# The Declining Effect of Insurance on Life Expectancy

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{1}(how education affects life expectancy) is a constant when in truth β

_{1}varies with q

_{i}(race), and this ignoring of Equation (2) creates an omitted variables problem. The αs and βs are coefficients to be estimated, Y is the dependent variable, X is the explanatory variable, u is random error, and “q

_{t}” represents the combined influence of all omitted variables plus any random variation in β

_{1}itself.

_{t}= α

_{0}+ β

_{1}X

_{t}+ u

_{1}= α

_{1}+ α

_{2}q

_{t}

_{t}= α

_{0}+ α

_{1}X

_{t}+ α

_{2}X

_{t}q

_{t}+ u

_{t}.

^{True}= α

_{1}+ α

_{2}q

_{t}

_{t}:

_{t}/X

_{t}= α

_{0}/X

_{t}+ α

_{1}+ α

_{2}q

_{t}+ u

_{t}/X

_{t}

_{1}+ α

_{2}q

_{t}= Y

_{t}/X

_{t}− α

_{0}/X

_{t}− u

_{t}/X

_{t}

^{True}= Y

_{t}/X

_{t}− α

_{0}/X

_{t}− u

_{t}/X

_{t}

_{t}is random error which should be relatively small, and u

_{t}/X

_{t}even smaller if |X

_{t}| > 1. Leightner et al. (2021) show that eliminating u

_{t}/X

_{t}from Equation (7) does not bias the results, and that elimination produces Equation (8).

_{t}/X

_{t}− α

_{0}/X

_{t}

_{t}/X

_{t}is then subtracted from the corresponding layer’s slope to produce a new dependent variable; and then a final regression is run between that new dependent variable and 1/X

_{t}to find an α

_{0}which is then plugged into Equation (8) along with Y

_{t}and X

_{t}. The mathematical equations underlying RTPLS are explained in Leightner (2015). In this paper’s application, Y is life expectancy and X is insurance premiums per capita.

_{0}obtained from this final regression along with values for Y and X are plugged into Equation (8) to produce an estimated slope value for each observation where differences in these slope estimates are due to omitted variables, q. The purpose of this final regression is to create more accurate estimates. If every observation on every frontier in the peeling down and up process corresponded to exactly the same value for q (for example, 95, 95, 95, and 95 for the first iteration and 93, 93, 93, and 93 for the second iteration, etc.), then the TPLS estimates would be 100 percent accurate. This final regression eliminates most of the inaccuracy added to the TPLS estimates by the q values along a given frontier not being identical.

^{2}being 0.47. Since the estimated coefficient for X is highly significant and 47 percent of the variation in Y is explained, this regression looks successful, but it is not. Remember the correct equation is 300 + 10X + 0.7Xq. The OLS regression did the best it could given its assumption of a constant dY/dX; indeed OLS produced an estimated dY/dX in the ballpark of 10 + 0.7E[q] where E[q] is the expected (or mean) value for q. For Figure 1, E[q] is 49.7 and 10 + 0.7E[q] is 44.8 which is in the ballpark of the estimated 38.9.

_{n−1,α/2}

_{n−1,α/2}is taken off the standard t table for the desired level of confidence. Leightner et al. (2021) used an estimate along with the 4 estimates before it and a 95% confidence level to create a moving confidence interval (much like a moving average) for a given set of RTPLS estimates. This 95% confidence interval can be interpreted as meaning that there is only a five percent chance that the next RTPLS estimate will lie outside of this range if omitted variables maintain the same amount of variability that they recently have.

## 3. Results

## 4. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Barlow, Robin, and Bilkis Vissandjee. 1999. Determinants of National Life Expectancy. Canadian Journal of Development Studies/Revue Canadienne D’études Du Développement 20: 9–29. [Google Scholar] [CrossRef]
- Bergh, Andreas, and Therese Nilsson. 2010. Good for Living? On the Relationship between Globalization and Life Expectancy. World Development 38: 1191–203. [Google Scholar] [CrossRef]
- Branson, Johannah, and Charles Albert (Knox) Lovell. 2000. Taxation and Economic Growth in New Zealand. In Taxation and the Limits of Government. Edited by Gerald W. Scully and Patrick James Caragata. Boston: Kluwer Academic, pp. 37–88. [Google Scholar]
- Chetty, Raj, Michael Stepner, Sarah Abraham, Shelby Lin, Benjamin Scuderi, Nicholas Turner, Augustin Bergeron, and David Cutler. 2016. The Association Between Income and Life Expectancy in the United States, 2001–2014. Journal of the American Medical Association 315: 1750–66. [Google Scholar] [CrossRef] [PubMed]
- Leightner, Jonathan E. 2015. The Limits of Fiscal, Monetary, and Trade Policies: International Comparisons and Solutions. Singapore: World Scientific. [Google Scholar]
- Leightner, Jonathan E., Tomoo Inoue, and Pierre Lafaye de Micheaux. 2021. Variable Slope Forecasting Methods and COVID-19 Risk. Journal of Risk and Financial Management 14: 467. [Google Scholar] [CrossRef]
- Lemaire, Jean. 2005. The Costs of Firearm Deaths in the United States: Reduced Life Expectancies and Increased Insurance Costs. Journal of Risk and Insurance 72: 359–74. [Google Scholar] [CrossRef] [Green Version]
- Mathers, Colin D., Gretchen A. Stevens, Ties Boerma, Richard A. White, and Martin I. Tobias. 2015. Causes of international increases in older age life expectancy. The Lancet 385: 540–48. [Google Scholar] [CrossRef] [PubMed]
- Meara, Ellen R., Seth Richards, and David M. Cutler. 2008. The Gap Gets Bigger: Changes In Mortality And Life Expectancy, By Education, 1981–2000. Health Affairs 27: 350–60. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Olshansky, S. Jay, Douglas J. Passaro, Ronald C. Hershow, Jennifer Layden, Bruce A. Carnes, Jacob Brody, Leonard Hayflick, Robert N. Butler, David B. Allison, and David S. Ludwig. 2005. A Potential Decline in Life Expectancy in the United States in the 21st Century. New England Journal of Medicine 352: 1138–45. [Google Scholar] [CrossRef] [PubMed]

1983 | 1984 | 1985 | 1986 | 1987 | 1988 | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | |

Australia | 177 | 92 | 109 | 208 | 67 | 52 | 46 | 41 | 43 | 47 | 34 | 67 | 66 |

Austria | 82 | 61 | 53 | 54 | 44 | 43 | 38 | 37 | 34 | 30 | |||

Belgium | 113 | 120 | 119 | 86 | 68 | 62 | 62 | 50 | 48 | 43 | 46 | 43 | 35 |

Canada | 69 | 64 | 57 | 50 | 51 | 48 | 44 | 42 | 46 | 53 | 53 | 51 | |

Chile | |||||||||||||

Columbia | |||||||||||||

Costa Rica | |||||||||||||

Czech Rep. | 659 | 505 | 409 | ||||||||||

Denmark | 128 | 115 | 93 | 70 | 53 | 45 | 48 | 38 | 37 | 32 | 33 | 27 | 24 |

Estonia | |||||||||||||

Finland | 109 | 114 | 105 | 72 | 56 | 48 | 45 | 33 | 33 | 36 | 87 | 81 | 61 |

France | 106 | 106 | 100 | 70 | 53 | 45 | 43 | 36 | 34 | 29 | 28 | 26 | 22 |

Germany | 88 | 95 | 94 | 69 | 56 | 50 | 51 | 43 | 38 | 28 | 28 | 25 | 22 |

Greece | 5976 | 522 | 453 | 392 | 321 | ||||||||

Hungary | 678 | 623 | 567 | 537 | |||||||||

Iceland | 127 | 134 | 134 | 109 | 79 | 61 | 66 | 59 | 52 | 50 | 60 | 61 | 59 |

Ireland | 112 | 81 | 55 | 56 | 51 | 45 | 43 | 40 | 38 | 37 | 31 | ||

Israel | |||||||||||||

Italy | 426 | 409 | 372 | 248 | 181 | 156 | 149 | 113 | 99 | 83 | 84 | 77 | 63 |

Japan | 90 | 81 | 71 | 43 | 33 | 23 | 23 | 25 | 23 | 21 | 18 | 16 | 15 |

Korea (S) | 51 | 39 | |||||||||||

Latvia | |||||||||||||

Lithuania | |||||||||||||

Luxembourg | 151 | 138 | 13 | 5 | |||||||||

Mexico | 850 | 736 | 717 | 1183 | |||||||||

Netherlands | 77 | 85 | 83 | 60 | 48 | 43 | 42 | 33 | 33 | 28 | 30 | 27 | 23 |

NewZealand | 336 | 184 | 94 | 97 | 114 | 113 | 124 | 111 | 102 | ||||

Norway | 72 | 74 | 66 | 50 | 43 | 40 | 42 | 37 | 36 | 33 | 37 | 83 | 76 |

Poland | 1113 | 1045 | 830 | ||||||||||

Portugal | 1682 | 1596 | 1392 | 871 | 625 | 479 | 411 | 270 | 228 | 180 | 163 | 143 | 108 |

Slovak | |||||||||||||

Slovania | |||||||||||||

Spain | 830 | 773 | 686 | 311 | 209 | 115 | 154 | 142 | 120 | 104 | 106 | 84 | 76 |

Sweden | 58 | 59 | 79 | 65 | 59 | ||||||||

Switzerland | 28 | 32 | 30 | 21 | 16 | 15 | 15 | 13 | 12 | 11 | 11 | 10 | 8 |

Turkiye | 8754 | 8293 | 8229 | 7924 | 6314 | 5717 | 4787 | 2974 | 2684 | 2273 | 1801 | 2650 | 2097 |

UK | 68 | 49 | 73 | 65 | 64 | 54 | 48 | 41 | 21 | 22 | 21 | ||

USA | 52 | 48 | 40 | 33 | 29 | 19 | 23 | 21 | 21 | 20 | 19 | 18 | 18 |

Argentina | |||||||||||||

Brazil | |||||||||||||

Indonesia | |||||||||||||

Russia | |||||||||||||

South Africa | |||||||||||||

mean | 1108 | 688 | 593 | 526 | 408 | 351 | 301 | 201 | 177 | 216 | 241 | 243 | 220 |

1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | |

Australia | 29 | 26 | 28 | 25 | 29 | 32 | 28 | 26 | 22 | 22 | 21 | 17 | 17 |

Austria | 26 | 32 | 32 | 32 | 34 | 35 | 31 | 25 | 22 | 22 | 21 | 18 | 17 |

Belgium | 34 | 36 | 31 | 29 | 29 | 29 | 28 | 19 | 15 | 13 | 15 | 13 | 13 |

Canada | 51 | 52 | 56 | 34 | 30 | 29 | 27 | 22 | 19 | 17 | 16 | 13 | 16 |

Chile | 179 | ||||||||||||

Columbia | |||||||||||||

Costa Rica | |||||||||||||

Czech Rep. | 345 | 345 | 304 | 289 | 287 | 246 | 188 | 139 | 120 | 108 | 98 | 82 | 66 |

Denmark | 22 | 23 | 21 | 23 | 26 | 24 | 19 | 18 | 16 | 13 | 12 | 10 | 9 |

Estonia | 537 | ||||||||||||

Finland | 51 | 58 | 51 | 45 | 43 | 50 | 47 | 42 | 38 | 35 | 36 | 34 | 31 |

France | 21 | 22 | 25 | 25 | 25 | 26 | 25 | 19 | 16 | 14 | 12 | 11 | 12 |

Germany | 22 | 24 | 24 | 24 | 26 | 26 | 22 | 18 | 15 | 15 | 16 | 16 | 14 |

Greece | 281 | 286 | 254 | 217 | 239 | 240 | 208 | 155 | 127 | 119 | 97 | 81 | 75 |

Hungary | 505 | 479 | 441 | 418 | 381 | 347 | 263 | 203 | 171 | 147 | 131 | 100 | 99 |

Iceland | 60 | 65 | 64 | 60 | 59 | 65 | 57 | 43 | 40 | 360 | 35 | 28 | 36 |

Ireland | 27 | 24 | 18 | 13 | 9 | 14 | 8 | 6 | 6 | 5 | 4 | 3 | |

Israel | 48 | 43 | 36 | ||||||||||

Italy | 61 | 58 | 48 | 42 | 44 | 41 | 34 | 26 | 23 | 21 | 21 | 21 | 22 |

Japan | 18 | 19 | 22 | 20 | 20 | 22 | 23 | 22 | 21 | 20 | 21 | 19 | 17 |

Korea (S) | 36 | 38 | 49 | 45 | 39 | 46 | 43 | 40 | 36 | 29 | 24 | 21 | 24 |

Latvia | |||||||||||||

Lithuania | |||||||||||||

Luxembourg | 6 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 2 | 2 | 2 | 2 | 2 |

Mexico | 1110 | 917 | 749 | 587 | 446 | 437 | 389 | 472 | 428 | 418 | 360 | 314 | 299 |

Netherlands | 22 | 23 | 21 | 21 | 22 | 21 | 20 | 16 | 14 | 14 | 15 | 13 | 12 |

New Zealand | 76 | 75 | 97 | 120 | 137 | 160 | 116 | 80 | 70 | 76 | 67 | 72 | |

Norway | 33 | 32 | 32 | 32 | 31 | 29 | 23 | 19 | 16 | 14 | 15 | 13 | 10 |

Poland | 630 | 511 | 432 | 413 | 404 | 355 | 348 | 303 | 257 | 203 | 161 | 123 | 79 |

Portugal | 94 | 103 | 87 | 76 | 75 | 67 | 51 | 43 | 33 | 34 | 30 | 25 | |

Slovak | 533 | 447 | 473 | 456 | 408 | 336 | 234 | 184 | 389 | 152 | 118 | 92 | |

Slovania | 47 | 37 | |||||||||||

Spain | 71 | 74 | 71 | 60 | 55 | 56 | 47 | 45 | 38 | 36 | 33 | 31 | 27 |

Sweden | 52 | 32 | 31 | 40 | 24 | 23 | 19 | 16 | 15 | 16 | 16 | 16 | |

Switzerland | 10 | 11 | 10 | 11 | 11 | 10 | 9 | 9 | 9 | 9 | 10 | 9 | 7 |

Turkiye | 1872 | 1610 | 1438 | 1190 | 1008 | 1417 | 1334 | 987 | 712 | 655 | 591 | 423 | 397 |

UK | 20 | 18 | 16 | 14 | 12 | 13 | 12 | 10 | 9 | 9 | 6 | 5 | 7 |

USA | 17 | 16 | 14 | 14 | 13 | 13 | 11 | 9 | 9 | 9 | 9 | 8 | 8 |

Argentina | |||||||||||||

Brazil | |||||||||||||

Indonesia | |||||||||||||

Russia | 433 | 320 | 231 | ||||||||||

South Africa | |||||||||||||

mean | 193 | 185 | 164 | 146 | 136 | 143 | 135 | 104 | 84 | 95 | 96 | 63 | 55 |

2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | Mean | |

Australia | 20 | 17 | 14 | 14 | 14 | 13 | 16 | 18 | 18 | 19 | 22 | 24 | 42 |

Austria | 18 | 18 | 22 | 23 | 23 | 22 | 23 | 32 | |||||

Belgium | 14 | 15 | 14 | 14 | 16 | 16 | 19 | 20 | 20 | 18 | 17 | 18 | 37 |

Canada | 24 | 21 | 20 | 19 | 19 | 20 | 23 | 24 | 22 | 23 | 35 | ||

Chile | 141 | 108 | 93 | 81 | 79 | 85 | 83 | 77 | 76 | 71 | 79 | 103 | 97 |

Columbia | 428 | 356 | 308 | 259 | 235 | 251 | 308 | 310 | 282 | 273 | 277 | 312 | 300 |

Costa Rica | 331 | 304 | 264 | 240 | 218 | 243 | 213 | 198 | 199 | 189 | 188 | 235 | |

Czech Rep. | 72 | 67 | 62 | 70 | 69 | 73 | 89 | 92 | 87 | 79 | 78 | 77 | 182 |

Denmark | 9 | 9 | 8 | 9 | 9 | 8 | 8 | 8 | 8 | 30 | |||

Estonia | 198 | 121 | 122 | 111 | 88 | 81 | 90 | 84 | 74 | 63 | 63 | 65 | 131 |

Finland | 30 | 24 | 28 | 31 | 22 | 21 | 25 | 29 | 29 | 57 | 44 | 64 | 49 |

France | 11 | 12 | 12 | 14 | 13 | 12 | 14 | 11 | 11 | 11 | 11 | 12 | 29 |

Germany | 18 | 18 | 17 | 14 | 13 | 13 | 15 | 15 | 14 | 13 | 13 | 12 | 30 |

Greece | 81 | 85 | 86 | 101 | 108 | 115 | 145 | 147 | 136 | 128 | 126 | 122 | 381 |

Hungary | 125 | 126 | 125 | 150 | 142 | 141 | 169 | 160 | 144 | 134 | 127 | 128 | 268 |

Iceland | 61 | 45 | 41 | 43 | 41 | 40 | 42 | 37 | 30 | 29 | 32 | 36 | 66 |

Ireland | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 6 | 23 |

Israel | 39 | 36 | 33 | 34 | 31 | 31 | 32 | 30 | 27 | 26 | 25 | 25 | 33 |

Italy | 19 | 19 | 21 | 23 | 20 | 17 | 20 | 21 | 21 | 20 | 20 | 20 | 83 |

Japan | 14 | 13 | 12 | 15 | 20 | 20 | 22 | 16 | 18 | 17 | 17 | 18 | 25 |

Korea (S) | 26 | 22 | 19 | 16 | 16 | 15 | 15 | 15 | 15 | 14 | 14 | 29 | |

Latvia | 209 | 243 | 188 | 180 | 163 | 147 | 171 | 169 | 136 | 110 | 102 | 107 | 160 |

Lithuania | 262 | 223 | 228 | 199 | 187 | 206 | 186 | 162 | 139 | 136 | 131 | 187 | |

Luxembourg | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 13 |

Mexico | 326 | 296 | 259 | 253 | 222 | 224 | 248 | 259 | 238 | 226 | 206 | 231 | 462 |

Netherlands | 13 | 17 | 15 | 17 | 18 | 19 | 24 | 12 | 11 | 11 | 28 | ||

New Zealand | 77 | 69 | 51 | 46 | 45 | 53 | 53 | 50 | 37 | 97 | |||

Norway | 28 | 13 | 11 | 10 | 11 | 10 | 14 | 14 | 14 | 13 | 13 | 14 | 30 |

Poland | 119 | 110 | 103 | 104 | 109 | 115 | 137 | 141 | 121 | 116 | 120 | 122 | 308 |

Portugal | 28 | 27 | 36 | 41 | 33 | 30 | 40 | 46 | 43 | 37 | 41 | 50 | 252 |

Slovak | 96 | 99 | 93 | 100 | 94 | 94 | 117 | 56 | 101 | 101 | 217 | ||

Slovania | 35 | 37 | 36 | 39 | 39 | 39 | 46 | 46 | 42 | 39 | 38 | 36 | 40 |

Spain | 29 | 33 | 29 | 34 | 33 | 33 | 38 | 34 | 34 | 32 | 35 | 36 | 125 |

Sweden | 19 | 20 | 18 | 21 | 19 | 10 | 13 | 14 | 12 | 11 | 11 | 28 | |

Switzerland | 7 | 7 | 6 | 6 | 6 | 6 | 6 | 7 | 7 | 7 | 7 | 7 | 11 |

Turkiye | 432 | 372 | 368 | 335 | 300 | 327 | 346 | 301 | 320 | 375 | 356 | 2215 | |

UK | 10 | 10 | 10 | 9 | 10 | 9 | 10 | 9 | 9 | 8 | 9 | 9 | 22 |

USA | 8 | 8 | 8 | 7 | 7 | 7 | 6 | 6 | 6 | 7 | 6 | 6 | 16 |

Argentina | 153 | 130 | 118 | 114 | 114 | 123 | 114 | 185 | 189 | 138 | |||

Brazil | 147 | 187 | 178 | 159 | 174 | 171 | 224 | 177 | |||||

Indonesia | 751 | 786 | 879 | 864 | 741 | 666 | 693 | 673 | 743 | 755 | |||

Russia | 393 | 296 | 267 | 420 | 401 | 327 | 303 | 312 | 337 | ||||

South Africa | 46 | 42 | 47 | 45 | 49 | 55 | 62 | 64 | 51 | ||||

mean | 90 | 84 | 81 | 92 | 87 | 92 | 105 | 99 | 90 | 91 | 96 | 92 | 173 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Leightner, J.
The Declining Effect of Insurance on Life Expectancy. *J. Risk Financial Manag.* **2023**, *16*, 6.
https://doi.org/10.3390/jrfm16010006

**AMA Style**

Leightner J.
The Declining Effect of Insurance on Life Expectancy. *Journal of Risk and Financial Management*. 2023; 16(1):6.
https://doi.org/10.3390/jrfm16010006

**Chicago/Turabian Style**

Leightner, Jonathan.
2023. "The Declining Effect of Insurance on Life Expectancy" *Journal of Risk and Financial Management* 16, no. 1: 6.
https://doi.org/10.3390/jrfm16010006