Fun With the Y Axis
This suggestive chart from Andrew Biggs at AEI seems to have impressed Greg Mankiw. It shows, allegedly, that the growth in health care spending has tracked the growth in veterinary spending:
But look at the Y axes. They don’t match up! This is almost a chart in which the same vertical distance that denotes a $2 billion increase in veterinary expenditures represents a $500 billion increase in human health care expenditures. But not quite. Note that the distance between $2,000 billion and $2,500 billion on the right axis is clearly larger than the distance between $10 billion and $12 billion on the left.
I’m not sure what difference cleaning the charts up would make, but it would certainly make them a lot easier to interpret. One would also want to do some kind of normalizing by population size. Has the number of pets grown relative to the number of people? Shrunk? We know that the demographics of the human population has been aging, but probably not the pet population.
57 Responses to “Fun With the Y Axis”
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July 14th, 2009 at 11:30 am
Yeah, whatever. I demand a snarky comment on this.
July 14th, 2009 at 11:30 am
Matt criticizing other people’s charts. In a post in which he screws up the formatting of a chart.
Priceless.
(Which in no way is intended to suggest Matt is wrong in substance).
July 14th, 2009 at 11:34 am
I can’t see the right axis.
July 14th, 2009 at 11:35 am
I think it’s a fair point to say that Yglesias should never criticize other people’s graphs.
It’s also fair to say that if two functions grow at the same growth rate (2.5% a year or whatever) then that’s significant even if the absolute growth rates are very different, so changing the y-axis is not an inherently illegitimate manuever. However, since the two graphs are basically linear on the timescales graphed, this graph isn’t a very rigorous way to compare growth rates. And even if they do have the same growth rate, the relationship could be more complicated than the graph implies. So yes, it is in fact a flawed graph.
July 14th, 2009 at 11:35 am
(Which in no way is intended to suggest Matt is wrong in substance).
Uh, Matt is wrong on substance. The only thing relevant is if the Zeros are lined up (they are), and they are on a linear scale (they are). The only trick here is that vet spending starts from a slightly higher basis, so its growth is actually slower, but the main implication of the chart is not deceptive.
July 14th, 2009 at 11:36 am
The chart looks OK to me–each billion on the left corresponds to about $208 billion on the right. I do not see the problem.
July 14th, 2009 at 11:36 am
My dog is aging, we can’t go on long walks in the winter anymore on account of her thritis.
July 14th, 2009 at 11:38 am
What are you talking about? The two scales are proportional. $1250 billion on the right matches up with $6 billion on the left; twice those numbers ($2500 billion and $12 billion) also match up.
The chart shows that the rate of change is the same. One of the reasons this is interesting is that pets aren’t “over-insured”. One of the Right’s arguments against health-care reform is that the problem is really an over-insurance problem — people have so much insurance they overspend on health-care, so there’s no restriction on the growth in health-care expenses. That’s not true for pets, yet pet health-care is increasing at the same rate.
You’re right, Matt, that it would be better if the figures were on a per-capita basis.
July 14th, 2009 at 11:38 am
Yeah, the charts are fine – it’s showing that pet spending is approximately proportional to human spending. The axes are fine, if a little weird that they didn’t make the lines match up. I would like to see both y-axes as per capita / per pet, though.
July 14th, 2009 at 11:42 am
nuance nuance nuance…
Does this chart include large animal veterinary medicine, or only small animal practices? Because the real problem in veterinary medicine is that no one wants to go into large animal practice. The supply is dwindling, but the demand is as big as ever, and you can guess what happens to cost from there.
July 14th, 2009 at 11:43 am
What is AEI trying to show? That a totally free market results in cost increases similar to ours? Isn’t that the opposite of what they try to argue?
July 14th, 2009 at 11:43 am
Megan McArdle had this graph up the other day. In the comments, someone made an attempt at “normalizing by population size”, as Matt puts it. The result was that (between 2001 and 2007), there was a 12% increase in spending per pet, and a 38% increase in spending per human.
Link: http://meganmcardle.theatlantic.com/archives/2009/07/the_price_of_innovation.php#comment-224812
July 14th, 2009 at 11:44 am
Note that the distance between $2,000 billion and $2,500 billion on the right axis is clearly larger than the distance between $10 billion and $12 billion on the left.
Well the first distance represents a 25% increase, while the second distance represents a 20% increase. So why is it interesting that the first is larger than the second?
July 14th, 2009 at 11:47 am
the distance between $2,000 billion and $2,500 billion on the right axis is clearly larger than the distance between $10 billion and $12 billion
Which is exactly as it should be, since 2500 is 25% larger than 2000, but 12 is only 20% larger than 10.
The chart is fine, and Matt shows his innumeracy. Oops.
July 14th, 2009 at 11:47 am
right,
I meant I wasn’t expressing an opinion on that subject. Moving on to that subject, I think the chart obviously should have been set with the 1984 points overlapping. Just a little less obviously, I agree with Matt his doesn’t really show much without knowing anything about the size and nature of the pet population over time.
But going back to bashing Matt, this is just funny:
Someone isn’t particularly good at calculating ratios.
July 14th, 2009 at 11:49 am
I should have known as I was composing that last post that a bunch of other people would jump on Matt for the same reason.
July 14th, 2009 at 11:49 am
This from a petplace.com:
So I guess 40% increase in number of households having pets explains, say, a 40% increase in spending (from approx 5bn to 7bn). Also, maybe the number of pets per household has changed, or the mix of pets (high maintenance vs low).
July 14th, 2009 at 11:53 am
pwned
July 14th, 2009 at 11:53 am
@14 and 15 == You guys are missing Matt’s point. He’s talking about the ratios. The physical distance is the same, but the numerical ratios aren’t. That’s what’s wrong with the chart.
Admittedly, Matt could have explained that better. But the problem isn’t innumeracy.
July 14th, 2009 at 12:04 pm
Matt, as others have pointed out, is wrong about the graph. It is a little hard to read, but the axes are fine. The best way to display this data would be as a ratio normallized to the average ratio. It would show that overall spending on the two track fairly well.
The better point is about the number of animals getting care. I don’t know how that would affect the plot, but it would be a better data set.
There is also a big “so what?” factor.
July 14th, 2009 at 12:09 pm
The physical distance is the same, but the numerical ratios aren’t. That’s what’s wrong with the chart.
Uh no, the physical distances are not the same, and neither are the numerical ratios. There’s nothing wrong with the chart in this sense.
There’s the population issue, and the “so what?” factor as Njorl says, but the graph is fine.
July 14th, 2009 at 12:09 pm
I get a 144% increase for pets (4.5 bn to 11 bn) and a 193% increase for humans (750 bn to 2200 bn) from 1984 to 2006. Keep in mind that all veterinary drugs are orphan drugs and, unless also used for humans, can be quite costly.
July 14th, 2009 at 12:10 pm
Complicating matters even further, pet population might not tell the whole tale. For instance, I live in an area where most pets die of “lead poisoning.” Meaning that putting Rover to sleep entails a trip to the ammo box and a quick ride to the outskirts of town. Apart form a few old ladies, I don’t think anyone here has ever even considered surgery for a pet. For better or worse.
So let’s say the pet population here has soared over the past 20 years. That would have no impact on veterinary spending. Unless, of course, you count 22 shells in the total expenditures. Effectively, whole sections of the pet population are “uninsured,” insofar as they get no real vet care under any circumstances.
Versus an explosion in pet population in places where people dispatch with the pets a bit more quietly. And pay for surgery.
Seems the real number to be looking for is the growth in pets that operate within the purview of veterinary care, which is a certain subset of the total pet population. But I think this number is basically impossible to determine.
July 14th, 2009 at 12:14 pm
“$2,000 billion and $2,500 billion on the right axis is clearly larger than the distance between $10 billion and $12 billion on the left”
Shocking I tell you that a 25% increase looks bigger on a chart then a 20% increase.
Inflation adjusted the chart is just fine, nothing to see here folks.
July 14th, 2009 at 12:18 pm
Sam M,
That seems like a quibble to me, unless you have a prima facie reason to believe there is some relevant correlation between growth in pet population and areas where people spend more or less on veterinary care per pet.
July 14th, 2009 at 12:19 pm
That isn’t a problem with this chart. He could have left the dashes off the right axis, and labled the lines there 0, 417, 833, 1250, 1666, 2083, and 2500. As long as the axes are linear, and start with zero, the shape of the curve is what matters. Using different scales just shows the shape similarity more easily.
July 14th, 2009 at 12:21 pm
Looking at cost/pet is a bad idea. A person with X cats and Y disposable income will not experience X times the vet costs of a person with 1 cat.
July 14th, 2009 at 12:21 pm
Matt, really, correct this. Admit a brain fart, say you were distracted, or that you need to get new glasses, or that there was a lot of glare on your screen, or whatever. Most of us are on your side, and don’t want to see you embarrass yourself and your credibility tank.
July 14th, 2009 at 12:26 pm
To reiterate, the chart is fine. In that the gradations are correctly spaced, etc. Of course it isn’t controlled for population size. Which is what actually matters. When one does that, human health care spending is shown to be massively outstriping pet health care. Thus proving the opposite of McArdle’s point.
But isn’t this always the case? Someone (typically a conservative pseudo-intellectual) posts some data thinking it proves their point. People with actual understanding of statistics work to fix the data, and then use said data to prove the former poster wrong. It’s glorious.
July 14th, 2009 at 12:27 pm
I think the key point Biggs are Mankiw are trying to make is that our health care system has the same incentives at veterinary care. Namely, if Fluffy gets too sick, you let Fluffy die and get a new dog … unless you are Leona Helmsley and can afford Fluffy’s $100k heart transplant and lifetime of anti-rejection medication.
July 14th, 2009 at 12:35 pm
Kudos to Matt for the update in light of the well-founded objections in the comments.
I might also note I hope this becomes a more common practice here (namely Matt taking objections from his commentators seriously).
July 14th, 2009 at 12:40 pm
[...] Matthew Yglesias: But look at the Y axes. They don’t match up! This is almost a chart in which the same vertical [...]
July 14th, 2009 at 12:43 pm
I too would like to thank Matt for responding to the overwhelming good sense of the commenters (not, obviously, including me)
July 14th, 2009 at 12:44 pm
Since when does Matthew read comments? This is almost unprecedented.
BTW, Kevin Drum has the numbers on the population issue. Apparently pet population has grown faster than human population.
July 14th, 2009 at 12:46 pm
I don’t think i’m bad a math, but those 2 scales are off. The divisions are designed to make pet health care look larger.
You’ve got 6 divisions on the left, 5 on the right. This is basically 2 charts with the same x axis and completely unrelated y-axis, but you’re being tricked because the percentages are similar, but one has an additional mark compared to the other, an obvious distortion of the line.
redo the vet line with the $3000 mark added in, then you have a valid comparison.
July 14th, 2009 at 1:13 pm
I might also note I hope this becomes a more common practice here (namely Matt taking objections from his commentators seriously).
Seconded.
July 14th, 2009 at 1:20 pm
redo the vet line with the $3000 mark added in, then you have a valid comparison.
Uh no. The two axes are on the same proportional scale. The tick marks are just to help you read off the values corresponding to points on the graph. They don’t have any effect on the data in the graph.
July 14th, 2009 at 1:21 pm
Apologies . . . as you can read in the comments I’ve got this wrong.
Ouch. Bad move, Matt, real dumb. Now you’ll be expected to correct mistakes in your posts all the time, and respond to criticisms. You just doubled your workload.
July 14th, 2009 at 1:25 pm
I’m sorry Matt, but these aren’t growth rates… Would be nice to see though what the growth rates are. It’s always better to compare growth rates of two series that are on a different level in absolute terms, rather than plotting the absolute values against each other.
July 14th, 2009 at 2:00 pm
Cyrus’s comment notwithstanding, three cheers to Matt for a) reading his comments, and b) correcting mistakes. Maybe the inappropriate Megan McArdle comments yesterday, while lamentable on their own, actually started a positive trend.
July 14th, 2009 at 2:41 pm
Oops. You guys were right. I didn’t see the little hyphens in the right-hand axis at all.
July 14th, 2009 at 2:45 pm
“Veterinary care”, broadly defined, includes a lot more than just pet care. Farm animals, lab animals, and possibly zoo animals would likely be a much bigger percentage than pets. And it wouldn’t be surprising to me that the cost of lab animal vet care has increased if it has kept up with increased NIH funding over the same period. The title of the chart says “pets” but the line is labeled “veterinary care”; which is it?
July 14th, 2009 at 3:00 pm
Another problem is the amounts involved. You can’t really compare an activity that involved spending 10 billion dollars with an activity that spends 2.5 trillion dollars.
July 14th, 2009 at 3:10 pm
“Veterinary care”, broadly defined, includes a lot more than just pet care. Farm animals, lab animals, and possibly zoo animals would likely be a much bigger percentage than pets. And it wouldn’t be surprising to me that the cost of lab animal vet care has increased if it has kept up with increased NIH funding over the same period. The title of the chart says “pets” but the line is labeled “veterinary care”; which is it?
The data apparently comes from the BLS’ “Consumer Expenditures Survey”, so it’s household survey data, and won’t include zoo, lab, or farm animals.
Unfortunately, this particular series isn’t available online. There’s definitely a question on the survey about veterinary expenses (and another about “purchase of pets, pet supplies, and medicines), but in the tables available on the web, it’s aggregated into spending on “Pets, toys, hobbies, and playground equipment”.
It appears that one would have to order the survey microdata CDs, or email a contact at the BLS to get the series apparently presented in the chart, and it’s unclear what that is exactly. (E.g., does it include medicine?)
Not that it matters – problems with the chart aside, it’s a pretty tendentious comparison to begin with (people do not spend money on their pets health as they would on their own), and I’m not sure what the point was supposed to be.
July 14th, 2009 at 4:14 pm
Cyrus’s comment notwithstanding, three cheers to Matt for a) reading his comments, and b) correcting mistakes.
My crack about doubling the workload aside, I was kind of serious. Blogging is a medium in punctilious accuracy is beside the point. I mean, yeah, of course correct errors of fact like in this post, and typos so severe they make understanding the post genuinely impossible, and if that’s all there is in response to comments, good. But a blog post can get a discussion started and raise interesting points even if what it links to turns out to be outdated or beside the point or whatever. It doesn’t take much editing to be too much. Keep it real, if you’ll forgive the clichéd expression.
July 14th, 2009 at 4:24 pm
I’m pretty sure that the point they are trying to make is that cost growth is due to people demanding more care for those they care about rather than inefficiencies in the system.
Seems kind of desperate. Not to mention deceiving when you take the above objections to the graph into account.
July 14th, 2009 at 5:32 pm
I’ve changed my mind. The graph is deceptive – not mathematically, but visually.
An honest plot claiming to compare curve shapes with intersection at the (0,0) point would use axes that caused the average magnitude of the physical curves to be the same. This graph implies that at the dawn of time, there was a significant expenditure for veterinary care.
It’s hard to explain what I mean without drawing.
The contention is that the curve shapes are similar. If so, they should be able to choose axes that make them overlay, not just look similar. For that to happen here, the left axis would have to be from about 0.4 to 12.4. The problem with that is that it implies $400 million in vet spending at a time when there is negligible human care spending.
A good plot would have the left axis going from 0 to about $14 billion. That would minimize the area between the curves for a more legitimate comparisson. It would also flatten the vet curve noticeably, and eliminate the argument.
July 14th, 2009 at 5:32 pm
the charts are almost scaled right. Actually, to make the scale right the Vet spending should be 12.5 M rather than 12.0 m.
But the charts are almost close enough that they would show almost identical rates of growth in both series.
July 14th, 2009 at 5:48 pm
In case the above comments don’t make it clear:
There IS a problem with the axes on the charts, even though they are technically scaled correctly, just not quite the one Matt initially complained about.
If you don’t see how it’s misleading, try punching the numbers into a spreadsheet and graphing both on the same scale. They do NOT have the same slope (or growth rate).
(It’s easy to make ANY two upward sloping lines appear to have the same growth rate if you’re allowed to use different scales: just set the conversion factor between the scales to the ratio of the original slopes. Voila: two perfectly parallel lines–and an apparently unimportant vertical offset.
But that offset is everything. If the growth rates were really equal, there would be no vertical offset.)
July 14th, 2009 at 5:59 pm
In this case, if veterinary spending growth had really matched human health care, it would have ended up at about $12.25 billion in 2006, not $11B.
(That’s aside from the other problems of course, like this really should be per capita/pet. Also: add this to the long list of reasons not to take Mankiw seriously.)
July 14th, 2009 at 6:14 pm
This chart does give the lie to some familiar rightwing talking points: that healthcare inflation is due to excess govermment regulation, to third party insurance payments, to the preferrential tax treatment of health insurance, to Medicare and Medicaid. And it also shows that a laissez faire free market does not necessarily rein in escalating medical costs, not even when euthanasia is an option and not much of a moral issue even. To be fair, one leftwing talking point is also given the boot: that it’s all due to insurance company greed. But on the whole it trashes the rightwing POV far more than the Left’s.
July 14th, 2009 at 8:00 pm
I noted above that Kevin Drum addressed the flaws in the numbers pertaining to population growth. Jim Manzi did the same, here.
July 14th, 2009 at 11:14 pm
(It’s easy to make ANY two upward sloping lines appear to have the same growth rate if you’re allowed to use different scales: just set the conversion factor between the scales to the ratio of the original slopes. Voila: two perfectly parallel lines–and an apparently unimportant vertical offset.
But that offset is everything. If the growth rates were really equal, there would be no vertical offset.)
I don’t think this is quite right. If variable A doubles in size and variable B triples in size, you’re not going to get the two lines to be exactly parallel. The slopes of the two lines are independent of the axis scale, so you can’t make them parallel by changing the scale.
But you are 100% right that the vertical offset is a cheat. Why is the health care curve entirely under the vet services curve? All we can tell from the graph is that health care expenditures went up faster than the vet services between
July 14th, 2009 at 11:16 pm
1984 and 2001, and that vet services have gone up faster since 2001, with a fairly big divergence since 2004.
But this isn’t even worth discussing in this much detail.
July 15th, 2009 at 2:58 am
I wonder what the Socialists are doing over there in Europa when it comes to veterinary care. I would be pissed-as-hell to find out they surpass us in this endeavor as well -provide superb universal pet care, or some such crazy nonsense.
Please tell me the United States tops the UN charts in providing overall quality of life for our uniquely patriotic, American cats, dogs, and hamsters.
July 15th, 2009 at 6:54 am
I think your criticism should be about the fact that the rise in veterinary services reflects increases in the number of pets getting care (an increase in quantity purchased) whereas the health spending reflects rising cost per treatment (inflation).
July 16th, 2009 at 10:33 am
That’s embarrassing.