Pictured from left to right an alarm clock, increasingly high stacks of coins and a bell jar labeled, Retirement, brimming with coins.

Part 1 - Introduction

Abstract

We are interested in the funding level of individual pension plans and whether or not there is a statistical difference between the funding levels for plans that are sponsored for a single employer or for many employers under one plan.

The idea being that the Tragedy of the Commons could apply to pension plans. Maybe a pension plan with decisions made by and for a single employer might evidence more responsibility and care taken than a pension plan where multiple employers make decisions for the many without individual responsibility for the ultimate fate of the plan, and the opportunity to withdraw.

We can’t determine causation since this is an observational study, but we can look for statistically significant differences in the data.

To this end we are collecting data from the Department of Labor’s website for all of the Schedule SBs that are filed on behalf of the pension plans in the USA. This data contains the funding percentage of individual pension plans required to file a Schedule SB. (An example of plans that are not required are government plans and church plans.) And in an observational analysis we will compare funded percentages across two different plan types: the single employer plan type, and the two multiple employer plan types.

Ultimately we find that single employer plans are better funded than multiple employer plans however this could be explained by incentives in the tax code to use a single-employer pension plan to reduce taxes beyond the contribution limits of a normal individual retirement plan, or the greater range of investments afforded to the pension plan compared to it’s sponsoring organization.

For future studies we propose comparing year-over-year longitudinal data, or doing more extensive exploratory analysis to identify more factors that have a relationship to pension funded percentage.


Part 2 - Data

Data Overview

The data is compiled by the Employee Benefits Security Administration to comply with the Freedom of Information Act. The data is not processed, it’s the raw data fields from when a pension plan files their annual Form 5500 with the Department of Labor.

The data is stored on the DOL’s website. I’ve downloaded the Schedule SB information from the 2020 Form year filings as the 2021 filings have not all been submitted.

Each case is a Schedule SB that was filed with the Department of Labor regarding a defined benefit pension plan’s funding status using a 2020 Form 5500. We have 39,524 cases.


Libraries

We are coding in the TidyVerse, and we need the infer package to perform statistical inference.

# Load packages --------------------------------------
library(tidyverse)
library(infer)


Load Data

I uploaded a copy of the data to my publicly available github account to read from.

# Load data --------------------------------------
datalocation = 'https://raw.githubusercontent.com/pkofy/DATA606/main/Data%20Project/F_SCH_SB_2020_latest.csv'
schsb <- read.csv(file = datalocation)


Part 3 - Exploratory data analysis

Summary Statistics

We show for 39,524 cases the mean is 125.8%, the median is 115.6%. The standard deviation is an unexpected 51.7%. With the min and the max being between 0% funded and 999.99% which seems to be a maximum entry amount.

It may be that there are a number of plans, probably small, that use the high maximum allowable tax-deductible contribution to pension plans as a way to defer taxes on income. Similarly, credit unions are unable to invest in securities being low-risk institutions for community banking; However within a pension plan they are able to invest in securities and by being superfunded are able to report income powered by securities on their accounting books by having the expected return on the pension assets greatly exceeding the new benefits earned and interest on previously earned benefits as employees get closer to retirement.

In this case it may be better to remove superfunded pension plans to more clearly isolate the effect of multiple employers on funded status however that is out of the scope of today’s analysis.

schsb %>%
  summarise(mean_ad   = mean(SB_ADJ_FNDNG_TGT_PRCNT, na.rm=TRUE), 
            median_ad = median(SB_ADJ_FNDNG_TGT_PRCNT, na.rm=TRUE), 
            n         = n(),
            sd_ad     = sd(SB_ADJ_FNDNG_TGT_PRCNT, na.rm=TRUE),
            var_ad    = var(SB_ADJ_FNDNG_TGT_PRCNT, na.rm=TRUE),
            iqr_ad    = IQR(SB_ADJ_FNDNG_TGT_PRCNT, na.rm=TRUE),
            min_ad    = min(SB_ADJ_FNDNG_TGT_PRCNT, na.rm=TRUE),
            max_ad    = max(SB_ADJ_FNDNG_TGT_PRCNT, na.rm=TRUE))
##    mean_ad median_ad     n    sd_ad   var_ad iqr_ad min_ad max_ad
## 1 125.7874    115.64 39524 51.68257 2671.088  32.34      0 999.99


Dependent Variable: Funding Percentage

Here we show our response variable. This is the plans’ assets divided by their liabilities. This is a measure of the health of pension plans.

schsb$SB_ADJ_FNDNG_TGT_PRCNT <- as.numeric(schsb$SB_ADJ_FNDNG_TGT_PRCNT)/100

qplot(schsb$SB_ADJ_FNDNG_TGT_PRCNT,
     xlab="Funding Percentage",
     xlim=c(0,3),
     bins = 50)


Qualitative Independent Variable: Plan Type

Here we show our independent variable. This is whether the plan benefits employees of a single employer or multiple employers. We will combine the Multi-employer and Multiple-employer groups for our analysis. Please note since there are so many more single employer plans compared to multiple employer plans we will have an issue with arriving at meaningful results.

table(schsb$SB_PLAN_TYPE_CODE)
## 
##     1     2     3 
## 39378    58    88


Exploration of Liability

We’re not going to use total liability as a variable to look at in today’s analysis. A different research question could be; Is there correlation between the size of a pension plan and the likelihood that it’s better funded? The idea being that if a plan is small it might be easier for a sponsor to maintain, but if it’s vast, does that mean sponsors have a harder time coming back from adverse asset or demographic experience? Or in some ways is a larger plan less risky than a smaller plan because of greater access to investing and actuarial resources and greater board oversight and dedicated systems?

schsb$SB_TOT_FNDNG_TGT_AMT <- as.numeric(schsb$SB_TOT_FNDNG_TGT_AMT)

qplot(schsb$SB_TOT_FNDNG_TGT_AMT,
     xlab="Pension Plan Liability in Dollars",
     xlim=c(0,10000000),
     bins = 50)


Part 4 - Inference

Statistical Input

Here we show the variables we will use for our statistical test.

Code Summary
- Create a column to combine both multiple employer plan types
- Display a boxplot comparing single and multiple employer plan types’ funding level

# Create a column to combine both multiple employer plan types
schsb <- schsb %>% 
  mutate(multi = ifelse(schsb$SB_PLAN_TYPE_CODE > 1, "multi", "single"))
# Display a boxplot comparing single and multiple employer plan types' funding level
ggplot(schsb, aes(x=SB_ADJ_FNDNG_TGT_PRCNT, y=multi),
     xlab="Pension Plan Liability in Dollars",
       ) + geom_boxplot(xlab="Pension Plan Liability in Dollars")


Test Selection

The necessary conditions for inference are random, normal and independent. In this case we have access to the entire population of pension plans required to file Form 5500s. The items may not be 100% independent because one employer could sponsor multiple single employer pension plans for different employee populations.

We are going to select a comparison of confidence intervals to determine if there is a difference in funding levels between single and multiple employer plans.


Hypotheses for Testing

Null Hypothesis

H0: Multiple employer plans have the same average funding level as single employer plans.

Alternative Hypothesis

H1: Multiple employer plans have a different average funding level as single employer plans.


Confidence Intervals

Here we have a p-value of 5% and a test statistic of 1.96 to generate 95% confidence intervals.

schsb %>%
  group_by(multi) %>%
  summarise(mean_funding = mean(SB_ADJ_FNDNG_TGT_PRCNT, na.rm = TRUE),
            sd_funding = sd(SB_ADJ_FNDNG_TGT_PRCNT, na.rm = TRUE),
            number_type = n())
## # A tibble: 2 × 4
##   multi  mean_funding sd_funding number_type
##   <chr>         <dbl>      <dbl>       <int>
## 1 multi          1.12      0.296         146
## 2 single         1.26      0.517       39378
CImulti_low <- 112 - 1.96 * 29.6 / sqrt(146)
CImulti_high <- 112 + 1.96 * 29.6 / sqrt(146)

CIsingle_low <- 126 - 1.96 * 51.7 / sqrt(39378)
CIsingle_high <- 126 + 1.96 * 51.7 / sqrt(39378)

Using the formulas above we get a 95% confidence interval for the mean funding level of all multiple employer plan types of (107.1986, 116.8014).

And we get a 95% confidence interval for the mean funding level of all single employer plan types of (125.4894, 126.5106).


Interpretation

Since the intervals do not overlap, we can say with a degree of confidence that there is a statistical difference between the mean funding level of the two groups.


Part 5 - Conclusion

While we were able to determine that Single and Multiple employer plan types have a different mean funding level, it may have been trivial.

We should find a way to filter out super-funded single-employer plans so we can compare again without that influence. Similarly there may be Health and Welfare plans that aren’t penalized for being underfunded that we could remove from the data to reduce variability.

Additionally we could do more exploratory analysis to determine if there are any confounding variables that once isolated are able to show a clearer correlation between Single and Multiple Employer plans and funding level.

This topic is important because pension plans, while available to fewer people in the USA since the advent of the 401(k) in the 1980s, still represents a significant variable in the USA economy. If pension plans were to fail en masse it would have implications for the government budget, corporate sector health, and ultimately spending and hardship experienced by USA’s retirees. If pension plans were to fail en masse it would bankrupt the Pension Benefit Guarantee Corporation, whose assets are currently used by the USA government to balance the budget even though the assets aren’t spendable by the government. Mass pension plan failure would also make it difficult for corporations and organizations sponsoring pension plans to meet their operations budgets. Since there is political incentive to remove undue burdens from corporations and protect retirees, making sure pension plans succeed in satisfying all of their liabilities to pensioners could influence macro economic factors such as the Fed’s interest rate and the Fed’s policy towards inflation.

Consider the largest pension scheme, not included in our data, the Social Security Administration. Knowing factors that contribute to pension plan funded status could help increase solvency with the SSA. In lieu of that understanding, solvency with the SSA could be side-stepped with a policy of higher inflation but at what cost to the economy and average people?

There are limitations of the analysis presented today from a data perspective. We have not looked at potentially confounding variables available in the data such as which State the plan is in. Knowing the state could allow us to layer in additional data about economic disparities between States.

We have not isolated plans that use market value of assets versus asset-smoothing methods. If 2020 had been a year when many pension plans experienced a significant drop in assets, plans with asset-smoothing would have higher than actual asset values.

We have not looked at assumptions that a pension plan could use to arrive at lower liabilities than had they used the average of their peer’s methodologies. A pension plan may have pressure, either to a board, an acquisition partner or other employers interested in participating in the multi-employer plan to portray an optimistic future and may be using assumptions, each of which may be individually reasonable, but collectively may represent an overly optimistic portrayal of the plan’s future.

There are limitations of the analysis presented today from a methodology perspective. We have selected the comparison of confidence intervals for our initial inquiry however there are a number of other statistical models that we could use.

While pension plan terminating in distress, unable to meet their liabilities, are rare and difficult to assess statistically without upsampling or downsampling, we could do a year-over-year comparison of the plans viewed as of 2020 against 2019 to see how many improved their funding levels and if there are common characteristics of plans that improve or have lower funding levels.


References

R Core Team (2019) R: A language and environment for statistical computing. https://www.R-project.org/

Wickham et al. (2019) Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686, https://doi.org/10.21105/joss.01686

DOL (2022) Data made available by the Employee Benefit Security Administration through the Freedom of Information Act https://www.dol.gov/agencies/ebsa/about-ebsa/our-activities/public-disclosure/foia/form-5500-datasets


Appendix

Actuarial Value of Assets are either the market value of assets as of valuation date, or market smoothing can be applied by deferring recognition of asset gains or losses. For two year asset-smoothing, 50% of the asset gains or losses compared to expected returns would be recongized immediately, and the remaining 50% the subsequent year.

Pension Liability is measured by (1) using a cost method to determine how benefits earned are counted, (2) applying assumptions about when participants leave active service, possibly become disabled, elect to start benefits, and die, to create a projected stream of expected future payments. (3) These payments are discounted with segmented interest rates to arrive at a present value, or pension liability as of the valuation date.

Segmented Interest Rates the IRS mandates what interest rates to use to discount expected future payments. Payments in the next five years are discounted at the first rate. Payments in the next 20 years, after the first five years, are discounted at the second rate. Payments further than 20 years out are discounted at the third rate. The IRS mandates which rates to use for purposes of determining contribution requirements however different rules are in effect for accounting purposes or the termination of the pension plan.

Pension Plan Termination is the satisfaction of all pension plan liabilities by paying out lump sums in lieu of retirement benefits or purchasing annuities on behalf of participants. A distress termination is when the sponsor is unable to satisfy the liabilities to the participants and the Pension Benefit Guarantee Corporation has to take over what remaining assets are in the plan to administer the payments going forward. Depending on the facts and circumstances of the sponsor and the distress termination, the PBGC may requisition additional assets from the former sponsor.

Pension Benefit Guarantee Corporation, or the PBGC, is a paragovernmental organization which acts as the mandatory insurance coverage for pension plans to cover administrative services and the payment of (possibly reduced) pension benefits to retirees in the event the sponsor is no longer able to meet obligations such as due to a bankruptcy or a shift in business conditions.