Compound Growth and Health Care
Alex Tabarrok observes:
In my TED talk on growth and the economics of ideas I pointed out that average real world “GDP” per capita will be around $200,000 in 2100 if the world economy grows at the fairly modest rate of 3.3% per year on average. Many of the commentators at the TED website were incredulous. I think one of the reasons why is that most people have great difficulty understanding exponential processes.
That’s certainly been my observation as well. People are inclined to think that the difference between 3.3 percent and 3.1 percent must be tiny. But when you’re talking about 0.2 percent of a very big number—world output—and projecting it across a ninety-year span, you can get a big difference.
Much the same principle is illustrated by this chart from the Council on Economic Advisers illustrating the enormous gains that can be reaped through relatively small reductions in the rate of health care cost growth:
The 1.5 percent number would have big impacts, but looks it could really be achievable. Indeed, private industry at least claims that they’d be able to achieve those kind of reductions purely through voluntary measures that don’t even make key stakeholders scream and cry. That’s probably somewhat optimistic, but when you consider that a certain amount of screaming and crying could be inflicted you balance out and see that you’re looking at a quite plausible goal. The politics of getting there are difficult, but it’s really worth doing.
13 Responses to “Compound Growth and Health Care”
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June 3rd, 2009 at 2:06 pm
On the topic of people having difficulty understanding exponential growth, this essay, linked from TheBrowser, is really interesting. A bit long, but very much worth the read.
http://www.scottaaronson.com/writings/bignumbers.html
June 3rd, 2009 at 2:08 pm
Another word is compounding. I know it can be converted into an exponent, but it’s the power of compounding that drives numbers up exponentially.
June 3rd, 2009 at 2:26 pm
The other thing about exponential growth is that a resource that is 50% depleted over the course of 200 years can be completely depleted in 230 years. The failure to understand exponential processes cuts both ways here and fails to bolster the argument that everyone’s going to be really well off in 90 years as much as Mr. Tabarrok thinks it does.
June 3rd, 2009 at 2:32 pm
Shouldn’t slowing growth by more (ie 1.5 points vs .5 points) lead to a smaller portion of GDP?
What the hell is this graph saying?
June 3rd, 2009 at 2:35 pm
Seriously, I’ve been floored recently by how few people understand this phenomenon. I mean, it’s just inexcusable for professional people to not grasp this phenomenon in the age of 401(k)s.
People should intuitively understand this in a “oh, yeah, it’s the same reason it’s a bazillion times better for retirement to invest a small part of your income at 25 than a larger part of your income at 50, right.” It’s basically compound interest. It’s the old grains of rice on a chessboard. It’s “would you rather be paid a penny a day and every day have it doubled for a year, or would you rather be paid $10,000 a day.”
People in professional positions should immediately start looking for this kind of phenomena when they’re dealing with long time horizons, instead of being surprised by it. Pah.
June 3rd, 2009 at 2:41 pm
See Atul Gawande’s piece in the June 1 – ish New Yorker on cost disparities between locations. The culture of the practice of medicine locale by locale has an enormous impact on the cost of care in the US. Given his admittedly-partly-anecdotal account, a 1.5 % reduction in the rate of growth does not sound unrealistic.
June 3rd, 2009 at 3:01 pm
I’m skeptical of ANYTHING that looks like it’s on an exponential curve, especially growth. If you zoom out into the future, you find it’s actually a logistical curve far too often (carrying capacity being of course the standard 10th grade math class example). Note that plotting the number of blades on a safety razor gets you similar results: http://gizmodo.com/gadgets/gadgets/moores-law-for-razor-blades-14-blades-by-2100-161751.php
All of this applies a lot more to Alex Tabarrok than it does to your health care post, which seems within the realm of possibility, but it’s a thing to keep in mind.
June 3rd, 2009 at 3:13 pm
I like how MattY is copying arguments from Libertarianism lately. Government confiscating 30% of our wealth and redistributing it may cost us only 5-10% of actual possible growth… trivial in the short run, huge when you children are asking why we still drive around in polluting, inefficient, cars when they were invented 100 years ago.
June 3rd, 2009 at 3:43 pm
It’s not the result of 90 years of compound growth that should inspire incredulity, but the notion that 1) such a growth rate would necessarily be maintained for 90 years, and 2) the life of a population with $200K per capita annual income would resemble the life of those with such an income today.
June 3rd, 2009 at 3:55 pm
One quibble “But when you’re talking about 0.2 percent of a very big number”, when compounding whether it is a big number or not the relative difference at different rates will be large after 100 years, its the years that make a difference not the starting number.
In fact the chart you show doesn’t show or care about the beginning GDP value.
June 3rd, 2009 at 6:23 pm
Imagine a graph that also included a scenario of declining costs. Savings going one way and costs going the other and the gap between them growing, and growing and…you get picture.
But this is America. We are not allowed -by the Constitution- to cut health care costs. Instead, we have to take great pride in slowing the growth of costs.
Similar things are happening everywhere. Take military spending. Obama is clearly weak on defense because he cut military spending by increasing it only a little bit. As a result, my backyard, which used to be filled with sprightly Robins and Blue Jays, is now infested with unshackled terrorists.
June 3rd, 2009 at 7:06 pm
The problem is that 1.033^91 = 19.2. Going by the CIA estimate that global GDP per capita is $10,400, then that means that productivity per capita would have to grow by 3.3% per year for global average GDP to equal $200,000, unless there’s zero population growth and dependency ratios stay the same. If dependency ratios are rising, then productivity growth on a per worker rather than per capita basis would ahve to be greater than 3.3%. I wouldn’t call annual per worker productivity growth greater than 3.3% a “fairly modest rate.”
June 3rd, 2009 at 11:20 pm
Isn’t there something odd about saying that private industry can commit to slowing cost growth indefinitely? When you’re talking about exponential growth, there’s a big difference between “reducing growth by 1.5% every year for the next 10 years” and “reducing growth by 1.5% every year for the next 30 years”. I can imagine that people in industry would have a realistic idea of how to cut costs today, and even perhaps how to slow the growth of costs in the medium term, but are there really realistic policies that could be expected to cut cost growth every year in perpetuity?