Forecasting Social Security Actuarial Assumptions

Abstract

This paper presents a forecasting model of economic assumptions that are inputs to projections of the Social Security system. Social Security projections are made to help policy-makers understand the financial stability of the system. Because system income and expenditures are subject to changes in law, they are controllable and not readily amenable to forecasting techniques. Hence, we focus directly on the four major economic assumptions to the system: inflation rate, investment returns, wage rate, and unemployment rate. Population models, the other major input to Social Security projections, require special demographic techniques and are not addressed here.

Our approach to developing a forecasting model emphasizes exploring characteristics of the data. That is, we use graphical techniques and diagnostic statistics to display patterns that are evident in the data. These patterns include (1) serial correlation, (2) conditional heteroscedasticity, (3) contemporaneous correlations, and (4) cross-correlations among the four economic series. To represent patterns in the four series, we use multivariate autoregressive, moving average (ARMA) models with generalized autoregressive, conditionally heteroscedastic (GARCH) errors.

The outputs of the fitted models are the forecasts. Because the forecasts can be used for nonlinear functions such as discounting present values of future obligations, we present a computer-intensive method for computing forecast distributions. The computer-intensive approach also allows us to compare alternative models via out-of-sample validation and to compute exact multivariate forecast intervals, in lieu of approximate simultaneous univariate forecast intervals. We show how to use the forecasts of economic assumptions to forecast a simplified version of a fund used to protect the Social Security system from adverse deviations. We recommend the use of the multivariate model because it establishes important lead and lag relationships among the series, accounts for information in the contemporaneous correlations, and provides useful forecasts of a fund that is analogous to the one used by the Social Security system.     

Forecasting Mortality Trends Allowing for Cause-of-Death Mortality Dependence

Longevity risk is among the most important factors to consider for pricing and risk management of longevity products. Past improvements in mortality over many years, and the uncertainty of these improvements, have attracted the attention of experts, both practitioners and academics. Since aggregate mortality rates reflect underlying trends in causes of death, insurers and demographers are increasingly considering cause-of-death data to better understand risks in their mortality assumptions. The relative importance of causes of death has changed over many years. As one cause reduces, others increase or decrease. The dependence between mortality for different causes of death is important when projecting future mortality. However, for scenario analysis based on causes of death, the assumption usually made is that causes of death are independent. Recent models, in the form of Vector Error Correction Models (VECMs), have been developed for multivariate dynamic systems and capture time dependency with common stochastic trends. These models include long-run stationary relations between the variables and thus allow a better understanding of the nature of this dependence. This article applies VECMs to cause-of-death mortality rates to assess the dependence between these competing risks. We analyze the five main causes of death in Switzerland. Our analysis confirms the existence of a long-run stationary relationship between these five causes. This estimated relationship is then used to forecast mortality rates, which are shown to be an improvement over forecasts from more traditional ARIMA processes, which do not allow for cause-of-death dependencies.     

Management earnings forecasts and IPO performance: evidence of a regime change

Companies undertaking initial public offerings (IPOs) in Greece were obliged to include next-year profit forecast in their prospectuses, until the regulation changed in 2001 to voluntary forecasting. Drawing evidence from IPOs issued in the period 1993–2015, this is the first study to investigate the effect of disclosure regime on management earnings forecasts and IPO long-term performance. The findings show mainly positive forecast errors (forecasts are lower than actual earnings) and higher long-term returns during the mandatory period, suggesting that the mandatory disclosure requirement causes issuers to systematically bias profit forecasts downwards as they opt for the safety of accounting conservatism. The mandatory disclosure requirement artificially improves IPO share performance. Overall, our results show that mandatory disclosure of earnings forecasts can impede capital market efficiency once it goes beyond historical financial information to involve compulsory projections of future performance.     

Volatility Forecasting in the Hang Seng Index using the GARCH Approach

The aim of this paper is to add to the literature on volatility forecasting using data from the Hong Kong stock market to determine if forecasts from GARCH based models can outperform simple historical averaging models. Overall, unlike previous studies we find that the GARCH models with non-Normal distributions show a robust volatility forecasting performance in comparison to the historical models. The results indicate that although not all models outperform simple historical averaging, the EGARCH based models, with non-normal conditional volatility, tend to produce more accurate out-of-sample forecasts using both standard measures of forecast accuracy and financial loss functions. In addition we test for asymmetric adjustment in the Hang Seng, finding strong evidence of asymmetries due to the domination of financial and property firms in this market.     

The forecasting ability of correlations implied in foreign exchange options

This paper evaluates the forecasting accuracy of correlations derived from implied volatilities in dollar-mark, dollar-yen, and mark-yen options from January 1989 to May 1995. As a forecast of realized correlation between the dollar-mark and dollar-yen, implied correlation is compared against three alternative forecasts based on time series data: historical correlation, RiskMetrics' exponentially-weighted moving average correlation, and correlation estimated using a bivariate GARCH(1,1) model. At the 1-month and 3-month forecast horizons, we find that implied correlation outperforms, often significantly, these alternative forecasts. In combinations, implied correlation always incrementally improves the performance of other forecasts, but not the converse; in certain cases, historically-based forecasts contribute no incremental information to implied forecasts. The superiority of the implied correlation forecast holds even when forecast errors are weighted by realized variances, reflecting correlation's contribution to the dollar variance of a multicurrency portfolio.     

Predicting stock returns: A regime-switching combination approach and economic links

This paper introduces a regime-switching combination approach to predict excess stock returns. The approach explicitly incorporates model uncertainty, regime uncertainty, and parameter uncertainty. The empirical findings reveal that the regime-switching combination forecasts of excess returns deliver consistent out-of-sample forecasting gains relative to the historical average and the Rapach et al. (2010) combination forecasts. The findings also reveal that two regimes are related to the business cycle. Based on the business cycle explanation of regimes, excess returns are found to be more predictable during economic contractions than during expansions. Finally, return forecasts are related to the real economy, thus providing insights on the economic sources of return predictability.     

Modeling cause-of-death mortality using hierarchical Archimedean copula

Studying changes in cause-specific (or competing risks) mortality rates may provide significant insights for the insurance business as well as the pension systems, as they provide more information than the aggregate mortality data. However, the forecasting of cause-specific mortality rates requires new tools to capture the dependence among the competing causes. This paper introduces a class of hierarchical Archimedean copula (HAC) models for cause-specific mortality data. The approach extends the standard Archimedean copula models by allowing for asymmetric dependence among competing risks, while preserving closed-form expressions for mortality forecasts. Moreover, the HAC model allows for a convenient analysis of the impact of hypothetical reduction, or elimination, of mortality of one or more causes on the life expectancy. Using US cohort mortality data, we analyze the historical mortality patterns of different causes of death, provide an explanation for the ‘failure’ of the War on Cancer, and evaluate the impact on life expectancy of hypothetical scenarios where cancer mortality is reduced or eliminated. We find that accounting for longevity improvement across cohorts can alter the results found in existing studies that are focused on one single cohort.     

Statistical Inference for Lee-Carter Mortality Model and Corresponding Forecasts

Although the Lee-Carter model has become a benchmark in modeling mortality rates, forecasting mortality risk, and hedging longevity risk, some serious issues exist on its inference and interpretation in the actuarial science literature. After pointing out these pitfalls, this article proposes a modified Lee-Carter model, provides a rigorous statistical inference, and derives the asymptotic distributions of the proposed estimators and unit root test when the mortality index is nearly integrated and errors in the model satisfy some mixing conditions. After a unit root hypothesis is not rejected, future mortality forecasts can be obtained via the proposed inference. An application of the proposed unit root test to U.S. mortality rates rejects the unit root hypothesis for the female and combined mortality rates but does not reject the unit root hypothesis for the male mortality rates.     

Evaluating Interest Rate Covariance Models Within a Value-at-Risk Framework

A key component of managing international interest rate portfoliosis forecasts of the covariances between national interest ratesand accompanying exchange rates. How should portfolio managerschoose among the large number of covariance forecasting modelsavailable? We find that covariance matrix forecasts generatedby models incorporating interest-rate level volatility effectsperform best with respect to statistical loss functions. However,within a value-at-risk (VaR) framework, the relative performanceof the covariance matrix forecasts depends greatly on the VaRdistributional assumption, and forecasts based just on weightedaverages of past observations perform best. In addition, portfoliovariance forecasts that ignore the covariance matrix generatethe lowest regulatory capital charge, a key economic decisionvariable for commercial banks. Our results provide empiricalsupport for the commonly used VaR models based on simple covariancematrix forecasts and distributional assumptions.     

Processes and Accuracy of Cash Flow Forecasting: A Case Study of a Multinational Corporation

Despite its pivotal importance in enterprise management, cash flow forecasting gets little attention from academics perhaps because few of them have access to internal processes and data. In this article, however, the authors explain how cash flow forecasting is organized at Bayer, a large multinational company headquartered in Germany, and which factors influence the accuracy of its forecasts. The research focuses on cash flow forecasts based on the direct method, prepared three times a yearat Bayer, involving about 62,000 individual forecasting items each time. These forecasts form the basis of the company's liquidity and financial risk management, in particular, its foreign exchange risk hedging. The authors explain how local managers in Bayer's entities across the world derive the forecasts, i.e., what information they use as input, how they validate it, and how they deal with potential bias caused by managerial incentive systems. They also analyze whether forecasting processes are affected by characteristics such as business area, size, region, or specific local conditions, and ultimately whether forecasting practices and entity characteristics affect forecast accuracy. The findings show that cash flow forecasting procedures vary substantially across Bayer. While the central finance department gives general guidance on the required cash flow forecasting output and provides direction on the input to be used, there are no detailed instructions on how forecasts are to be prepared. Instead, local managers are free to determine their own forecasting practices. They use different forecasting inputs and validate forecasting inputs and output with different intensities, and they also differ in how they treat possible biases in input data. These findings document the limits of standardization and central control in large multinational corporations resulting from local managers’ need for flexibility to cope with the heterogeneity and dynamism of their environments. At the same time, however, local differentiation increases complexity and may increase errors. Quantitative analysis of forecasting errors shows that forecasts of receipts from customers (cash inflows) are more accurate than forecasts of payments to suppliers (cash outflows). Moreover, forecasting practices affect forecast accuracy. Outflow forecasts are more accurate if managers intensively validate forecasting input; inflow forecasts, if they eliminate input biases that may result from internal target setting or from other managerial incentives, and if they carefully validate their forecasting output. The study provides several insights.

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