# Online Appendix for Limited Life Expectancy, Human Capital and Health Investment

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1 Online Appendix for Limited Life Expectancy, Human Capital and Health Investment Authors: Emily Oster, E. Ray Dorsey, Ira Shoulson Appendix A: Incentive Calculations In section 6 we calculate the elasticity of demand for education and job training with respect to three outcomes: life years, disability-adjusted life years and discounted monetary return to investment. In this appendix we outline the details of these calculations. Appendix Table A1 provides the summary numbers for each group. For the symptom onset groups we simply do the described calculations for each particular age in the group and provide an average for the group. For the gene-positive and at-risk individuals we combine this type of calculation with information about age of onset. For example: for individuals who are gene-positive but without symptoms at 35 (the requirements for the education analysis) we calculate the probability of onset at each age after 35 given no symptoms at 35. We then calculate life expectancy for each age of onset, and average weighting based on the probability of onset by age. For at risk individuals we do a similar calculation but include as one of the possible outcomes the chance that they do not have the HD gene. The weight for this probability depends on the age at which they are still at risk without symptoms. Someone without symptoms at 40 is less likely to carry the gene than someone without symptoms at 30. This can be visualized based on Figure 1, and is taken into account in the analysis. A.1 Life Years Life expectancy is calculated based on information on the life course of HD. We use life table information from Newcombe (1981) on survival by years of symptom onset. To give a sense, he calculates that 4% of individuals will have died in the first four years, half by the end of 15 years and 95% by 30 years from onset. In addition, we take into account the fact that people might die from something else prior to HD. We incorporate overall death rates from US life tables as our background death probabilities (CDC, 2010).?? As we describe in Section 6, we calculate for each group the years of life after the possible completion of the human capital investment (either education or job training). This is important because, for example, the magnitude of the impact on education in the 23 to 27-year-old onset group is calculated relative to the share of individuals who are at risk for completion in that period. But those individuals will not accrue benefits to college starting at age 25; in fact, among individuals who have not completed college by this time, expected age of completion is 31. We calculate life years (or earnings returns) after this period. Denote ˆα as the age at which the investment would be completed. Further, define the probability of dying at each age as d a ; this probability is based on the time from symptoms and the background death rate. Life years after age ˆα are calculated as: [ T ] a=â (d a )(a) ˆα Column 1 of Table A1 reports this life year calculation by group. The figures in square parentheses in the symptom group labels indicate ˆα used for that group. A.2 Disability-Adjusted Life Years It is common in health economics to focus not only on life years but also on disability-adjusted life years. The idea is that individuals will not (and, hence, policy makers should not) value all years equally. If someone is in a vegetative state their quality of life is assumed to be low, and should not be counted as equal to a year of perfect health. To calculate disability-adjusted life years in this case we need to take a stand on the quality of life for individuals with varying symptom levels. There is no standard way to do this, but our data provides a natural 1

3 Life Years DALYs Return to College Return to Job Training (1) (2) (3) (4) Groups for Gene Testing Analysis Without Gene [ ˆα =25] \$412,199 With Gene, No Symptoms at 35 [ ˆα =25] \$311,485 Groups for Education Symptom Analysis Symptoms [ ˆα =25] \$23,161 Symptoms [ ˆα =25] \$38,565 Symptoms [ ˆα =31] \$28,517 At risk at 30 [ ˆα =25] \$336,495 Groups for Job Training Analysis Symptoms 20-29[ ˆα =25] \$3534 Symptoms [ ˆα =35] \$3605 At risk at 40 [ ˆα =25] \$15,138 A.4. Smoking Summarizing the incentives to quit smoking (or not start at all) is a bit more complicated. In general, cigarette smoking leads to an increased probability of death from a variety of causes, including lung cancer and emphysema. Much of this excess death occurs later in life, so a shortened lifespan will limit the incentive to avoid smoking. Calculating detailed returns by group as we did for education and job training is difficult, because there are many possible behaviors never start smoking, start early and quit early, start early and don t quit, start late, smoke more, smoke less, etc. What we can do, however, without needing such detailed information on exact smoking behavior, is give a sense of the benefits to either (a) never smoking or (b) quitting for people with varying life expectancy. The evidence in Table A1 demonstrates that life expectancy is limited for people with HD; if the benefits to not smoking or quitting are larger for those with greater life expectancy, we can conclude there is some added incentive to quit for those without HD. We use data on total probability of death by age for smokers, non-smokers and former smokers from As our benchmark, we consider someone who begins smoking at age 20, and smokes one pack a day. We calculate the excess probability of death for individuals with alternative life expectancy of 40, 50, 60, 70 and 80; that is, we calculate the excess chance of dying from smoking if you knew you would die at age 40 independent of the cigarettes. We look both at the benefits to never starting to smoke, and the benefits to quitting at age 40 (again, assuming an age 20 start). The gains to not smoking or quitting are shown in Appendix Figure A1. Individuals with higher non-smoking life expectancy have higher benefits from either never smoking or quitting. Since this figure shows the difference in death in percentage points, it decreases at the oldest ages since, ultimately, everyone dies in both groups. The impact of smoking is large. For someone who would otherwise live only to 40, the benefit of not smoking is only about a 3 percentage point difference in the chance of death. For someone who would otherwise live to 70, it is 25 percentage points. The impacts of quitting are smaller, of course, but still very different based on life expectancy. 3

4 Figure A1: Benefits to Not Smoking Excess Survial Probability Non Smoking Life Expectancy Never Starting Quitting at 40 A.5 Cancer Screening The simplest way to document the varying benefits to cancer screening by group is to look at the chance of ever developing breast or colon cancer by group. Since screening is an effective way to detect cancer, the benefits to screening are higher if the incidence of cancer is higher. Put differently, since both breast and colon cancer are typically fatal without treatment and survival is fairly good with treatment, we can think of the benefits to screening as scaling with incidence. For each type of cancer we compare the chance of developing that cancer by group, where the groups are as in the regression: individuals with symptoms by screening age versus those at risk but without symptoms by that age. For breast cancer, we compare the lifetime breast cancer probability for individuals with onset between 30 and 40 to those at risk without symptoms at 40. For colon cancer, the groups are those with symptoms between 35 and 45 versus no symptoms at 45. Cancer incidence by age is taken from the SEER cancer statistics ( We compute the lifetime risk of cancer by combining these incidence numbers with the chance of still being alive at each age. The results are shown in Appendix Table A2. Lifetime cancer risk is much higher for the at-risk individuals. Comparing the two cancer groups, we see the percentage increase is higher for colon cancer, although the absolute numbers are higher for breast cancer, which is more common. 4

5 Table A2: Cancer Probabilities by Group Chance of Ever Developing Breast Cancer Colon Cancer (1) (2) Groups for Breast Cancer Analysis At risk at % Symptoms % Groups for Colon Cancer Analysis At risk at % Symptoms % 5

6 Appendix B: Tables and Figures Table B1: Balancing Across Individual Groups for Symptom Analysis Panel A: Education and Job Training Education Grouping: Onset Age Job Training Grouping: Onset Age Over Over 40 (n=25) (n=45) (n=86) (n=1991) (n=26) (n=60) (n=255) Male (0/1) White Current Age a,b 53.9 a,b,c d 58.1 d,e In US Mom HD Parent Panel B: Health Smoking Grouping: Current Symptoms Cancer Screening Grouping: Onset Age None Early Over 45 (n=172) (n=359) (n=140) (n=950) Male (0/1) f White f Current Age f g In US g Mom HD Parent Notes: This table shows balancing by the symptom onset groups. Significance marks (all at 5% level): a compared to onset 15-18; b compared to onset 19-22; c compared to onset 23-28; d compared to onset 20-29; e compared to onset 30-39; f compared to no symptoms; g compared to onset 30 to 45. 6

7 Table B2: Gene Testing and Educational Attainment, Only Tested Individuals Panel A: Main Results and Robustness Main Results Control Referral Method # Post-HS Years Bachelor # Post-HS Years Bachelor Education Degree Education Degree Sample Finish HS Finish HS Finish HS Finish HS Tested, Negative (.369) (.096) (.378) (.103) Standard Controls YES YES YES YES # of Observations Panel B: Falsification Pre-Symptom Education Older Testers Complete # Post-HS Years Bachelor High School Education Degree Sample Finish HS Finish HS Tested, Negative (.049) (.370) (.093) Standard Controls YES YES YES # of Observations Notes: This table shows the impact of test results on educational attainment. The omitted category is individuals who have been tested and learn they do carry the HD mutation. The main results include individuals who are tested before or at the age of 28, and (if positive) do not develop symptoms before 35. Columns 3 and 4 of Panel B show results for individuals who were tested between 35 and 45, but did not have symptoms before 45. Standard controls: gender, country dummies, race and a control for age. Referral group control simply controls for whether the individual was recruited by a doctor (the primary recruitment method) or in another way (at a meeting, online, etc). Standard errors in parentheses. significant at 10% significant at 5% significant at 1% Table B3: Gene Testing and Smoking, Only Tested Individuals Smoke Now Smoke Now Sample All Ever Smoke=1 Tested, Negative (.029) (.101) Standard Controls YES YES # of Observations Notes: This table shows the impact of test results on smoking. The omitted category is individuals who have been tested and learn they do carry the HD mutation. Standard controls: gender, country dummies, race, age, dummies for education. Standard errors in parentheses. significant at 10% significant at 5% significant at 1% 7

8 Figure B1: College Completion by Age % of College Completion Done Age Notes: This figure shows the timing of college completion by age. To construct this graph we use data from the 1980, 1990 and 2000 census and the 2010 American Community Survey. We begin with the 1980, 1990 and 2000 census. We take individuals who are 35 to 54 in the 2000 census and match them to the same birth cohort in the 1980 and 1990 census. We assume the 2000 data represents the final education for that cohort. We generate the share of college completion by age X as the level at age X divided by the final level in that group. We do a similar thing for the 1990, 2000 and 2010 combination. We average by age and graph. Figure B2: Within-Sibling Group Education Effects (N=24) Share Completing This Level High School Start College Bachelor Degree Onset by 28 No Sympt by 30 Notes: This figure shows educational attainment for sibling groups in which we observe more than one sibling and one of the siblings has earlier HD onset. The sample size is very small. 8

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