Discounting Grief

how much grief is the right amount?

As I mentioned on Wednesday, we said goodbye to our dog Marley on Tuesday morning. We’re still sad about losing her of course, and it has had me thinking about grief and loss. And of course I started thinking about it in economic terms, and I thought I’d share that with you today. 

Marley was very old for a dog of her size (about 70 lbs) - she was about 15 - my understanding is 12 is more the norm. I’m not an expert by any means on dog life spans, but we think she lived a pretty good, long life. We would not have expected her to live much longer, regardless. And yet we are quite sad. Right up until Monday afternoon when her back legs suddenly gave out, almost certainly due to spinal degeneration (she was having other neurological issues), I would have imagined her living another year. In a sense, I feel like I lost a year of her company. You get a little bit of happiness every day from having a dog. When you come home, you know, without thinking about it, that someone is going to be very excited that you have returned. You know while you are cooking dinner that someone will be wandering about the kitchen waiting for scraps to be tossed from the cutting board. I had unconsciously counted on that company, and it was part of my psychological wealth. Then suddenly on Tuesday morning I lost that whole year’s worth of happiness all at once. I think that is why the grief of loss is so intense - it hits all at once. The small doses of happiness you were counting on to be titrated into your life suddenly aren’t going to come. The feeling of loss is not just for the immediate moment, but all of the moments that you had counted on. Had Marley been much younger, the sense of loss would have been much greater, because I would have counted on more years of company. 

I think this sense of loss generalizes to all relationships, not just pet relationships. Relationships with humans can go on for far longer than relationships with animals because of our life spans, so there is more time to potentially lose. When a romantic relationship ends, you are saddened, especially if you are the one who is rejected, because you had been counting on a future flow of happiness coming from the relationship. Maybe it was years of happiness you had imagined, now just gone. Certainly the devastation of losing a child is in part the loss of the life-time of happiness and meaning you imagined, and maybe even the thought of a legacy going on beyond your own death - so in this case the years go on and on, potentially into some sort of infinite future. 

Let’s now play around with discounting the value of future happiness, using the time value of money approach. I’ll go back to thinking about Marley so as not to be too dark. Let’s assume it is Sunday, the day before she gets sick. I had been walking around the yard with her, blowing the leaves. She was keeping me company. I assumed I had at least another year with her. Let’s assume I can put a number on that total amount of happiness. Let’s call it 10. But it was 10 I was going to get over the course of the year. On Tuesday, she passes, and I feel the weight of losing 10 units of happiness all at once. It’s a lot. It’s been five days and I am processing her loss still. I am not as sad as I was on Tuesday. It takes some days to process a loss of 10 - it haunts my quiet moments. But in a couple of weeks, I know I won’t tear up when I think about her. She did live a good, long life, and I didn’t expect for her to be around too much longer. But what if I had thought she would be around for five more years instead of one. How much loss would I have experienced? Let’s assume each year’s happiness is 10. Well, 5x10 = 50, so 50, right?

I’ll discount on a yearly basis. “EOY” stands for end of year. So at the end of each year, I will have experienced 10 units of happiness. If I treat all the future flows of happiness as the same as the flow of happiness I feel this year, then I would indeed have 50 units of happiness. The “discount rate” measures how much less I value the future vs. the present. We all discount the future to some degree. Every time you say, “I will eat this piece of cake today and be better about my diet tomorrow” you are engaging in discounting the future. You are choosing happiness today over happiness tomorrow, because you will enjoy the cake today, but deal with the costs tomorrow. How much we discount the future affects how we behave in the present. People with high discount rates treat things that come in the future as having much less value; people with low discount rates treat things that come in the future as having closer value to things in the present. People with low discount rates have higher levels of patience because they see the things in the future as worth the same as things today. 

So what’s a more realistic value of loss? Let’s say I discounted the future at 10%. The result is quite a bit different.

Now five years worth of companionship would be worth only 37.91, rather than 50. And if I go even higher, to a 25% discount rate, the value is only 26.89.

A person who discounts the future at a higher rate will feel the loss less sharply than a person who does not simply because the person with the high discount rate feels like they have lost less. 

We all make judgments about people’s grief. All relationships can be thought of as having flows of happiness. When a relationship ends, as a result of a break up, or the result of death, how long should someone grieve the loss of that relationship? If a friend gets dumped by their girlfriend/boyfriend, how long is it reasonable to support them grieving? At what point do you tell them to get over it and move on? How long should someone grieve the loss of a parent? Grandparent? Spouse? Child? It would depend on their assumptions about their flow of happiness each year, the number of expected years, and their discount rate about the future. All unknowable things in any precise way, and yet we have cultural norms that give us general expectations. 

I remember when my 92 year old grandmother passed. I was heartbroken, but it was hardly a surprise. I felt the grief acutely for a week or so, and then it gradually began to lift. My mother died when she was 50. That was much harder, and the grief lingered much longer, because so many more years were lost. I hope I never have the challenge of grieving the loss of a child, but having listened to people who have, I know that grief is overpowering because of its magnitude. And yet, eventually even people who lose children are able to return to functioning. Even after more than 20 years, I am sometimes sad that I can’t share something with my mother or even my grandmother, and that is a feeling of loss, but I am well past grief. 

Thirty minutes after Marley passed, I was in the classroom teaching. I didn’t tell the students until after the class what had happened (and then by email) because all I wanted at that moment was to delay processing. Had this been a human relationship, I couldn’t have done that. The grief would have been too powerful. 

This is a very simplistic model. I’m sure someone has done something more complex - I haven’t bothered to look in the literature. I think it’s useful to have a model like this in one’s mind, and I think intuitively we do. We all have some sense of how long someone should grieve, and it depends on the nature of the loss. Appropriately grieving fits into Smith’s distributive justice - a becoming use of one’s own, and of course getting it right depends on estimative justice. 

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Thanks for indulging me. I promise not to write about Marley except in passing in the future. 

I had planned on sharing my interview with Marc Hubbard, the UNH Men’s Soccer Coach, this week, but Marley’s passing threw my week off. It’s a great interview - he has a lot of insight about leadership. I should have it out next Sunday. I hope you check it out.