Stochastic Infinite Horizon Forecasts for Social Security and Related Studies
This paper consists of three reports on stochastic forecasting for Social Security, on infinite horizons, immigration, and structural time series models. 1) In our preferred stochastic immigration forecast, total net immigration drops from current levels down to about one million by 2020, then slowly rises to 1.2 million at the end of the century, with 95% probability bounds of 800,000 to 1.8 million at the century's end. Adding stochastic immigration makes little difference to the probability
... to the probability distribution of the old age dependency ratio. 2) We incorporate parameter uncertainty, stochastic trends, and uncertain ultimate levels in stochastic models of wage growth and fertility. These changes sometimes substantially affect the probability distributions of the individual input forecasts, but they make relatively little difference when embedded in the more fully stochastic Social Security projection. 3) Using a 500-year stochastic projection, we estimate an infinite horizon balance of -5.15% of payroll, compared to the -3.5% of the 2004 Trustees Report, probably reflecting different mortality projections. Our 95% probability interval bounds are -10.5 and -1.3%. Such forecasts, which reflect only "routine" uncertainty, have many problems but nonetheless seem worthwhile. This report consists of three sub-reports, which are listed below, followed by brief summaries of the conclusions of each. Report I. A Probabilistic Forecast of Net Migration to the United States. (Miller and Lee) Summary of Conclusions 1. Given the history of immigration to the US, a number of key assumptions must be made without a satisfactorily firm basis, such as whether to model numbers or rates, over what historical period to fit the model, and whether to include a trend in the forecast, or to impose central tendency based on expert opinion. 2. Experiments with a variety of approaches suggest that the probability distribution of the immigration forecast is not highly sensitive to these variations, although forecasts of the rate, with a trend, do lead to forecasts of higher numbers in the future. 3. Our preferred projection is based on numbers of immigrants rather than rates, and randomly samples trends between 0 and the historical average for each sample path. In this case, the projected number of net immigrants (legal and illegal) drops from current levels down to about one million in 2020, and then slowly rises to 1.2 million at the end of the century. The lower 2.5% probability bound is near 800,000 throughout the century, after the first decade or two. The upper 97.5% bound starts at 1.3 million, and rises quite linearly to 1.8 million at the end of the century. 4. With this range of models and forecasts, including immigration in the population forecasts makes little difference to the probability distribution of the old age dependency ratio, which is the item of prime importance for the Social Security forecasts. Report II. Structural time series models and parameter uncertainty in Stochastic Projections of Social Security Finances. (Anderson and Lee) Summary of Conclusions We have experimented with a variety of different specifications of the time series models for wage growth and fertility, which are two of the key inputs for the projections. The expectation was that introducing parameter uncertainty, stochastically varying trends terms, and uncertain ultimate levels, would make the projections more uncertain. We did indeed find this to be so in every case, although one version of Homer's model, in which fertility was first logged, then modeled, then exponentiated, turned out to give a narrower probability interval than our other models including the standard ones. In some cases, the change in probability intervals for the individual input series was very slight, for example when parameter uncertainty was introduced to the fertility model, or when we used structural methods for wage growth. The big differences come from using an uncertain ultimate level for wage growth, or a structural estimate for fertility. Although some of these new models have a substantial effect on the estimated probability distributions for the forecasts of the inputs themselves, they seem to make much less difference when they are embedded in a more fully stochastic Social Security projection. This is good news for the stochastic projections, because it suggests that they are not so sensitive to the specifications of the input series as one might have feared. This is true in our stochastic forecasting model which has only four stochastic inputs. It would be even 2 more true in the forecasting models of Social Security and CBO with their greater number of inputs. One would not want to push this argument too far, of course. Ultimately, the stochastic forecasts of Social Security are only as good as the stochastic forecasts of the key input series. Report III. Stochastic Infinite Horizon Forecasts of Social Security Sustainability. (Lee and Anderson). Summary of Conclusions 1) Many issues surround infinite horizon forecasts, and the whole enterprise can certainly be questioned. Nonetheless, we have found it useful simply to extend the range of the stochastic forecasting models to very distant horizons. We call these "routine" or "business as usual" stochastic forecasts, because their uncertainty does not reflect the possibility of structural shifts. They understate actual uncertainty. 2) Both the Flat Fund Ratio Tax measure and the Unstable measure are useful simple approximations to the deterministic or median infinite horizon open group imbalance measure. The Flat Fund Ratio is the immediate and permanent tax increase that would be needed to hold the ratio of the Trust Fund to Costs constant over the last two years of the 75-year projection. It is more intuitive and therefore easier to explain than the Unstable measure, but it underestimates the imbalance, whereas the Unstable measure (explained in the report) gives a very good approximation to the infinite horizon measure, at least under current circumstances. 3) The 2004 Trustees Report indicates an infinite horizon open group imbalance equal to 3.5% of payroll, consistent with Lee and Yamagata's (2003) calculation using SSA mortality assumptions. Based on our 500-year projection with our own mortality forecasts, we estimate it to be 5.15%, substantially larger. Our two simple methods, based on our 75 year projections, indicate levels of 4.36% for the Flat Fund Ratio measure, and 5.21% for the Unstable measure. 4) Good estimates of the uncertainty of the simple measures cannot be derived from stochastic forecasts over the 75 year horizon, at least using the methods we have attempted. Therefore the simple measures are useful only for central tendency. 5) The "routine" uncertainty surrounding the infinite horizon estimates of Summary Actuarial Balance is about 40% greater than the uncertainty of the 75 year projections: the 95% probability interval is 9% wide versus 6.5% for the 75-year horizon. 6) Raising tax rates immediately by an amount intended to achieve sustainability would imply substantial chances of huge Trust Fund accumulations that neither could nor should be realized in practice, at least not through holdings of government bonds. Adaptive policies that maintain the Trust Fund ratio at a desirable level seem more attractive, but have not yet been explored.