PIMS 

may therefore remove data constraints. That potential benefit does not extend to 

ME-PIMS, because all explanatory variables are based on Form 5500 filings. Still, the 

current model’s complexity does not necessarily translate into greater accuracy of 

the PBGC’s expected financial assistance payments. 

Mass withdrawal probabilities are based on six factors that are combined into a 

probability. Page 50 of Key Differences Between SE-PIMS and ME-PIMS describes the 

process as follows. Consider six factors S1 through S6, each of which is a 
 33 

transformation of financial status or number of plan participants. One of those 

factors, S2, is a transformation of funded ratio (FR), which also enters the algorithm 

directly. The mass withdrawal probability (MWP) is given by: 

Term1 = min ( 1 , ( S1 + S2+ S3 ) / 3.5 + S4 / 20 ) 

Term2 = max ( S1, S2, S3 ) * 0.4 

MWP = max ( Term1, Term2 ) * S5 * S6

If ( FR >= 0.9 + S1 ) then MWP = 0. 

MWP = MWP ^ ( 2 - MWP ) 

MWP = MWP / max ( 1 , 100 * max ( 0.25 - MWP , 0 ) ) 

MWP = MWP * 0.5 

The algorithm to combine and transform the six factors is not immediately 

transparent. It appears to be increasing in all six factors, each of which it itself 

constructed such that it increases with financial health or decreases with plan size. 

The first four lines combine the six factors into an intermediate number, which we 

here label as “mass withdrawal risk score.” The last three lines transform the mass 

withdrawal risk score into a final mass withdrawal probability. Figure 18 numerically 

illustrates the transformation of risk score into probability, i.e., it represents the last 

three formulae above. The orange line at 0.4% denotes the weighted average annual 

mass withdrawal probability cited by French (2017)20 and confirmed by our own 

analysis based on mass withdrawals in 2011–2018. 

20 Darren French (2017). “ME-PIMS Mass Withdrawal Assumptions.” PBGC-PRAD 

memorandum dated March 2, 2017. Available at 

https://www.pbgc.gov/sites/default/files/me-pims-masswithdrawalassumptions.pdf. 
 34 

Figure 18. Transformation of Mass Withdrawal Risk Score into a Probability 

The algorithm was “retro-fit” to PBGC data indicating which ME plans were booked 

from 2003 to 2008, “so as to yield overall [mass withdrawal] probabilities on the 

order of 1⁄2% or less, with significantly higher than average probabilities for the plans 

that were actually booked during that period.” (PBGC 2011, p. 49). We did not have 

access to simulation data to verify that simulated mass withdrawal rates were 

approximately 0.5%. However, we identified 40 mass withdrawals in 2011–2018, 

which translates into a rate of approximately 0.4%. This suggests that the average 

target rate remains approximately correct. 

An important issue is whether the transformation is superior to a statistical model, 

such as a simple logit model. The “retro-fit” presumably involved extensive 

calibration of the functional form and scaling factors, and it is difficult to assess the 

six factors’ relative contributions and trade-offs. In addition, the risk score 

transformation into a probability is much steeper above the average probability 

(0.4%) than below it. In other words, around the mean, positive changes in any of 

the six factors affect the probability more strongly than negative changes. 

The properties of the algorithm are unclear. For example, it is unclear whether 

funded ratio is statistically significantly related to mass withdrawal probability. In 

contrast, the statistical properties of a logit model are well established. A statistical 

model may also be better equipped to evaluate other factors highlighted in other 

research that may influence mass withdrawals. For example: 

 As argued above, PBGC’s potential financial assistance payments are most 

directly affected by the total unfunded vested liability, suggesting that MEPIMS may become more accurate if the mass withdrawal probability model 

controls for total unfunded vested liability. 

The recent historical average is about 0.4%

0%

5%

10%

15%

20% Mass withdrawal probability

0.0 0.1 0.2 0.3 0.4 0.5

Mass withdrawal risk score based on six factors
 35 

 A statistical model can readily test for non-linear effects. According to Kiska et 

al. (2017),21 “CBO expects that employers in severely underfunded plans are 

more likely to withdraw than employers in less underfunded plans because 

required contributions, particularly contributions to reduce underfunding, will 

place a larger financial burden on those employers. At the same time, CBO 

expects that employers in fully funded plans have a greater probability of 

withdrawing and switching to other forms of retirement benefits than do 

employers in underfunded plans that withdraw because of the plans’ distress.” 

These hypotheses may be tested by controlling for funded ratio squared. 

 According to French (2017): “there appears to be some fairly clear and 

possibly predictive relationship between the number of contributing employers 

and the likelihood of pre-insolvency mass withdrawal.” Again, this hypothesis 

is readily tested in a statistical model. 

 French (2017) also noted differences in mass withdrawals across industries, 

which suggests industry indicators may improve the model. 

Our companion report on contagion effects of mass withdrawals discusses several 

factors that, at least theoretically, should play a role in employers’ withdrawal 

decisions. We recommend that future research identify metrics to capture those 

factors in a statistical model. 

Withdrawals by Individual Contributing Employers 

ME-PIMS does not currently model withdrawals by individual participating employers. 

Participating employers are assumed to either collectively withdraw or collectively 

remain in the plan. 

A company that withdraws from a plan faces withdrawal liability payments. In 

principle, these payments aim to cover the unfunded vested liability attributable to 

the departing employer. A departing employer thus effectively shrinks the total 

unfunded vested liability of the plan. Ignoring individual withdrawals would therefore 

systematically overstate future liabilities. However, the withdrawal liabilities are 

merely assessed or estimated to be assessed and may not be collected in full. This 

issue is addressed in the next section. 

Plans need to report on their Form 5500 filings the number of participating 

employers. We seek to explore the intensity of individual withdrawals over time and 

recommend whether the ME-PIMS model needs to be adjusted to accommodate such 

individual withdrawals. 

Using data from the Form 5500 filings, we use two fields that contain information on 

withdrawals by individual employers. These are (1) the number of employers who 

withdrew during the preceding plan year (Schedule R, line 16a) and (2) the 

aggregate amount of withdrawal liability assessed or estimated to be assessed 

against such withdrawn employers (Schedule R, line 16b). 

21 Wendy Kiska, Jason Levine, and Damien Moore (2017). “Modeling the Costs of the 

Pension Benefit Guaranty Corporation’s Multiemployer Program.” Congressional 

Budget Office Working Paper 2017-04. Available at https://www.cbo.gov/system/ 

files/115th-congress-2017-2018/workingpaper/52749-pbgcwp.pdf. 
 36 

As Figure 19 shows, between 2010 and 2017, an annual average of 2,961 employers 

withdrew and were (estimated to be) assessed approximately $2.23 billion in 

withdrawal liabilities in the preceding year. 

Figure 19. Amount of Withdrawal Liabilities (Estimated to be) Assessed and 

Number of Withdrawing Employers in Preceding Plan Year (2010–2017) 

To place individual and mass withdrawals in context: The average annual number of 

individually withdrawing employers was 2,961, compared with 51 employers that 

withdrew annually as part of a mass withdrawal. The average annual withdrawal 

liabilities were $2.2 billion for individually withdrawing employers and $85 million for 

employers that withdrew collectively. In other words, individual withdrawals have 

been a much more important source of leakage from multiemployer plans than mass 

withdrawals in recent years. 

In addition to individual employers leaving multiemployer plans, we also notice that 

there is a separate, general decline in the number of contributing employers to ME 

plans. A review of data captured on the Form 550022 shows this decline is larger than 

what can be explained by the number of individual employers withdrawing. This 

implies that employers are leaving multiemployer plans for reasons that are not 

classified as a “withdrawal.” 

Figure 20 shows change in contributing employers after accounting for individual 

withdrawals in the main industry sectors (Construction, Retail, Transportation, and 

22 Form 5500, line 7: Enter the total number of employers obligated to contribute to 

the plan (only multiemployer plans complete this item). 

1.2

1.4

2.7

1.4

3.1

2.5

2.2

3.2

3,998 

4,243 

3,621 

2,406 

2,970 

2,647 

2,120 

1,684 

0

1,000

2,000

3,000

4,000

5,000

0

1

2

3

4

2010 2011 2012 2013 2014 2015 2016 2017 Number of Withdrawing Employers Amount of Withdrawal Liabilities $ Billions
 37 

Other) between 2011 and 2017. Especially in the Construction industry, many 

employers appear to have left plans without having been reported as individual 

withdrawals; also see below. 

Figure 20: Change in Contributing Employers Net of Individual Withdrawals 

for Major Industries, 2011–2017 

As a fraction of outstanding unfunded liabilities, assessed withdrawal liabilities 

averaged 0.43% over 2010–2017 (Figure 21). Recall that approximately 0.4% of 

multiemployer plans experienced a mass withdrawal each year. In that light, 

individual withdrawal liabilities are sizeable, and an argument can be made for 

incorporating them into ME-PIMS. 

-12,000 -10,000 -8,000 -6,000 -4,000 -2,000 0 2,000 4,000 6,000

2011

2012

2013

2014

2015

2016

2017

Construction

Retail

Transportation

Other
 38 

Figure 21. Ratio of Withdrawal Liabilities to Unfunded Liabilities, 2010–2017 

Withdrawals by individual employers correlate with industry and financial risk zone, 

as discussed next. 

Withdrawals by individual employers are concentrated in certain industries. Between 

2010 and 2016, withdrawals by individual employers from Truck Transportation, 

Retail Trade, Food Beverage Tobacco, Printing and Related, and Paper Manufacturing 

accounted for 64% to 84% of the total individual withdrawals (Figure 22). (In 2017, 

a large withdrawal by a company in the mining sector dominated and pushed this 

value down to 27%.) The Construction sector, which is subject to a different set of 

withdrawal liability rules, is conspicuously absent from Figure 22. The Construction 

industry accounted for almost 50% of the total unfunded liabilities in 2010–2017 but 

its withdrawal liabilities were low (2% of the total in 2017). This is presumably 

because the Construction industry and the Entertainment industry have special 

withdrawal and withdrawal liability rules.23 

23 Employee Retirement Income Security Act of 1974 (ERISA) §4203. 

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.7%

2010 2011 2012 2013 2014 2015 2016 2017
 39 

Figure 22. Proportion of Withdrawal Liabilities in Selected Industries 

(2010–2017) 

Separately, individual employers appear to be much more likely to withdraw from 

financially weak than from stable plans. Figure 23 shows that Critical (red) and 

Critical and Declining (purple) plans account for approximately 30% of current 

liabilities and 35% of unfunded liabilities during 2010–2017. However, these two risk 

categories account for over 80% of the withdrawals by individual employers during 

the same time period (Figure 24). 

0%

20%

40%

60%

80%

100%

2010 2011 2012 2013 2014 2015 2016 2017

Truck Transportation Retail Trade Food Beverage Tobacco Printing And Related

Paper Manufacturing Mining All Others
 40 

Figure 23. Proportion of Unfunded Liabilities by Plan Risk, 2010–2017 

Figure 24. Proportion of Withdrawal Liabilities by Plan Risk, 2010–2017 

In summary, individual withdrawals are a sizeable drain on the contribution base of 

multiemployer plans, and their occurrence is related to industry and plans’ financial 

status. If withdrawal liabilities were collected in full, the solvency of plans would not 

be dented by the departure of employers. However, if only a portion of unfunded 

liabilities are collected from formerly participating employers, individual withdrawals 

can hurt a plan’s stability. The next section addresses this issue. 

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

2010 2011 2012 2013 2014 2015 2016 2017

Green Orange/Yellow Red Purple Black

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

2010 2011 2012 2013 2014 2015 2016 2017

Green Orange/Yellow Red Purple Black
 41 

Collectability of Withdrawal Liabilities 

For plans in mass withdrawal, ME-PIMS calculates a withdrawal liability that serves to 

pay off the plan’s unfunded vested liability. The withdrawal liability is typically 

payable in installments that are roughly equal to historical contributions. ME-PIMS 

assumes a collectability rate of 40%, which is applied to the entire payment 

schedule. In addition, ME-PIMS assumes a rate of decay in the annual payment over 

the ensuing years, modifying the schedule downward accordingly. The assumed 

decay-rate is the average annual rate of decline, if any, in the actively employed 

population of the plan’s collective sponsorship over the 5-year period immediately 

preceding mass withdrawal, and updated annually for future years in the simulation 

(Key Differences Between SE-PIMS and ME-PIMS, pp. 51–52). 

We attempted to validate the collection assumptions in ME-PIMS. Unfortunately, the 

data currently at our disposal do not support this analysis. Schedule R asks about 

contributions by employers that contribute at least 5% of the total plan 

contributions. In rare cases, the filing indicated (on line 13e(2)) that the contribution 

represents a withdrawal liability payment. However, to our knowledge there is no 

complete accounting of withdrawal liability payments on the Form 5500. 

It is our understanding that the PBGC recently conducted a survey among 

multiemployer plans to gain insight into withdrawal liability payments. Its results 

may be expected to shed light on collectability assumptions in ME-PIMS and, 

ultimately, the importance of modeling individual withdrawals in ME-PIMS. The issue 

affects not just plans with individual withdrawals, but also plans that experienced a 

mass withdrawal and possibly even insolvent plans. 

Modeling the Population Rather Than a Sample 

In 2017, ME-PIMS simulated future events for a sample of 321 multiemployer plans, 

which were weighted to represent the entire universe of PBGC-insured multiemployer 

plans (FY 2017 PBGC Projections Report). SE-PIMS is similarly based on a sample of 

DB plans, in part because little financial information is available for the majority of 

insured single-employer plans and their sponsors. In contrast, ME-PIMS relies 

predominantly on Form 5500 filings for its predictive modeling, i.e., data availability 

is presumably a lesser concern. 

Analyses of a population based on a sample invariably require extrapolation, which 

introduces additional uncertainty. We explored whether ME-PIMS can include the 

population of multiemployer plans, i.e., approximately 1,400 plans. Among the 

obstacles to modeling the entire universe are the following. 

 Not all information required by ME-PIMS is available in electronic format. All 

fields on the Form 5500 and its schedules are available, but PDF attachments 

are not. Some information that is important to actuarial calculations needs to 

be manually entered from PDF attachments. For example, pursuant to line 8 

of Schedule MB, additional information may need to be attached regarding 

expected benefit payments over the next ten years, the numbers of active 

participants by age and years of service, average compensation or cash 

balances for each age/service category, retirement rates by age, and other 

factors that affect actuarial calculations. 
 42 

 Even with sufficient data entry resources, the required information cannot be 

obtained for smaller plans because the requirements for detailed information 

generally apply to large plans only.24

As described in the FY 2018 PBGC Projections Report (which was released in August 

2019), ME-PIMS was recently recoded and expanded to include all multiemployer 

plans. To solve the issue of incomplete data, plans were grouped by major industry 

sectors and by categories of the ratio of active to inactive participants. Detailed 

information was manually entered for a sample of 348 plans; the remainder of the 

plans were assumed to have similar provisions, age/service distributions, average 

salaries or cash balances, et cetera, as plans of the same industry and 

active/inactive category in the sample. 

While we are unable to verify the implementation of this imputation process or 

evaluate potential unforeseen complications, we believe that the approach taken to 

extend ME-PIMS to the universe of multiemployer plans is sensible and scientifically 

sound. 

24 Such information is also not filed by plans that did not submit a Schedule MB. We 

found that all or almost all such plans are receiving financial assistance from the 

PBGC, i.e., the PBGC presumably has access to the required information. 
 43 

4. CONCLUSION 

This document reports on our review of bankruptcy aspects in SE-PIMS and mass 

withdrawal aspects in ME-PIMS. While sometimes hampered by limited available 

data, we found several issues that raise questions about embedded assumptions or 

relationships among simulated metrics. Some issues may be important; many others 

likely have only modest implications for the results generated by SE-PIMS and MEPIMS. We did not identify any issues that, with a reasonable degree of confidence, 

would generate a sizeable bias in a known direction. 

SE-PIMS and ME-PIMS are undergoing continuous development. Some of the issues 

raised in this report have already been addressed. For example, mass withdrawals 

are no longer assigned a stochastic probability of occurrence prior to plan insolvency, 

and ME-PIMS already simulates the entire universe of multiemployer plans (FY 2018 

PBGC Projections Report). 

Our review emphasizes issues that may have implications for projections of new 

claims to the PBGC. Much less emphasis was placed on the numerous cases in which 

we encountered something that raised questions but that, upon closer inspection, 

was in fact carefully thought through and properly addressed by SE-PIMS or MEPIMS. Despite potential issues, the care and thoughtfulness with which the models 

have been developed is to be commended. 
 44 

This document is the Part 2 Report of the Bankruptcy Component of Contract 

16PBGC18C0023 (Pension Insurance Modeling System MAP-21 Peer Review Service). 

DISCLAIMER 

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including the possibilities that additional or different information or data might be 

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