# Stochastic Models of the Social Security Trust Funds

by Clark Burdick and Joyce Manchester
Social Security Bulletin, Vol. 65 No. 1, 2003/2004

## Text descriptions and table equivalents for three panels of Chart 1.Trust fund ratio projections from the CBOLT, TL, and OCACT stochastic models

### CBOLT model

This fan chart depicts various percentiles of the simulated trust fund ratios from the CBOLT model over time. The 2.5th and 97.5th percentiles are shown in addition to the 9 deciles from 10% to 90%. The line representing the 2.5th percentile rises steadily from its initial value (the 2002 trust fund ratio) of 2.81, reaches a peak of 3.72 in 2009, and then steadily declines until hitting zero in 2025 (the trust fund exhaustion date). Each higher percentile has the same basic shape, with the exception of the 97.5th percentile, but lies everywhere above the lower percentiles. The 97.5th percentile reaches its peak, begins a moderate decline with some minor fluctuations before beginning a steeper decline about 2052. For each percentile shown, the 2002 trust fund ratio, the peak trust fund ratio and the year in which the peak value was attained are listed in the following table. Also listed in the following table are the trust fund exhaustion dates (the years in which the trust fund ratio hits zero) for each percentile.

Trust fund ratios, peak year, and exhaustion year for the CBOLT model, by percentile
2.50% 10% 20% 30% 40% 50% 60% 70% 80% 90% 97.50%
2002 trust fund ratio 2.81 2.84 2.86 2.88 2.90 2.91 2.92 2.94 2.95 2.97 3.00
Peak trust fund ratio 3.72 3.92 4.16 4.36 4.54 4.73 4.97 5.21 5.53 6.00 6.77
Peak year 2009 2011 2011 2012 2013 2013 2014 2015 2016 2018 2018
Exhaustion year 2025 2028 2031 2032 2034 2037 2039 2043 2048 2063 a
a. The 97.5th percentile for the CBOLT model does not indicate trust fund exhaustion by 2076, the last year shown in the graph. The final trust fund ratio in that year is 2.84.

### TL Model

This fan chart depicts various percentiles of the simulated trust fund ratios from the TL model over time. The 2.5th and 97.5th percentiles are shown in addition to the 9 deciles from 10% to 90%. The line representing the 2.5th percentile rises steadily from its initial value (the 2002 trust fund ratio) of 2.71, reaches a peak of 3.22 in 2007, and then declines steadily until hitting zero in 2026 (the trust fund exhaustion date). Each higher percentile has the same basic shape, with the exception of the 97.5th percentile, but lies everywhere above the lower percentiles. The 97.5th percentile reaches its peak, begins a very gradual decline with some moderate fluctuations before beginning a steeper decline in about 2050. For each percentile shown, the 2002 trust fund ratio, the peak trust fund ratio and the year in which the peak value was attained are listed in the following table. Also listed in the following table are the trust fund exhaustion dates for each percentile.

Trust fund ratios, peak year, and exhaustion year for the TL model, by percentile
2.50% 10% 20% 30% 40% 50% 60% 70% 80% 90% 97.50%
2002 trust fund ratio 2.71 2.71 2.71 2.71 2.71 2.71 2.71 2.71 2.71 2.71 2.71
Peak trust fund ratio 3.22 3.55 3.79 4.10 4.34 4.60 4.91 5.19 5.59 6.50 8.30
Peak year 2007 2010 2012 2012 2013 2014 2014 2016 2017 2018 2019
Exhaustion year 2026 2029 2031 2033 2035 2037 2040 2043 2047 2056 a
a. The 97.5th percentile for the CBOLT model does not indicate trust fund exhaustion by 2076, the last year shown in the graph. The final trust fund ratio in that year is 0.85.

### OCACT model

This fan chart depicts various percentiles of the simulated trust fund ratios from the OCACT model over time. The 2.5th and 97.5th percentiles are shown in addition to the 9 deciles from 10% to 90%. The line representing the 2.5th percentile rises steadily from its initial value (the 2002 trust fund ratio) of 2.60, reaches a peak of 3.66 in 2013, and then declines steadily until hitting zero in 2032 (the trust fund exhaustion date). Each higher percentile has the same basic shape but lies everywhere above the lower percentiles. For each percentile shown, the 2002 trust fund ratio, the peak trust fund ratio and the year in which the peak value was attained are listed in the following table. Also listed in the following table are the trust fund exhaustion dates for each percentile.

Trust fund ratios, peak year, and exhaustion year for the OCACT model, by percentile
2.50% 10% 20% 30% 40% 50% 60% 70% 80% 90% 97.50%
2002 trust fund ratio 2.60 2.60 2.60 2.60 2.61 2.61 2.61 2.61 2.61 2.61 2.61
Peak trust fund ratio 3.66 3.99 4.22 4.40 4.58 4.76 4.94 5.14 5.39 5.76 6.42
Peak year 2013 2013 2014 2015 2015 2015 2016 2015 2016 2017 2017
Exhaustion year 2032 2034 2036 2038 2039 2041 2043 2046 2050 2057 2075

## Text descriptions and table equivalents for two panels of Chart 2.Comparison of trust fund ratio projections from the SSASIM model

### Structural time-series model

This fan chart depicts various percentiles of the simulated trust fund ratios from the SSASIM Structural model over time. The 2.5th and 97.5th percentiles are shown in addition to the 9 deciles from 10% to 90%. The line representing the 2.5th percentile rises steadily from its initial value (the 2002 trust fund ratio) of 2.51, reaches a peak of 3.61 in 2012, and then declines steadily until hitting zero in 2030 (the trust fund exhaustion date). Each higher percentile has the same basic shape but lies everywhere above the lower percentiles. For each percentile shown, the 2002 trust fund ratio, the peak trust fund ratio and the year in which the peak value was attained are listed in the following table. Also listed in the following table are the trust fund exhaustion dates for each percentile.

Trust fund ratios, peak year, and exhaustion year for the structural time-series model, by percentile
2.50% 10% 20% 30% 40% 50% 60% 70% 80% 90% 97.50%
2002 trust fund ratio 2.51 2.55 2.58 2.59 2.61 2.62 2.64 2.65 2.67 2.70 2.73
Peak trust fund ratio 3.61 3.84 4.00 4.11 4.20 4.29 4.38 4.47 4.60 4.77 5.01
Peak year 2012 2013 2014 2014 2014 2015 2015 2015 2015 2015 2016
Exhaustion year 2030 2033 2034 2035 2036 2037 2039 2040 2043 2046 2061

### ARIMA Model

This graph depicts various percentiles of the simulated trust fund ratios from the SSASIM ARIMA model over time. The 2.5th and 97.5th percentiles are shown in addition to the 9 deciles from 10% to 90%. The line representing the 2.5th percentile rises steadily from its initial value (the 2002 trust fund ratio) of 2.50, reaches a peak of 3.76 in 2014, and then declines steadily until hitting zero in 2034 (the trust fund exhaustion date). Each higher percentile has the same basic shape but lies everywhere above the lower percentiles. For each percentile shown, the 2002 trust fund ratio, the peak trust fund ratio and the year in which the peak value was attained are listed in the following table. Also listed in the following table are the trust fund exhaustion dates for each percentile.

Trust fund ratios, peak year, and exhaustion year for the ARIMA model, by percentile
2.50% 10% 20% 30% 40% 50% 60% 70% 80% 90% 97.50%
2002 trust fund ratio 2.50 2.54 2.57 2.59 2.61 2.62 2.64 2.66 2.68 2.70 2.75
Peak trust fund ratio 3.76 3.95 4.08 4.16 4.23 4.31 4.37 4.46 4.55 4.66 4.87
Peak year 2014 2014 2014 2014 2014 2014 2015 2015 2014 2015 2015
Exhaustion year 2034 2035 2036 2037 2037 2038 2038 2039 2040 2042 2045