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Mathematical Models and Statistical Methods

Accounting for Geographic Variation in Social Security Disability Program Participation
from Social Security Bulletin, Vol. 78, No. 2 (released May 2018)
by John Gettens, Pei-Pei Lei, and Alexis D. Henry

There is wide geographic variation in Social Security Disability Insurance and Supplementary Security Income participation across the United States. The authors describe the variation. Using data from Social Security Administration reports and results from the Census Bureau's American Community Survey, the authors decompose the geographic variation in program participation into component parts including variation in disability prevalence and variation in program participation among working-age persons with disabilities. The variation in participation among persons with disabilities is further decomposed into socioeconomic subcomponents.

A Field Guide to Social Security Distributional Analysis
Research and Statistics Note No. 2017-02 (released December 2017)
by Mark A. Sarney

A stylized example neatly and efficiently answers the question of how much Social Security benefits would change because a stylized worker's situation is straightforward and does not require demographic or statistical knowledge to understand. However, it leaves other questions unanswered, such as how many people are like that worker and would anyone fall into poverty? To answer these types of questions, you need to use distributional analysis, which examines how something, such as income, benefits, or policy effects, is distributed across a group of people. This note describes the use of distributional analysis in Social Security policy discussions by analyzing the distributional effects of three real-life Social Security policy options.

Exits from the Disability Insurance Rolls: Estimates from a Competing-Risks Model
from Social Security Bulletin, Vol. 77, No. 3 (released August 2017)
by Lakshmi K. Raut

This article explores the causes of growth in the number of disabled workers on the Social Security Disability Insurance (DI) rolls from 1980 through 2010 by estimating the probability of a DI beneficiary's program exit because of recovery, death, or conversion to retired-worker beneficiary. The author uses Social Security administrative data and a competing-risks model to estimate DI exit probabilities by cause and beneficiary sex, age, and disability type. Cumulative exit probabilities are calculated for beneficiaries over their first 9 years on the DI rolls. The author also examines possible changes over time by comparing outcomes for the 1980s with those for the 1990s.

Discount Rate Specification and the Social Security Claiming Decision
from Social Security Bulletin, Vol. 76, No. 2 (released May 2016)
by Brian J. Alleva

Choosing the claiming age that maximizes the expected present value of lifetime Social Security retirement benefits requires a survival function to account for an individual's prospective longevity along with the specification of a rate by which to discount the future benefit payments for each claiming age. This article evaluates optimal claiming ages for prospective beneficiaries across a range of 81 real discount rate options (specified in increments of one-tenth of 1 percent) from 0 percent to 8 percent, considering the survival functions for men and women born in 1952. It examines the implications of choosing a given rate as well as the sensitivity of the optimal claiming age to a specific rate choice.

Longitudinal Patterns of Disability Program Participation and Mortality Across Childhood SSI Award Cohorts
from Social Security Bulletin, Vol. 75, No. 1 (released February 2015)
by Kalman Rupp, Jeffrey Hemmeter, and Paul S. Davies

This article follows six annual cohorts of childhood Supplemental Security Income (SSI) disability awardees between 1980 and 2000, for a time horizon up to 30 years after initial SSI award, in many cases well into adulthood. The authors compare trajectories of successive awardee cohorts as the SSI program evolves from 1980 to recent years. The results show that the proportion of awardees in SSI-only status declines over the life cycle, with over half transitioning to other statuses roughly after 10 to 15 years. Many awardees transition from the SSI program to concurrent or Disability Insurance–only benefit status, and increasing proportions of awardees are deceased or off the rolls and alive. These patterns are common for all awardee cohorts, but there are major changes in trajectories across cohorts. Compared with the early cohorts, the more recent cohorts display sharper declines in mortality and steeper increases in the proportion off the disability rolls for other reasons. These two trends have opposite effects on the duration of disability program participation over the life cycle, with important policy implications.

Recruitment in the Mental Health Treatment Study: A Behavioral Health/Employment Intervention for Social Security Disabled-Worker Beneficiaries
from Social Security Bulletin, Vol. 74, No. 2 (released May 2014)
by David S. Salkever, Brent Gibbons, William D. Frey, Roline Milfort, Julie Bollmer, Thomas W. Hale, Robert E. Drake, and Howard H. Goldman

The recent development of evidence-based behavioral health and vocational rehabilitation interventions for persons with serious psychiatric impairments created the impetus for exploring the efficacy of those interventions if they were widely available to Social Security Disability Insurance beneficiaries. As a first step in this endeavor—a multisite randomized trial for providing interventions to beneficiaries with psychiatric impairments—the Mental Health Treatment Study was implemented. The authors report on the subject recruitment patterns for the study, including assessment of take-up rates, and on the statistical analysis of the relationships between beneficiaries' characteristics and the probability of enrollment. Results indicated that take-up rates among potential MHTS subjects with confirmed telephone contacts met or exceeded rates for previous Social Security Administration randomized trials, and beneficiaries with administrative records of recent vocational or labor-market activity were most likely to enroll. The authors discuss implications of their analyses on recruitment in similar interventions in the future.

The Effects of Alternative Demographic and Economic Assumptions on MINT Simulations: A Sensitivity Analysis
Research and Statistics Note No. 2014-03 (released April 2014)
by Patrick J. Purcell and Dave Shoffner

The Social Security Administration's (SSA's) Modeling Income in the Near Term (MINT) estimates income/wealth of future retirees. Estimates are based on demographic information from the Survey of Income and Program Participation: individual earnings histories and projections of interest rates, wage growth, mortality rates, and disability rates. Historically, MINT simulations were based exclusively on SSA's Office of the Chief Actuary's (OCACT's) intermediate-cost projections of key demographic/economic variables. The authors present the results of a sensitivity analysis in which they ran MINT using OCACT's low-cost/high-cost projections of mortality and disability trends. Those simulations estimated characteristics of the population aged 65 or older in 2040 under alternative projections of mortality/disability trends. The authors then describe simulations in which future real rates of return on stocks held in retirement accounts differ from the historical mean real rate of return used in baseline simulations. Sensitivity analyses can help MINT users choose model parameters with the greatest impact on simulation results.

Growth in New Disabled-Worker Entitlements, 1970–2008
from Social Security Bulletin, Vol. 73, No. 4 (released November 2013)
by David Pattison and Hilary Waldron

We find that three factors—(1) population growth, (2) the growth in the proportion of women insured for disability, and (3) the movement of the large baby boom generation into disability-prone ages—explain 90 percent of the growth in new disabled-worker entitlements over the 36-year subperiod (1972–2008). The remaining 10 percent is the part attributable to the disability “incidence rate.” Looking at the two subperiods (1972–1990 and 1990–2008), unadjusted measures appear to show faster growth in the incidence rate in the later period than in the earlier one. This apparent speedup disappears once we account for the changing demographic structure of the insured population. Although the adjusted growth in the incidence rate accounts for 17 percent of the growth in disability entitlements in the earlier subperiod, it accounts for only 6 percent of the growth in the more recent half. Demographic factors explain the remaining 94 percent of growth over the 1990–2008 period.

Social Security Income Measurement in Two Surveys
from Social Security Bulletin, Vol. 73, No. 3 (released August 2013)
by Howard M. Iams and Patrick J. Purcell

The deduction of Medicare premiums from Social Security benefit payments complicates the estimation of Social Security income in household surveys. Although the Census Bureau's Current Population Survey (CPS) and Survey of Income and Program Participation (SIPP) both aim to collect and record gross Social Security benefit income before Medicare premium deductions, comparing the survey data with Social Security records indicates that the CPS and SIPP estimates differ and suggests that some survey respondents may report net benefit income.

Outcome Variation in the Social Security Disability Insurance Program: The Role of Primary Diagnoses
from Social Security Bulletin, Vol. 73, No. 2 (released May 2013)
by Javier Meseguer

This article investigates the role that primary impairments play in explaining heterogeneity in disability decisions. Using claimant-level data within a hierarchical framework, the author explores variation in outcomes along three dimensions: state of origin, adjudicative stage, and primary diagnosis. The findings indicate that the impairments account for a substantial portion of claimant-level variation in initial allowances. Furthermore, the author finds that the predictions of an initial and a final allowance are highly correlated when applicants are grouped by impairment. In other words, diagnoses that are more likely to result in an initial allowance also tend to be more likely to receive a final allowance.

Modeling Behavioral Responses to Eliminating the Retirement Earnings Test
from Social Security Bulletin, Vol. 73, No. 1 (released February 2013)
by Anya Olsen and Kathleen Romig

The retirement earnings test (RET) is an often-misunderstood aspect of the Social Security program. Policymakers have proposed reforming the RET as a way to encourage working at older ages. However, this could also cause earlier benefit claiming. We use Modeling Income in the Near Term data to analyze the complete repeal of the earnings test for beneficiaries aged 60 or older, first assuming no behavioral responses to repeal and secondly assuming changes to benefit claiming and workforce participation behaviors. Our lifetime results show that the assumed behavioral response—particularly the benefit claiming change—has a bigger effect than the RET policy change itself.

Factors Affecting Initial Disability Allowance Rates for the Disability Insurance and Supplemental Security Income Programs: The Role of the Demographic and Diagnostic Composition of Applicants and Local Labor Market Conditions
from Social Security Bulletin, Vol. 72, No. 4 (released November 2012)
by Kalman Rupp

Various factors outside the control of decision makers may affect the rate at which disability applications are allowed or denied during the initial step of eligibility determination in the Social Security Disability Insurance (DI) and Supplemental Security Income (SSI) programs. This article, using individual-level data on applications, focuses on the role of three important factors—the demographic characteristics of applicants, the diagnostic mix of applicants, and the local unemployment rate—in affecting the probability of an initial allowance and state allowance rates. A random sample of initial determination administrative records for the 1993–2008 period is used for the analysis in a fixed-effects multiple regression framework. The empirical results show that the demographic and diagnostic characteristics of applicants and the local unemployment rate substantially affect the initial allowance rate. An increase in the local unemployment rate tends to be associated with a decrease in the initial allowance rate. This negative relationship holds for adult applicants in both the DI and SSI programs and for SSI childhood applicants.

The Sensitivity of Proposed Social Security Benefit Formula Changes to Lifetime Earnings Definitions
from Social Security Bulletin, Vol. 72, No. 2 (released May 2012)
by Hilary Waldron

Several Social Security proposals have included benefit formula changes that apply to earners above a specified percentage of the combined male and female (unisex) lifetime earnings distribution. This study finds that if Social Security's median unisex average indexed monthly earnings (AIME) amount is used to define an earnings threshold below which benefits will be held unreduced, the percentage of fully insured men subject to benefit reductions (70 percent) will exceed the unisex estimate of the population subject to benefit reductions (50 percent) by 20 percentage points. If policymakers wish to adjust future benefits and focus benefit reductions on middle or high primary or full-time wage earners in a household, the male, rather than unisex, AIME would come closer to achieving such a goal.

Using Matched Survey and Administrative Data to Estimate Eligibility for the Medicare Part D Low-Income Subsidy Program
from Social Security Bulletin, Vol. 70, No. 2 (released May 2010)
by Erik Meijer, Lynn A. Karoly, and Pierre-Carl Michaud

This article uses matched survey and administrative data to estimate, as of 2006, the size of the population eligible for the Low-Income Subsidy (LIS), which was designed to provide "extra help" with premiums, deductibles, and copayments for Medicare Part D beneficiaries with low income and limited assets. The authors employ individual-level data from the Survey of Income and Program Participation and the Health and Retirement Study to cover the potentially LIS-eligible noninstitutionalized and institutionalized populations of all ages. The survey data are matched to Social Security administrative data to improve on potentially error-ridden survey measures of income components and program participation.

Access Restrictions and Confidentiality Protections in the Health and Retirement Study
Research and Statistics Note No. 2009-01 (released July 2009)
by Lionel P. Deang and Paul S. Davies

Organizations involved in statistical surveys of human subjects face two important and competing challenges: protecting data confidentiality while maximizing data accessibility to potential researchers. This note examines how the Health and Retirement Study (HRS), conducted by the Institute for Social Research of the University of Michigan, attempts to balance data confidentiality with the desire to broaden the pool of potential data users. Current HRS procedures are summarized and compared with those of organizations with similar programs, and potential ways to expand HRS use without compromising confidentiality are discussed.

A Progressivity Index for Social Security
Issue Paper No. 2009-01 (released January 2009)
by Andrew G. Biggs, Mark A. Sarney, and Christopher R. Tamborini

Using the Social Security Administration's MINT (Modeling Income in the Near Term) model, this paper analyzes the progressivity of the Old-Age, Survivors and Disability Insurance (OASDI) program for current and future retirees. It uses a progressivity index that provides a summary measure of the distribution of taxes and benefits on a lifetime basis. Results indicate that OASDI lies roughly halfway between a flat replacement rate and a flat dollar benefit for current retirees. Projections suggest that progressivity will remain relatively similar for future retirees. In addition, the paper estimates the effects of several policy changes on progressivity for future retirees.

The Effects of Wage Indexing on Social Security Disability Benefits
from Social Security Bulletin, Vol. 68, No. 3 (released December 2008)
by L. Scott Muller

Researchers David Autor and Mark Duggan have hypothesized that the Social Security benefit formula using the average wage index, coupled with a widening distribution of income, has created an implicit rise in replacement rates for low-earner disability beneficiaries. This research attempts to confirm and quantify the replacement rate creep identified by Autor and Duggan using actual earnings histories of disability-insured workers over the period 1979–2004. The research finds that disability replacement rates are rising for many insured workers, although the effect may be somewhat smaller than that suggested by Autor and Duggan.

The Out-of-Sample Performance of Stochastic Methods in Forecasting Age-Specific Mortality Rates
ORES Working Paper No. 111 (released August 2008)
by Javier Meseguer

This paper evaluates the out-of-sample performance of two stochastic models used to forecast age-specific mortality rates: (1) the model proposed by Lee and Carter (1992); and (2) a set of univariate autoregressions linked together by a common residual covariance matrix (Denton, Feavor, and Spencer 2005).

Social Security Cost-of-Living Adjustments and the Consumer Price Index
from Social Security Bulletin, Vol. 67, No. 3 (released April 2008)
by Clark Burdick and T. Lynn Fisher

Old-Age, Survivors, and Disability Insurance (OASDI, Social Security) benefits are indexed for inflation to protect beneficiaries from the loss of purchasing power implied by inflation. In the absence of such indexing, the purchasing power of Social Security benefits would be eroded as rising prices raised the cost of living. Recently, the Consumer Price Index used to calculate the Cost-of-Living-Adjustment (COLA) for OASDI benefits has come under increased scrutiny. Some argue that the current index does not accurately reflect the inflation experienced by seniors and that COLAs should be larger. Others argue that the measure of inflation underlying the COLA has technical limitations that cause it to overestimate changes in the cost of living and that COLAs should be smaller. This article discusses some of the issues involved with indexing Social Security benefits for inflation and examines the ramifications of potential changes to COLA calculations.

Benefit Adequacy Among Elderly Social Security Retired-Worker Beneficiaries and the SSI Federal Benefit Rate
from Social Security Bulletin, Vol. 67, No. 3 (released April 2008)
by Kalman Rupp, Alexander Strand, Paul S. Davies, and James Sears

The federal benefit rate (FBR) of the Supplemental Security Income program provides an inflation-indexed income guarantee for aged and disabled people with low assets. Some consider the FBR as an attractive measure of Social Security benefit adequacy. Others propose the FBR as an administratively simple, well-targeted minimum Social Security benefit. However, these claims have not been empirically tested. Using microdata from the Survey of Income and Program Participation, this article finds that the FBR is an imprecise measure of benefit adequacy; it incorrectly identifies as economically vulnerable many who are not poor, and disregards some who are poor. The reason for this is that the FBR-level benefit threshold of adequacy considers the Social Security benefit in isolation and ignores the family consumption unit. The FBR would provide an administratively simple but poorly targeted foundation for a minimum Social Security benefit. The empirical estimates quantify the substantial tradeoffs between administrative simplicity and target effectiveness.

Literature Review of Long-Term Mortality Projections
from Social Security Bulletin, Vol. 66, No. 1 (released September 2005)
by Hilary Waldron

The Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance (OASDI) Trust Funds reports on the current and projected future financial status of the trust funds annually. The Trustees project trust fund finances 75 years into the future. Mortality is one key demographic assumption that feeds into these long-range projections. This article reviews a range of predictions about long-term mortality improvement and assesses where the Trustees' 75-year mortality projection falls within this range. In general, the predictions of future mortality declines in the 2004 Social Security Trustees Report tend to be in the mainstream of professional actuarial and international official government opinion and to be lower than the majority of the small group of demographers who produce comparable estimates.

Income Growth and Future Poverty Rates of the Aged
ORES Working Paper No. 94 (released September 2001)
by Seyda G. Wentworth and David Pattison

This paper estimates effects on elderly poverty rates of a steady growth in incomes for 50 years. It assumes that the poverty threshold continues to be adjusted for inflation but not for increases in real incomes. Simulations with the March 1998 Current Population Survey indicate that if Social Security and Supplemental Security Income (SSI) benefit rules are not changed and if earnings and other incomes grow by 1 percent per year (the growth rate in earnings assumed in the Social Security Trustees' Report intermediate scenario) in an otherwise unchanging population, poverty among the elderly will decrease from 10.5 percent to about 7.7 percent in 2020 and to 4.8 percent in 2047. Those projected poverty rates are quite sensitive to the earnings growth rate assumption and to the assumption that benefits are not further reduced to maintain solvency. The paper quantifies the sensitivity to these assumptions and discusses several other aspects that might affect future poverty rates—changes in other income components like SSI, earnings, and pensions; changes in longevity and marital patterns; and changes in the distribution of earnings.

A Guide to Social Security Money's Worth Issues
ORES Working Paper No. 67 (released April 1995)
by Dean R. Leimer

This paper discusses some of the major issues associated with the question of whether workers receive their money's worth from the Social Security program. An effort is made to keep the discussion as nontechnical as possible, with explanations provided for many of the technical terms and concepts found in the money's worth literature. Major assumptions, key analytical methods, and money's worth measures used in the literature are also discussed. Finally, the key findings of money's worth studies are summarized, with some cautions concerning the limitations and appropriate usage of money's worth analyses.

Statistical Methods for the Estimation of Costs in the Medicare Waiting Period for Social Security Disabled Worker Beneficiaries
ORES Working Paper No. 37 (released March 1989)
by Barry V. Bye and Gerald F. Riley

This paper presents the statistical methods used to estimate Medicare costs in the waiting period that were presented in text tables 2–3 of Bye and Riley (1989). The first part describes the development of Medicare utilization equations for each Social Security Disability Insurance (DI) program status group. The second part describes how these equations were used to predict expected costs per month and how the monthly estimates were aggregated to yield estimates of costs in the full 2-year waiting period and in the second year only. Finally, there is a brief discussion of the accuracy of the predictions.

Econometric Models and the Study of the Economic Effects of Social Security
from Social Security Bulletin, Vol. 47, No. 10 (released October 1984)
by John C. Hambor
A Note on Maximum Likelihood Estimation of Discrete Choice Models from the 1978 Survey of Disability and Work
ORES Working Paper No. 28 (released November 1982)
by Barry V. Bye and Salvatore J. Gallicchio

This paper demonstrates an alternative maximum likelihood procedure for estimating discrete choice models in retrospective samples, such as a model of SSA disability beneficiaries or application status in the 1978 Survey of Disability and Work.

Testing the Predictive Power of a Proportional Hazards Semi-Markov Model of Postentitlement Histories of Disabled Male Beneficiaries
ORES Working Paper No. 29 (released November 1982)
by John C. Hennessey

In the Disability Amendments of 1980 (P.L. 96-265), Congress mandated that certain experiments be carried out which are designed to encourage disabled beneficiaries to return to work and save trust fund monies. A research plan has been developed which would offer alternative program provisions, experimentally, to different samples of beneficiaries. An observation period of three to four years will be possible before a report to Congress must be written. However, a period of this length is not sufficient to observe, fully, the postentitlement experience of disabled beneficiaries. In order to estimate the long run effects of the experiments, a method is needed which can project postentitlement behavior beyond the observation period.

This paper tests the ability of proportional hazards semi-Markov model to make accurate predictions in this type of setting. The data are divided into two segments: the first 14 calendar quarters and the last 16 quarters. Various types of rate functions including proportional hazards rate functions are estimated on the first segment, then projected over the entire 30 quarters and compared to the actual data. The proportional hazards rate functions are then used in a simulation to estimate monthly benefit cost to the social security disability trust fund over the last 16 quarters, using an age-dependent, absorbing, semi-Markov model. The model does a very good job of capturing the dynamics of the process and should prove quite useful as one of the major components in an analysis of the Work Incentive Experiments.

Estimation of Disability Status as a Single Latent Variable in a Model with Multiple Indicators and Multiple Causes
ORES Working Paper No. 26 (released April 1982)
by Barry V. Bye, Janice M. Dykacz, and Jesse M. Levy

In this paper, we are concerned with the underlying structure of self-definitions of disability. Our purpose is to identify the contribution of exertional and nonexertional impairment and the contributions of such nonmedical factors as age, sex, and education to the individuals' assessment of their own situations. On a statistical level, we seek to accomplish a substantial reduction of a large number of data items into a form that can be used conveniently in subsequent behavioral analyses.

Economic Forecasting: Effect of Errors on OASDI Fund Ratios
from Social Security Bulletin, Vol. 45, No. 1 (released January 1982)
by Dwight K. Bartlett III and Joseph A. Applebaum
Long-Range Projection of Average Benefits Under OASDI
from Social Security Bulletin, Vol. 45, No. 1 (released January 1982)
by Steven F. McKay
The Income Survey Development Program: Design Features and Initial Findings
from Social Security Bulletin, Vol. 44, No. 11 (released November 1981)
by Martynas A. Yčas and Charles A. Lininger
Countercyclical U.S. Fertility and its Implications
from Social Security Bulletin, Vol. 42, No. 8 (released August 1979)
by William P. Butz and Michael P. Ward
Selection of Simple and Stratified Random Samples of Fixed Size Without Replacement
ORES Working Paper No. 9 (released June 1979)
by Michael H. Bostron

For the past few years, the Division of Disability Studies has been using simple random and stratified random sampling procedures for many of its studies. The beneficiary sample for the 1978 Survey of Disability and Work was a stratified random sample drawn from the Master Benefit Record. The samples used in the Study of Consistency and Validity of Initial Disability Decisions and the Trial Work Period Folder Study also used simple random sampling procedures. Simple random subsampling has been used to enable multivariate analysis to be performed on files that would otherwise have been too large for existing software.

Because of the Division of Disability Studies' wide use of simple and stratified random sampling designs, software was developed to efficiently accomplish these sampling schemes. This paper describes the algorithm and presents the computer programs that are currently being used in the division.

A Causative Matrix Approach to Mobility Studies
ORES Working Paper No. 5 (released April 1979)
by Barry V. Bye and John C. Hennessey

Markov models have been widely used for the analysis and prediction of shifts in population distribution over time. The point of departure for most of these analyses has been the finite state, time stationary Markov chain. The usual Markov chain model has, however, been shown to be inadequate for most social science applications.

This paper presents a particular kind of discrete time nonstationary Markov chain. Such chains will be built using a mathematical quantity called a causative matrix.