Mathematical Models and Statistical Methods

Estimated Retirement Benefits in the Social Security Statement

The Out-of-Sample Performance of Stochastic Methods in Forecasting Age-Specific Mortality Rates

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).

Literature Review of Long-Term Mortality Projections

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.

Statistical Methods for the Estimation of Costs in the Medicare Waiting Period for Social Security Disabled Worker Beneficiaries

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.

A Note on Maximum Likelihood Estimation of Discrete Choice Models from the 1978 Survey of Disability and Work

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

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

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.

Selection of Simple and Stratified Random Samples of Fixed Size Without Replacement

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

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.