The Canadian Pensioners Mortality Table

The Canadian Pensioners Mortality Table Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 Louis Adam, FSA, FCIA Université Laval, Québec City, QC, Canada December 3, 2012 Document 213012

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 2 Table of contents Summary... 10 Overview...10 Information on Phase I: Data...10 Information on Phase II: Level of mortality in 2005 2007...11 Information on Phase III: Mortality trends from 1967 to 2007...13 I. Introduction... 18 Structure of this document...19 Acknowledgements...20 II. Regression methodology to measure observed mortality improvement rates... 21 Results from Phase II Report...21 Observed probability of death and variance of this observation...22 Weight associated to an annual probability of death...22 Determination of a mortality improvement rate for each age (and each cell)...23 Linear regression...23 Weighted linear regression...25 Confidence interval and worth of the regression...25 III. Regression results available in appendices A to D... 27 Source of data...27 Income class and gender...27 Regression periods...27 First year and last year of regression periods...28 Results by age and regression period...28 Nature of results: weighted linear regression model...28 Mortality improvement rate IR x...28 95% confidence interval for the improvement rate and R 2...28 Limitations to calculations...29 IV. Explanations of and comments on the regression results... 30 Detailed examples and comments for the CAN-M-4 Age 70 cell...30 Improvement rate by age and gender at five-year intervals for CAN-M-4 and CAN-F-4...32 Comments on the gender differential in observed mortality improvement rate...34 Comments on the age-related pattern of mortality improvement rates...35 Comparison of weighted and unweighted regression models...38 Comparison of the impact of the length of the regression period...40 Comments on the varying trend in mortality improvement rate by end-year...42 Comments on the impact of the income class variable on the improvement rate...42 Comments on the impact of the data source: CAN versus CPP or QPP...46 Comments on QPP results ending in 2008, compared to those ending in 2007...48

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 3 V. Proposal for a set of mortality projection scales... 51 General comments on the projection process...51 Relative merit of various proposals of mortality projection...52 Proposal for a model with three projection scales: short-, mid-, and long-term...53 Short-term scale...54 Long-term scale...56 Mid-term scale...57 Formulas to obtain projected values of probabilities of death...58 Comparisons between mortality projection scales...58 VI. Impact on complete life expectancy and present value of an annuity due... 64 Static and generational projections of mortality tables...64 Uses of complete life expectancy and present value of an annuity due...65 Comparison of complete life expectancy figures...67 Comparison of present value figures...68 VII. Conclusion... 73 Appendix A: Average Rate of Decrease of Mortality by Observed Probabilities of Death for Canada Data Source (CAN Mortality Improvement Rate)... 75 Appendix B: Average Rate of Decrease of Mortality by Observed Probabilities of Death for Canada Pension Plan Data Source (CPP Mortality Improvement Rate)... 92 Appendix C: Average Rate of Decrease of Mortality by Observed Probabilities of Death for Québec Pension Plan Data Source (QPP Mortality Improvement Rate)... 109 Appendix D: 2008-12-31Average Rate of Decrease of Mortality by Observed Probabilities of Death for Québec Pension Plan Data Source (2008 QPP Mortality Improvement Rate) 126 Appendix E: Examples of Data for Canada, Male, Income Class 4, Age 70... 143 Appendix F: Examples of Regression Results at Selected Ages for Males and Females, Canada, Income Class 4, 15-Year Ending in 2007... 149 Appendix G: Excerpts of projection scales in latest CPP and QPP actuarial valuation reports, and proposed mortality projection scales... 159 Appendix H: Numerical values for the complete life expectancy... 168 Appendix I: Numerical values for the present value of a $1,000/year life annuity due... 175

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 4 List of Charts and Tables CHARTS CHART 1 CANADA, INCOME CLASS 4, 15-YEAR REGRESSION PERIODS, MALE FEMALE DIFFERENTIAL... 35 CHART 2 CANADA, MALE, INCOME CLASS 4, 15-YEAR REGRESSION PERIOD ENDING IN 2007, AVERAGE MORTALITY IMPROVEMENT RATE, 95% CONFIDENCE INTERVAL AND R 2 VALUE... 37 CHART 3 CANADA, FEMALE, INCOME CLASS 4, 15-YEAR REGRESSION PERIOD ENDING IN 2007, AVERAGE MORTALITY IMPROVEMENT RATE, 95% CONFIDENCE INTERVAL AND R 2 VALUE... 37 CHART 4 CANADA, MALE, INCOME CLASS 4 (OVER 35% OF MAXIMUM PENSION), COMPARISON OF WEIGHTED VS. UNWEIGHTED REGRESSION THE 15-YEAR REGRESSION PERIOD ENDING IN 2007... 39 CHART 5 CANADA, FEMALE, INCOME CLASS 4 (OVER 35% OF MAXIMUM PENSION), COMPARISON OF WEIGHTED VS. UNWEIGHTED REGRESSION OVER THE 15-YEAR REGRESSION PERIOD ENDING IN 2007... 39 CHART 6 CANADA, MALE, INCOME CLASS 4 (OVER 35% OF MAXIMUM PENSION), COMPARISON OF VARIOUS LENGTHS OF REGRESSION PERIOD ENDING IN 2007... 41 CHART 7 CANADA, FEMALE, INCOME CLASS 4 (OVER 35% OF MAXIMUM PENSION), COMPARISON OF VARIOUS LENGTHS OF REGRESSION PERIOD ENDING IN 2007... 41 CHART 8 CANADA, MALE, INCOME CLASS 4 (OVER 35% OF MAXIMUM PENSION), COMPARISON OF 15-YEAR REGRESSION PERIODS ENDING IN 1992 AND IN 2007, WITH 95% CONFIDENCE INTERVALS AND 30-YEAR REGRESSION... 43 CHART 9 CANADA, FEMALE, INCOME CLASS 4 (OVER 35% OF MAXIMUM PENSION), COMPARISON OF 15-YEAR REGRESSION PERIODS ENDING IN 1992 AND IN 2007, WITH 95% CONFIDENCE INTERVALS AND 30-YEAR REGRESSION... 43 CHART 10 CANADA, MALE, COMPARISON OF 15-YEAR REGRESSION PERIOD ENDING IN 2007, FOR VARIOUS INCOME CLASSES... 45 CHART 11 CANADA, FEMALE, COMPARISON OF 15-YEAR REGRESSION PERIOD ENDING IN 2007, FOR VARIOUS INCOME CLASSES... 45 CHART 12 CANADA, MALE, DATA SOURCE COMPARISON FOR INCOME CLASS 4... 47 CHART 13 CANADA, FEMALE, DATA SOURCE COMPARISON FOR INCOME CLASS 4... 47 CHART 14 QPP, MALE, INCOME CLASS 4, 15-YEAR REGRESSION RESULTS AT THE END OF 2008 AND 2007... 49 CHART 15 QPP, FEMALE, INCOME CLASS 4, 15-YEAR REGRESSION RESULTS AT THE END OF 2008 AND 2007... 49 CHART 16 PROPOSED SHORT-TERM PROJECTION SCALE FOR MALES... 55 CHART 17 PROPOSED SHORT-TERM PROJECTION SCALE FOR FEMALES... 55 CHART 18 PROPOSED SCALES FOR MALE (SHORT-, MID-, AND LONG-TERM), OBSERVED IMPROVEMENT RATES (1977 1992, 1992 2007), AA SCALE, C/QPP ASSUMPTIONS... 60 CHART 19 PROPOSED SCALES FOR FEMALE (SHORT-, MID-, AND LONG-TERM), OBSERVED IMPROVEMENT RATES (1977 1992, 1992 2007), AA SCALE, C/QPP ASSUMPTIONS... 60 CHART 20 PROJECTED PROBABILITIES OF DEATH WITH SHORT-, MID-, AND LONG-TERM SCALES: MALE, AGES 65 TO 85... 61 CHART 21 PROJECTED PROBABILITIES OF DEATH WITH SHORT-, MID-, AND LONG-TERM SCALES: FEMALE, AGES 65 TO 85... 61 CHART 22 PROJECTED PROBABILITIES OF DEATH WITH SHORT-, MID-, AND LONG-TERM SCALES: MALE, AGES 85 TO 100... 62 CHART 23 PROJECTED PROBABILITIES OF DEATH WITH SHORT-, MID-, AND LONG-TERM SCALES: FEMALE, AGES 85 TO 100... 62 CHART 24 COMPLETE LIFE EXPECTANCY ON A GENERATIONAL BASIS: UP-1994G VERSUS CPM-CAN-4: MALE... 66 CHART 25 COMPLETE LIFE EXPECTANCY ON A GENERATIONAL BASIS: UP-1994G VERSUS CPM-CAN-4: FEMALE.. 66

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 5 CHART 26 PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE (I=3%), UP-1994G VERSUS CPM-CAN-4: MALE... 70 CHART 27 PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE (I=3%), UP-1994G VERSUS CPM-CAN-4: FEMALE... 70 CHART E.1: MORTALITY TREND FROM 1967 TO 2007, OBSERVED PROBABILITY OF DEATH FOR CANADA, MALE, INCOME CLASS 4 (OVER 35 % OF MAXIMUM PENSION), AGE 70... 145 CHART E.2 EXAMPLE OF WEIGHTED REGRESSION RESULTS FOR LN (Q 70 ), CANADA, MALE, INCOME CLASS 4, AGE 70, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 146 CHART E.3 EXAMPLE OF WEIGHTED REGRESSION RESULTS: IMPROVEMENT RATIO (IR 70 ) FOR Q 70, CANADA, MALE, INCOME CLASS 4, AGE 70, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 146 CHART E.4 EXAMPLE OF UNWEIGHTED REGRESSION RESULTS: IMPROVEMENT RATIO (IR 70 ) FOR Q 70, CANADA, MALE, INCOME CLASS 4, AGE 70, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 147 CHART E.5 IMPROVEMENT RATIO (IR 70 ), CANADA, MALE, INCOME CLASS 4, AGE 70, 15-YEAR REGRESSION PERIOD ENDING IN 1992... 148 CHART F.1 IMPROVEMENT RATIO (IR 60 ), CANADA, MALE, INCOME CLASS 4, AGE 60, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 150 CHART F.2 IMPROVEMENT RATIO (IR 60 ), CANADA, FEMALE, INCOME CLASS 4, AGE 60, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 150 CHART F.3 IMPROVEMENT RATIO (IR 65 ), CANADA, MALE, INCOME CLASS 4, AGE 65, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 151 CHART F.4 IMPROVEMENT RATIO (IR 65 ), CANADA, FEMALE, INCOME CLASS 4, AGE 65, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 151 CHART F.5 IMPROVEMENT RATIO (IR 70 ), CANADA, MALE, INCOME CLASS 4, AGE 70, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 152 CHART F.6 IMPROVEMENT RATIO (IR 70 ), CANADA, FEMALE, INCOME CLASS 4, AGE 70, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 152 CHART F.7 IMPROVEMENT RATIO (IR 75 ), CANADA, MALE, INCOME CLASS 4, AGE 75, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 153 CHART F.8 IMPROVEMENT RATIO (IR 75 ), CANADA, FEMALE, INCOME CLASS 4, AGE 75, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 153 CHART F.9 IMPROVEMENT RATIO (IR 80 ), CANADA, MALE, INCOME CLASS 4, AGE 80, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 154 CHART F.10 IMPROVEMENT RATIO (IR 80 ), CANADA, FEMALE, INCOME CLASS 4, AGE 80, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 154 CHART F.11 IMPROVEMENT RATIO (IR 85 ), CANADA, MALE, INCOME CLASS 4, AGE 85, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 155 CHART F.12 IMPROVEMENT RATIO (IR 85 ), CANADA, FEMALE, INCOME CLASS 4, AGE 85, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 155 CHART F.13 IMPROVEMENT RATIO (IR 90 ), CANADA, MALE, INCOME CLASS 4, AGE 90, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 156 CHART F.14 IMPROVEMENT RATIO (IR 90 ), CANADA, FEMALE, INCOME CLASS 4, AGE 90, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 156 CHART F.15 IMPROVEMENT RATIO (IR 95 ), CANADA, MALE, INCOME CLASS 4, AGE 95, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 157 CHART F.16 IMPROVEMENT RATIO (IR 95 ), CANADA, FEMALE, INCOME CLASS 4, AGE 95, 15-YEAR REGRESSION PERIOD ENDING IN 2007... 157 CHART F.17 IMPROVEMENT RATIO (IR 100 ), CANADA, MALE, INCOME CLASS 4, AGE 100, 11-YEAR REGRESSION PERIOD ENDING IN 2007... 158

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 6 CHART F.18 IMPROVEMENT RATIO (IR 100 ), CANADA, FEMALE, INCOME CLASS 4, AGE 100, 11-YEAR REGRESSION PERIOD ENDING IN 2007... 158 TABLES TABLE 1 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 2, M (1/2)... 76 TABLE 2 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 2, M (2/2)... 77 TABLE 3 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 2, F (1/2)... 78 TABLE 4 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 2, F (2/2)... 79 TABLE 5 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 3, M (1/2)... 80 TABLE 6 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 3, M (2/2)... 81 TABLE 7 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 3, F (1/2)... 82 TABLE 8 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 3, F (2/2)... 83 TABLE 9 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 4, M (1/2)... 84 TABLE 10 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 4, M (2/2)... 85 TABLE 11 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 4, F (1/2)... 86 TABLE 12 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 4, F (2/2)... 87 TABLE 13 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 5, M (1/2)... 88 TABLE 14 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 5, M (2/2)... 89 TABLE 15 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 5, F (1/2)... 90 TABLE 16 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CAN, CLASS 5, F (2/2)... 91 TABLE 17 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 2, M (1/2)... 93 TABLE 18 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 2, M (2/2)... 94 TABLE 19 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 2, F (1/2)... 95 TABLE 20 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 2, F (2/2)... 96 TABLE 21 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 3, M (1/2)... 97 TABLE 22 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 3, M (2/2)... 98

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 7 TABLE 23 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 3, F (1/2)... 99 TABLE 24 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 3, F (2/2)... 100 TABLE 25 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 4, M (1/2)... 101 TABLE 26 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 4, M (2/2)... 102 TABLE 27 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 4, F (1/2)... 103 TABLE 28 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 4, F (2/2)... 104 TABLE 29 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 5, M (1/2)... 105 TABLE 30 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 5, M (2/2)... 106 TABLE 31 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 5, F (1/2)... 107 TABLE 32 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, CPP, CLASS 5, F (2/2)... 108 TABLE 33 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 2, M (1/2)... 110 TABLE 34 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 2, M (2/2)... 111 TABLE 35 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 2, F (1/2)... 112 TABLE 36 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 2, F (2/2)... 113 TABLE 37 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 3, M (1/2)... 114 TABLE 38 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 3, M (2/2)... 115 TABLE 39 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 3, F (1/2)... 116 TABLE 40 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 3, F (2/2)... 117 TABLE 41 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 4, M (1/2)... 118 TABLE 42 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 4, M (2/2)... 119 TABLE 43 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 4, F (1/2)... 120 TABLE 44 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 4, F (2/2)... 121 TABLE 45 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 5, M (1/2)... 122 TABLE 46 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 5, M (2/2)... 123

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 8 TABLE 47 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 5, F (1/2)... 124 TABLE 48 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 5, F (2/2)... 125 TABLE 49 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 2, M (1/2)... 127 TABLE 50 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 2, M (2/2)... 128 TABLE 51 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 2, F (1/2)... 129 TABLE 52 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 2, F (2/2)... 130 TABLE 53 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 3, M (1/2)... 131 TABLE 54 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 3, M (2/2)... 132 TABLE 55 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 3, F (1/2)... 133 TABLE 56 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 3, F (2/2)... 134 TABLE 57 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 4, M (1/2)... 135 TABLE 58 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 4, M (2/2)... 136 TABLE 59 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 4, F (1/2)... 137 TABLE 60 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 4, F (2/2)... 138 TABLE 61 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 5, M (1/2)... 139 TABLE 62 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 5, M (2/2)... 140 TABLE 63 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 5, F (1/2)... 141 TABLE 64 2008 AVERAGE RATE OF DECREASE OF MORTALITY BY OBSERVED PROBABILITIES OF DEATH, QPP, CLASS 5, F (2/2)... 142 TABLE 65 EXPOSURE, DEATHS AND PROBABILITY OF DEATH FROM 1967 TO 2007, CANADA, MALE, INCOME CLASS 4 (OVER 35 % OF MAXIMUM PENSION), AGE 70... 144 TABLE 66 EXAMPLE OF WEIGHTED REGRESSION DATA FOR CAN, MALE, INCOME CLASS 4, AGE 70, CALENDAR YEARS 1992 TO 2007... 145 TABLE 67 EXAMPLE OF UNWEIGHTED REGRESSION DATA FOR CAN, MALE, INCOME CLASS 4, AGE 70, CALENDAR YEARS 1992 TO 2007... 147 TABLE 68 EXAMPLE OF WEIGHTED REGRESSION DATA FOR CAN, MALE, INCOME CLASS 4, AGE 70, CALENDAR YEARS 1977 TO 1992... 148 TABLE 69 SHORT TERM PROJECTION SCALES FOR CPM TABLES... 160 TABLE 70 EXCERPTS OF PROJECTION SCALES USED IN CPP ACTUARIAL ANALYSIS AS AT DECEMBER 31, 2009 MALE... 161 TABLE 71 EXCERPTS OF PROJECTION SCALES USED IN CPP ACTUARIAL ANALYSIS AS AT DECEMBER 31, 2009 FEMALE... 162

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 9 TABLE 72 EXCERPTS OF PROJECTION SCALES USED IN QPP ACTUARIAL ANALYSIS AS AT DECEMBER 31, 2009 MALE... 163 TABLE 73 EXCERPTS OF PROJECTION SCALES USED IN QPP ACTUARIAL ANALYSIS AS AT DECEMBER 31, 2009 FEMALE... 164 TABLE 74 LONG TERM PROJECTION SCALES FOR CPM TABLES... 165 TABLE 75 MID TERM PROJECTION SCALES FOR CPM TABLES... 166 TABLE 76 PROJECTION SCALES FOR CPM TABLES, ANNUAL MORTALITY IMPROVEMENT RATE (%)... 167 TABLE 77 COMPLETE LIFE EXPECTANCY, UP-1994G, MALE... 169 TABLE 78 COMPLETE LIFE EXPECTANCY, UP-1994G, FEMALE... 170 TABLE 79 COMPLETE LIFE EXPECTANCY, CPM-CAN-4-M, MALE... 171 TABLE 80 COMPLETE LIFE EXPECTANCY, CPM-CAN-4-F, FEMALE... 172 TABLE 81 % INCREASE IN COMPLETE LIFE EXPECTANCY, FROM UP-1994G TO CPM-CAN-4-M, MALE... 173 TABLE 82 % INCREASE IN COMPLETE LIFE EXPECTANCY, FROM UP-1994G TO CPM-CAN-4-F, FEMALE... 174 TABLE 83 PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, UP-1994G, MALE, (I=3%)... 176 TABLE 84 PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, UP-1994G, FEMALE, (I=3%)... 177 TABLE 85 PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, CPM-CAN-4-M, MALE, (I=3%)... 178 TABLE 86 PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, CPM-CAN-4-F, FEMALE, (I=3%)... 179 TABLE 87 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-4-M, MALE, (I=3%)... 180 TABLE 88 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-4-F, FEMALE, (I=3%)... 181 TABLE 89 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-4-M, MALE, (I=5%)... 182 TABLE 90 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-4-F, FEMALE, (I=5%)... 183 TABLE 91 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-4-M, MALE, (I=6%)... 184 TABLE 92 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-4-F, FEMALE, (I=6%)... 185 TABLE 93 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-2-M, MALE, (I=3%)... 186 TABLE 94 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-2-F, FEMALE, (I=3%)... 187 TABLE 95 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-3-M, MALE, (I=3%)... 188 TABLE 96 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CAN-3-F, FEMALE, (I=3%)... 189 TABLE 97 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CPP-4-M, MALE, (I=3%)... 190 TABLE 98 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-CPP-4-F, FEMALE, (I=3%)... 191 TABLE 99 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-QPP-4-M, MALE, (I=3%)... 192 TABLE 100 % INCREASE IN PRESENT VALUE OF A $1,000/YEAR LIFE ANNUITY DUE, FROM UP-1994G TO CPM-QPP-4-F, FEMALE, (I=3%)... 193

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 10 Summary Overview This document contains results on the evolution of Canadian pensioners mortality over the period from 1967 to 2007. This Phase III report complements the findings of the Phase II report dated May 31, 2012, about the level of Canadian pensioners mortality over the 2005 2007 triennial period. These two reports provide a wealth of relevant information regarding the level and trend of mortality for Canadian pensioners, and should be of particular interest to pension actuaries interested in the determination of mortality assumptions after retirement for Canadian pensioners. Before presenting specific details on the findings from Phase III of this mortality study, we provide below an overview of relevant information pertaining to Phases I and II of the study, with some emphasis on the quality and comprehensiveness of the data. Information on Phase I: Data Phase I of this mortality study consisted of assessing the quality and appropriateness of the Canada Pension Plan (CPP) and Québec Pension Plan (QPP) administrative pensioners data used in this study, before performing the various tabulations required for the Phase II and Phase III reports. Excerpts from these tabulations are available in the Phase II report. We benefited from an excellent collaboration from CPP and QPP actuaries from the beginning of this study. Preliminary study results were submitted to them for validation during Phase I. Various questions regarding data issues and classification variables were settled at this stage and tabulations were consistent with their own internal administrative files for elements such as the number of observed annual deaths in the study. Data quality and comprehensiveness The combination of the two data sources (CPP, QPP) gives an aggregate measurement of mortality for all Canadian pensioners, as participation to either the CPP or QPP is mandatory for Canadian employees and the self-employed with earnings over a very low dollar figure. This combined data source is defined as Canada and abbreviated CAN in tables and charts. The quality and comprehensiveness of the Canadian data used in this mortality study are important characteristics that are critical in assessing the validity and importance of the results shown. The study is based on all individual administrative records of pensions paid to CPP or QPP pensioners from the inception of the plans up to December 31, 2008. Each record includes the dates of birth, retirement, death (when applicable), and the initial amount of retirement pension. This allows for a consistent measurement of mortality for each calendar period involved, without variations due to a change of methodology over time or a change of the sample size. It also allows taking into account income as a variable for the measurement of mortality. Income class Income class is determined by a measure of the monthly pension at time of retirement as a percentage of the maximum C/QPP retirement pension. Income class 1 is for pension below 35% of the maximum pension, class 2 for the 35% to 94% range, and class 3 for pension over 95% of the maximum pension. Income class 4 is the combination of classes 2 and 3 (over 35% of maximum pension), while class 5 combines classes 1, 2, and 3 (All income). The determination of income as a percentage of the maximum pension instead of a dollar figure avoids issues

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 11 regarding inflation adjustment. It also relates well to the 35% of YMPE criterion for participation found in pension legislations of various jurisdictions in Canada. The 95% level is consistent with a subset of the population with income over the average industrial wage in Canada (class 3), while income class 2 corresponds to those with income greater than the threshold required to participate in a private pension plan, but below the average industrial wage. The income class variable is useful in establishing an appropriate subset of the total population, thus providing an adequate measure of the mortality of pensioners who were or could have been participants in private pension plans. The exclusion of the income class 1 subset allows the findings to be more relevant for private pension plan purposes. Size of the population under study The total number of records involved is important in absolute numbers and in relation to the census figures of the total population. In percentage of the July 1, 2007, Canadian population over age 60 as recorded by Statistics Canada, the active lives in the study represent 82.4% of the male population and 68.8% of the female population. The number of individual records represents a total of 7.85 M lives in the available files as at December 31, 2008. In total, there are more than 86 M life-years of exposure and more than 3 M deaths for both genders from 1967 to 2008. The exposure and deaths included in a particular mortality table vary according to the data source, gender, income class, and period considered. For example, the following figures of life-years of exposure and deaths are included in the 2005 2007 triennial period, from age 60 to 111, for the Canada data source: Gender & Income Class Exposure (M life years) Deaths (,000) Male, class 2 2.85 111 Male, class 3 3.07 118 Male, class 4 5.92 229 Female, class 2 3.05 77 Female, class 3 0.69 18 Female, class 4 3.74 95 As discovered during Phase I, after comparisons of results with CPP and QPP actuaries, data for 2008 were excluded due to an issue regarding under-reporting of deaths in one of the data sources for that calendar year. The end point of this mortality study for the Canada data source is thus December 31, 2007. Results for the Canada data source, for income classes 2, 3, and 4, for the most recent triennial period 2005 2007 are thus the focal point in the determination of the level of mortality of Canadian pensioners in the Phase II report. Information on Phase II: Level of mortality in 2005 2007 The Phase II report provides measurements of the level of mortality according to gender and age, in addition to the following explanatory variables: data source (CPP, QPP, Canada), calendar period or calendar year, and income class. These results are compared to the 1994 Uninsured Pensioner mortality table (UP-94), with a static projection to calendar year 2006. Other results are shown with static projection up to calendar years 2010, 2015, and 2020, using the short-term projection scale described in the Phase III report for the Canadian pensioners mortality table, and the AA scale for the UP-94 mortality table.

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 12 Measurements and available results In addition to the measurement of exposure, deaths, expected value, and standard deviation for q x (the observed probability of death within a year), the results of various statistical tests and other measures are included in the Phase II report. This allows an assessment of the materiality of the five explanatory variables mentioned above. The Phase II report also presents the graduation process and the required extrapolations to obtain a set of graduated mortality tables at a recent point in time the 2005 2007 triennial period centered in 2006 from age 15 to age 120, according to the other variables (source, income class, gender). A complete set of mortality tables is included with the Phase II report. Various tables and charts provide values and illustrations of relevant results for the complete life expectancy or the present value of a life annuity. All values are calculated for the 2005 2007 calendar period without projection, or with a static projection up to specific calendar years from 2010 to 2020. Findings of the Phase II report More detailed information on the various results is available in the Phase II report and its own summary. However, we recall some key findings below. As expected, mortality increases significantly with age according to an exponential pattern, with some observed modifications to this pattern at extreme ages over 95. Age is significant at the 95% level for income class 4 until age 96 for males and until age 97 for females. Mortality for females is considerably lower than male mortality, with statistical significance at the 95% level until age 101 for income class 4. In addition to gender and age, income class is a significant variable to measure mortality. At the 95% confidence level, male mortality at a given age differs in a statistically significant matter between classes 1 and 2 until age 78, and between classes 2 and 3 until age 89. For females, the lower volume of data modifies the age range, as compared to males, but income is also a significant variable to measure female mortality. At a first level, this confirms the adequacy of removing income class 1 data from the whole set of data for private pension plans purposes. At a second level, the differences between mortality for income classes 2 and 3 (in short, income below and over the average industrial wage) provide evidence that these two classes exhibit a different pattern of mortality. These results are far-reaching and suggest that age, gender, and income class might be used as explanatory variables to determine qx values. There are differences in mortality by source (CPP vs. QPP), but we cannot statistically discriminate at the 95% confidence level the mortality between these two sources in the 2005 2007 period. At many individual ages for income class 4, QPP male mortality is higher than CPP male mortality, but the reverse is true for females. The same statistical test for the 1995 1997 period would have led to a different conclusion, with respect to differences between CPP and QPP male mortality in the 65 84 age range. This suggests that QPP mortality decreased faster in the recent past than CPP mortality, as will be shown later in the findings of the Phase III study. Additional results are presented to confirm that mortality is statistically different by calendar period. Comparing mortality for a specific combination of age, gender, and income class over a five-year interval, from 2000 2002 to 2005 2007, and from 1995 1997 to 2000 2002, gives a

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 13 statistically significant difference at the 95% level. This confirms the need to use some form of mortality projection over time, as calendar year is another significant explanatory variable to determine qx values. Comparisons of life expectancies and present value of an annuity figures obtained with the Canadian pensioners mortality tables, in comparison to UP-94@2006 figures (or with static projection until 2020) show significant differences for various combinations of gender and income class. Results in 2006 are not affected by the difference of projection scales after that calendar year, while results based on a static projection until 2020 are impacted by this factor. In general, results for males in 2006 for income class 4 indicate that the shapes of the two mortality curves are not identical. Looking at the percentage increase in the present value of an annuity calculated with the UP-94@2006 and with the CPM-CAN-4 2005 2007, we observe negative variations that increase in absolute value with age. Static projections over a short time period modify these disparities, with higher values for income class 4 for ages under 85 in 2020. However, results for the male in income class 3 are already higher in 2006 than those with the UP-94@2006 table for ages below 75. Static projections up to 2010, 2015, and 2020 increase the discrepancies between results based on these two mortality tables. For females, the results are already higher in 2006 at income classes 2, 3, and 4 for ages under 85. Static projections to 2010, 2015, or 2020 only increase the discrepancies already observed. The table below shows the percentage increase in the present value of a life annuity due (annual payment at the beginning of the year) at a 6% constant annual interest, in changing from the UP-94@2020 to the CPM-CAN-4 2005 2007@2020 or CPM-CAN-3 2005 2007@2020. All results are based on a static projection of mortality up to calendar year 2020. Class 4 Class 3 Age Male Female Male Female 60 2.21% 2.74% 3.91% 3.61% 65 2.21% 2.75% 4.06% 3.76% 70 1.86% 2.50% 3.66% 3.53% 75 1.62% 2.41% 3.12% 3.45% 80 0.98% 1.82% 2.15% 2.73% 85-3.34% -0.23% -2.42% 0.52% The findings of the Phase II study indicate that the UP-94 table might not be the most appropriate one for Canadian purposes. The present value results obtained with a static projection up to calendar year 2020 show material differences by age, gender, and income class compared to the expected results under the UP-94@2020. Information on Phase III: Mortality trends from 1967 to 2007 This Phase III report provides answers to other questions regarding mortality. While Phase II focused on mortality levels at a recent point in time, Phase III examines mortality trends over time. The first purpose of this Phase III report is thus to provide quantitative information on the measurement of mortality improvement rates according to several parameters of importance, as explained below.

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 14 Its second purpose is to use this information to propose a set of mortality projection scales. These scales should be used in conjunction with recent estimates of the level of mortality at a recent point in time, such as those provided in the Phase II report, to obtain a generational mortality table suitable for private pension plan purposes. Mortality improvement rates Mortality improvement rates, defined as IR x, are measured in this report using a weighted linear regression model applied to the natural logarithm of q year x, the observed probability of death within a year as a function of calendar year. This calculation is performed independently for various combinations of explanatory variables. A positive value for IRx infers that q x decreases over time at a constant average annual rate of IR for the period under consideration. In addition to the explanatory variables used in the Phase II report, which are data source, income class, gender, and age, we also provide measurement over various lengths of time (such as 15 or 25 years) and at a different end point for the period of measurement (such as 1992 or 2007). Separate results ending as at December 31, 2008, are also provided for the QPP data source. An important feature of the results found in the appendices is the quantity of information available to assess the adequacy of the mean value IR x : also provided are the bounds of the 95% 2 confidence interval for the improvement rate and the R value of the regression performed. A consistent methodology is applied over the various periods, taking into account the exposure and death values to determine the weight associated to each individual calendar measurement of mortality. Several results of interest are presented in this report, using charts and tables to highlight some of the most interesting findings. Some of these findings are mentioned below in this summary. Findings of the Phase III report Mortality is not constant over time: this may be obvious, but precise measures are required to determine if IRx is statistically different from 0, and if it varies according to the explanatory variables. This was also suggested by the simple tests performed in the Phase II report, where we verified if the mortality in 2000 2002 was statistically different from the mortality in 2005 2007. For most combinations of parameters, we obtain positive values for IR x. For example, regression results at age 70 for males in income class 4, with the Canada data source, over the 15-year period from 1992 to 2007, are such that we observe a value of 2.78% for IR 70, with a 95% 2 confidence interval going from 2.46% to 3.11%, and a high R value of 96%. IRx changes with age. High levels of improvement are observed toward the lower ages of retirement, while lower improvement rates are observed at higher ages (see charts 2 and 3 on page 42). This pattern of declining mortality improvement rates with age is observed at all combinations of the other variables. At ages over 90, we observe negative values for IR x, or 95% confidence intervals that do not allow to reject an assumption of a 0% improvement rate. The information provided by the confidence interval and the R 2 value invite greater caution in statements about mortality improvements over age 95. x

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 15 IR x is not constant over time. For the same age, observed improvement rates over a short recent period are higher than those in previous periods (see charts 6 and 7 on page 46). Increasing the length of the regression period ending in 2007 also has the impact of producing lower values for IR x. The difference in average improvement rates over the last two consecutive 15-year periods, 1977 1992 and 1992 2007, is significant (see charts 8 and 9 on page 48). Improvement rates have thus been accelerating in the recent history, and this observation creates an additional level of uncertainty in the estimation of future mortality improvement rates. IR x varies by gender. Males experience higher values of IR x than females for the same age, with a differential in improvement rates over 1% over the 65 75 age range (CAN-4-M vs. CAN- 4-F, 1992 2007 period, see chart 1 on page 40). Combined to the fact that females have lower values of q x than males, this suggests that there is more room in mortality improvement for males and a possible future narrowing of the differences in life expectancy between the two genders. IRx varies by income class. While disconcerting at first, the results for males are startling. Phase II showed that mortality levels by income are statistically different: higher pensions, associated to a higher socioeconomic status, as found in income class 3, are associated with a lower level of mortality when compared to lower pensions, such as those in income class 2. In addition, we observe in Phase III that income class 3 exhibits higher values of IR x than income class 2, which implies that these two sub-groups are diverging over time in terms of mortality curve. However, this statement is more applicable for males than for females (see charts 10 and 11 on page 50). This information reinforces the statement made previously that income is a significant variable to determine qx values. IRx varies by data source. QPP IR x are higher than CPP IR x : the five-year age group averages show a QPP CPP differential of more than 0.5% from 60 64 to 80 84 for males, and up to 75 79 for females (see charts 12 and 13 on page 52). Previously, QPP mortality for males was higher than CPP mortality, but the distance between the two subsets decreased over time, with still a somewhat higher mortality for QPP males compared to CPP males in 2005 2007. This is statistically not material in 2005 2007, but the difference was more significant 10 years ago. On average, QPP male improvement rates are higher than CPP improvement rates, and this suggests that there is more room for improvement for QPP mortality. For females, QPP improvement rates are also higher than those for CPP females, but the difference in improvement rates is lower than the difference between QPP males and CPP males. There might be qualitative or quantitative explanations for these observations, such as a potential greater decrease of tobacco use over time in Québec. However, it is not the purpose of this report to provide qualitative or quantitative explanations to the reasons why mortality evolved in a particular fashion for a particular combination of explanatory variables. The trend in high values for IRx is not receding at the end of 2008, at least from what can be observed from QPP data. The available QPP data allowed performing similar calculations at the end of 2008, such as a regression over the 15-year period ending in 2008 instead of 2007. A comparison of 15-year regression results between 2007 and 2008 shows an increase of IRx for males and relatively similar results for females (see charts 14 and 15 on page 54). This supports a continuation of high improvement rates in the near future after calendar year 2007.

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 16 Proposal for a set of mortality projection scales The task of coming up with a proposal for a mortality projection scale would have been simpler if we had simpler findings, such as constant value for IRx according to some or all the chosen explanatory variables. Unfortunately, this is not the case: improvement rates vary by age, gender, income class, data source, length of the measurement period, and end point of the measurement period. This complicates the problem, especially if we desire some form of simplicity in the retained projection model. Main features of the proposed projection scales The proposal is not the only model that may be deemed suitable, as it is based on a compromise in terms of simplicity. In this model, there is one set of projection scales for males and another one for females, irrespective of income or source. The proposal is based mainly on the observed values for income class 4 and data source Canada, for the short-term scale. The long-term scale is based on the long-term improvement rates assumptions of C/QPP actuaries. The proposed projection scales vary by age and capture the generally downward trend of high values at age 60 to low values at higher ages, with null values from age 95 onwards. Due to the high values of the improvement rates in the recent past 15 years, there is a need to transition from a set of large values for IRx in the short term to low values applicable in the long term, thus using a two-dimensional matrix (by age and calendar year) for each gender to define IR. x The proposal is simple in the sense that it uses only three values of IRx at each age to project qx values: a short-term projection scale, a mid-term one and a long-term one. When used in conjunction with the Phase II mortality tables, the short-term scale is applied at a constant rate for 15 years, from 2006 (the midpoint of the 2005 2007 triennial period) until 2021. The midterm scale is also applied at a constant rate, for nine years from 2021 to 2030. The long-term scale is applied to qx values in calendar year 2030 to obtain future values for 2031 onwards. Many alternative projection scale models would be possible, such as the use of varying improvement rates for each calendar year, from the initial projection year to an ultimate projection year. The choice of three scales is a compromise toward a simpler model including the need for a gradual decline in projection scales from the short term toward the long term. Other approaches involving linear interpolation between a short-term assumption and a long-term assumption are worthy of consideration. However, they are more complex since they require different IRx for each calendar year, until the attainment of an ultimate projection year, such as a set of 25 different scales for calendar years from 2006 to 2030 inclusive.

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 17 Short-term, mid-term and long-term projection scales The observed Canadian improvement rates for income class 4 over the past 15 years are used to design a projection scale applied in the near future on a mirror image basis, from 2006 to 2021 (see charts 16 and 17 on page 60). The long-term projection scale applicable from 2030 is based on a weighting of the CPP and QPP long-term projection scale assumptions, with adjustments, as found in the December 31, 2009, actuarial analyses of these two plans. We do not have additional information about the long-term evolution of Canadian mortality that would lead to a better opinion than those selected by C/QPP actuaries. The mid-term projection scale is obtained from a similar adjusted weighting of CPP and QPP improvement rate assumptions for calendar year 2020. The complete sets of projection scales are found in appendix G. For males and females, the improvement rate values for ages from 60 to 90 from the short-term and mid-term projection scales are higher than the corresponding AA scale value. However, the long-term scale value is lower, except for females, for whom the long-term scale values are lower from age 75 to 85 (see charts 18 and 19 on page 65). The impact of changing a projection scale from Scale AA to this proposal will thus be different according to the valuation date. Impact on complete life expectancy and present value figures Comparisons of complete life expectancy figures, and present value figures, are provided in section VI of this report. The comparison is made between the UP-94 with generational projection and the CPM-CAN 2005 2007 table with generational projection using the set of three projection scales. Results are shown for income classes 2, 3, and 4, with some comparisons also provided for QPP and CPP data sources at income class 4. For a valuation date varying from 2006 to 2056, the impact of changing from one table to the other is shown in appendix H (complete life expectancy) and appendix I (present value of an annuity due). Some results for calendar years 2006, 2012, and 2016 are excerpted in section VI (see charts 24 to 27, pages 71 and 74). For example, with a valuation date of January 1, 2012, the increases in present value of an annuity due (interest rate = 3%) for males in income class 4 are: 2.50% at age 65, 0.68% at age 75, and -0.83% at age 80 (see table 87). For females, the corresponding values are: 3.36% at age 65, 2.27% at age 75, and 1.19% at age 80 (see table 88). Results change significantly by age, by valuation date, and by income class. For example, for the higher income class 3, the corresponding increases in present value for males are: 4.87% at age 65, 2.53% at age 75, and 0.56% at age 80 (see table 95). For females, the corresponding values are: 4.66% at age 65, 3.55% at age 75, and 2.29% at age 80 (see table 96).

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 18 I. Introduction This report shows the results of a mortality study based on Canada Pension Plan (CPP) and Québec Pension Plan (QPP) pensioners data, with the specific purpose of analyzing historical improvement rates for mortality. It also contains a set of proposed projection scales developed to be applied for the future projection of mortality tables. Phase I of this mortality study consisted of data validation and processing to ensure the coherence and completeness of the available data. Phase II established the level of mortality exhibited by Canadian pensioners at a recent static point in time. It was the content of a previous report dated May 31, 2012. That Phase II report provided extensive results and a set of proposed mortality tables derived from this set of data, with an emphasis on results for the triennial period 2005 2007. The set of proposed mortality tables was named the Canadian Pensioners Mortality Table or CPM table, with additional information to add precision with respect to the particular source of data, gender, and income class (i.e., CPM-CAN-4-M for the table applicable to Canada, Male, Income class 4, 2005 2007 period ). This Phase III report presents the results of various calculations done to measure the trend of mortality over the period from 1967 to 2008, with special emphasis on the 15-year period from 1992 to 2007. As mentioned in the Phase II report, specifically in section VI (main results) and in the description of appendix F in section VII, statistical tests showed that a five-year time span was a significant variable and that there was ample evidence of mortality decrease over time. This result may not be surprising, because other mortality tables commonly use different techniques to decrease the level of mortality from a measurement period to the intended year of use. However, the determination of what type of projection scale is appropriate for the future, with the available information at a specific point in time, depends upon the model used, the required parsimony in the number of parameters and the materiality of the results, among other factors. For instance, the use of a constant projection scale, such as scale AA, allows the projection of the 1994 Uninsured Pensioner Mortality table (UP-1994) static mortality table from 1994 up to a specific projection year such as 2020, to obtain the static mortality table UP-1994@2020. The generational table UP-1994G uses the same AA projection scale to project known probability values from calendar year 1994 to any calendar year needed. For example, a person born in 1950 would need a projection of 1994 2015 q65 from 1994 to 2015 to obtain q 65, the probability of death at age 65 in 2015, then a projection of q 1994 66 from 1994 to 2016 to obtain q 2016 66, the probability of death at age 66 in 2016, and so on. Another example is provided by the actuarial assumptions used to project mortality in the actuarial analyses of the CPP and QPP, where the annual improvement factors vary by age and calendar year until an ultimate projection scale is reached in the long term. The choice of the number of projection scales, length of application of each scale, and value of each age-specific factor in a scale are elements to be considered in the choice of a suitable model. In this report, a set of three projection scales for the short term, mid term and long term is proposed for the purpose of projecting known probability values from 2006, the central year of the 2005 2007 triennial period, up to the required calendar year. The short-term projection scale is applicable for 15 years from 2006 to 2021. The mid-term scale is then used for nine years from 2021 until 2030, from which point in time the long-term projection scale is used thereafter. Each scale is used for the number of years mentioned without interpolation.

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 19 The contents of this report are explained below. Structure of this document In section II, we describe the methodology used to calculate the observed mortality improvement rates in the period from 1967 to 2008, with special emphasis on the 1992 2007 period. We recall prior formulas used in the Phase II report to obtain the observed probability of death and information on the variance of this value. We also present the weighted regression formula that is used to obtain the various results that are shown extensively in the appendices. Section III provides explanations on the layout of the available regression results. These detailed technical results of observed past improvement rates are in appendices A, B, C, and D. Results are sorted by data source (Canada, CPP, and QPP), ending calendar year of regression (2007 or 2008), income class (2, 3, 4, and 5), gender, age, and regression periods. The meaning of the various explanatory variables and available results are explained, with some emphasis on the confidence interval and the explanatory value of the R 2 figure obtained from the regression equation. Other explanatory variables are described, such as age, gender, end-point of the regression period, and the length of the regression period. Section IV provides comments and explanations on these results. Detailed explanations for a specific combination of parameters ( CAN-4-M, Age 70 cell) are provided at the beginning of this section, with background information and additional details in appendix E. Explanations on the impact of age and gender are then provided in the next part of this section, with references to detailed charts found in appendix F for males and females, from age 60 to age 100 at five-year intervals. We also present in this section the impact of using an unweighted regression model, changing the length of the regression period or the ending year of the regression period. We also compare the impact of using the income class variable on the regression results, and show the different results by data source. We also compare for the QPP data source the results available when we change the calendar year ending the regression period from 2007 to 2008, thus giving us an additional insight on the most recent trends available from the QPP data source. Section V presents the proposal for a set of projection scales to be used in conjunction with the 2005 2007 triennial mortality tables provided in the Phase II report. The short-term projection scale is derived from the 15-year regression period ending in 2007 for the CAN-4-M and CAN-4-F series of results. The long-term projection scale, as well as a mid-term projection scale, is based on a blend of the CPP and QPP long-term mortality projection assumptions, as contained in the most recent report of these two plans. Appendix G contains additional information on these assumptions and how they are used to obtain the proposed projection scales. Section VI presents the numerical results for the complete life expectancies and present values of an annuity due, when using the set of projection scales with the CPM tables of the Phase II report. These values are compared to results obtained with the UP-1994G mortality table in order to assess the materiality of changing from a currently-used mortality table to the proposed mortality table and projection scales. The conclusion appears in section VII. The contents of each appendix are described below in their order of appearance, even though some were mentioned in the presentation of the sections.

The Canadian Pensioners Mortality Table, Historical Trends in Mortality Improvement and a Proposed Projection Model Based on CPP/QPP Data as at December 31, 2007 20 The regression results over various periods for the data source Canada appear in Appendix A, with data ending in 2007. Appendices B and C show similar results for the CPP and QPP data source. Appendix D shows QPP regression results with an ending calendar year of 2008. Appendix E contains detailed explanations on the calculation of regression results for the specific case of males in income class 4 at age 70. The relationship of appendix E with appendix A is as follows. In appendix A, the most recent results for Canada, Income Class 4, Male are in tables 9 and 10. In table 9 for males (CAN-4-M), the results of a regression over the last 15-year period from 1992 to 2007 are in the fifth group of columns, with detailed results by ages on separate lines for ages 60 to 100. Appendix E provides extensive details by zooming in on how the results at age 70 are obtained, with comparisons to results from an ordinary least square regression formula and results for the preceding 15-year period ending in 1992. Appendix F shows charts of the observed and regression values for the annual probability of death in each calendar year from 1992 to 2007. This is shown sequentially from age 60 to age 100 by five-year intervals, for males and females in income class 4 for the Canada data source (CAN-4-M and CAN-4-F). These charts provide insights on specific results shown in table 9 (Male) and table 11 (Female) of appendix A. Appendix G provides excerpts of the projection scales used in the latest CPP and QPP actuarial valuation reports of these plans (as at December 31, 2009), for comparison purposes and design of the long-term projection scale. Appendix H contains numerical values for the complete life expectancy according to age and gender, while appendix I contains information on the present value of a $1,000/year life annuity due for various combinations of parameters. These results are computed on a generational basis at various selected calendar years from 2006 to 2056. Acknowledgements The author wishes to thank the Canadian Institute of Actuaries (CIA) for the grant that enabled the completion of this study. Also to be acknowledged is the support of the Society of Actuaries, the Chaire d actuariat de l Université Laval, and the Chaire d assurance et de services financiers L Industrielle-Alliance for their kind support in regard to previous works that led to the previous phases of this mortality study. Many thanks are due also to colleagues for their helpful comments and support at various stages of this project, in particular Professors Claire Bilodeau and Andrew Luong. As well, thanks are extended to former students and research assistants Thomas Landry and Zébret Konan Hagouagn Rin. The author wishes to thank actuaries at the Régie des rentes du Québec, in charge of the actuarial valuation of the Québec Pension Plan (QPP), for their support and help with the data issues and assistance pertaining to this study s results for QPP pensioners. Also, actuaries working at the Office of the Chief Actuary, in charge of the actuarial valuation of the Canada Pension Plan (CPP), are to be thanked for their support and help with the data issues and assistance pertaining to this study s results for CPP pensioners. The author is grateful for the helpful comments and suggestions made by members of the CIA Committee on Canadian Pensioners Mortality Experience (now known as the Pension Experience Subcommittee of the Research Committee).