I hope “fuzzy sets” is the correct mathematical term for the concept I’m interest in—ideas that have closely related meanings, without clear and distinct boundaries. In a recent post, Scott Alexander applied this concept in several different contexts. (Read his entire post, there is much more of interest than what I discuss here.) Here’s one example:
[If] you ask people to “value their lives today on a 0 to 10 scale, with the worst possible life as a 0 and the best possible life as a 10”, you will find that Scandinavian countries are the happiest in the world.
But if you ask people “how much positive emotion do you experience?”, you will find that Latin American countries are the happiest in the world.
If you check where people are the least depressed, you will find Australia starts looking very good.
And if you ask “how meaningful would you rate your life?” you find that African countries are the happiest in the world.
It’s tempting to completely dismiss “happiness” as a concept at all, but that’s not right either. Who’s happier: a millionaire with a loving family who lives in a beautiful mansion in the forest and spends all his time hiking and surfing and playing with his kids? Or a prisoner in a maximum security jail with chronic pain? If we can all agree on the millionaire – and who wouldn’t? – happiness has to at least sort of be a real concept.
The solution is to understand words as hidden inferences – they refer to a multidimensional correlation rather than to a single cohesive property. So for example, we have the word “strength”, which combines grip strength and arm strength (and many other things). These variables really are heavily correlated (see the graph above), so it’s almost always worthwhile to just refer to people as being strong or weak. I can say “Mike Tyson is stronger than an 80 year old woman”, and this is better than having to say “Mike Tyson has higher grip strength, arm strength, leg strength, torso strength, and ten other different kinds of strength than an 80 year old woman.” This is necessary to communicate anything at all and given how nicely all forms of strength correlate there’s no reason not to do it.
But the tails still come apart. If we ask whether Mike Tyson is stronger than some other very impressive strong person, the answer might very well be “He has better arm strength, but worse grip strength”.
This is a problem in economics and other social sciences. Consider:
1. What does it mean to say the labor market is “tight”? That’s not at all obvious. The unemployment rate? Wage growth? The prime age employment ratio? Weekly claims for unemployment compensation? These 4 metrics often give very different answers. And yet most people have an intuitive sense that 2009 was clearly not a tight labor market. So there is a sort of core concept buried here somewhere.
2. What does it mean to say a firm is a monopoly? Is Amazon a monopoly or is retailing highly competitive? While there are different ways of thinking about “monopoly”, almost everyone agrees that the local power company is more monopolistic than the dry cleaning business down the street. So there is a core meaning somewhere.
3. What about political and economic freedom? I recall that California showed up near the bottom in one freedom ranking of US states, and yet life here seems relatively free to me. But perhaps if I were a landlord or businessperson I’d feel differently.
4. There are many ways of measuring inflation, but almost everyone agrees that Venezuela has a high inflation rate. NGDP is also a fuzzy set, but seems less fuzzy than inflation, as you don’t have to worry about quality adjustments and other index number problems.
Alexander uses the example of Mike Tyson and the old lady to suggest that in the extreme cases there is often agreement. I think that’s true, but oddly the happiness example he uses sort of undercuts that claim. Certainly Scandinavia and Africa are pretty far apart under almost any given metric, and yet each leads on one measure of happiness. And even if you don’t think life having “meaning” is a plausible definition of happiness, the high levels of “positive emotion” observed in (poor) places like Central America do call into question our understanding of international happiness rankings. Positive emotion is certainly a plausible definition of happiness, albeit not the only valid one.
I’d say the same about rankings of economic freedom. Hong Kong and Singapore always come first and second, and New Zealand and Switzerland are third and fourth in the most recent Heritage and Cato rankings. So there seems to be a core underlying concept. But other people point to the fact that most of the real estate in Hong Kong is owned by the government. That’s also true in Singapore, which also owns big stakes in many businesses. When you get further down the Heritage and Cato rankings, you start to see significant divergences:
Heritage Cato
#10 UAE #6 USA
#12 Denmark #16 Denmark
#18 USA #37 UAE
I presume the US/Denmark comparison depends on the relative importance placed on high levels of government spending. As far as the US/UAE comparison, this is presumably one of those “apples and oranges” problems. I’d guess the UAE has really low taxes, but heavy government involvement in the energy industry (which is a huge share of their GDP.) The truth is that all governments are heavily involved in the economy, but in different ways.
So far I do not see any major scandal, just the inevitable problems we have in making sense out of a messy, highly complex world.
Until we get to monetary policy, where there doesn’t seem to be any coherent core meaning at all.
Economists frequently speak of changes in the “stance of monetary policy”, without having the slightest idea of what they are talking about. Easy money? Tight money? What do those terms even mean?
Just a few days ago, markets responded strongly to Jerome Powell’s comments regarding the removal of the term “accommodative” from the official statement of Fed policy. Most people believe Fed policy is gradually becoming less accommodative. I believe the Fed is now becoming more accommodative.
This scandalous lack of clarity on the meaning of the “stance of monetary policy” (and even a lack of clarity as to what we mean by “monetary policy” itself) causes real problems. The Great Recession of 2008-09 was partly caused by the Fed having the mistaken impression that money was “accommodative” during 2008, and hence that monetary policy was “not the problem”. When prominent New Keynesian economists went back and actually studied the period in question, they discovered that money was actually quite tight, in the sense that the policy rate (averaging roughly 2% during 2008) was way above the natural rate of interest (which was negative throughout 2008.) This graph is from an October 2015 paper by Vasco Cúrdia (and kudos to Cúrdia for a pretty accurate natural rate forecast for the following three years):
Just to be clear, this is not just a problem of slight differences in meaning; the disagreement is often most pronounced at the “tails”, such as 1980 and 2009. Thus most economists believe that money was quite tight in 1980 and very accommodative in 2009, whereas the opposite was actually true (and if Milton Friedman were alive he’d likely agree with me):
Low interest rates are generally a sign that money has been tight, as in Japan; high interest rates, that money has been easy.
. . .
After the U.S. experience during the Great Depression, and after inflation and rising interest rates in the 1970s and disinflation and falling interest rates in the 1980s, I thought the fallacy of identifying tight money with high interest rates and easy money with low interest rates was dead. Apparently, old fallacies never die.
This is much different from debates about whether the CPI or PCE is a more appropriate definition of inflation, as both price indices showed high inflation in 1980 and mild deflation in 2009. And even people who point to the heavy ownership of land by the HK government would freely concede that Hong Kong is nonetheless freer than North Korea. But in monetary economics we don’t even agree on the extreme cases.
Scandalous!
READER COMMENTS
Sniffnoy
Sep 30 2018 at 5:53pm
I don’t think fuzzy sets are the right abstraction here, no. (And not all of what you’re describing are sets in the first place.) Perhaps somewhat ironically, I think you’d have to make this substantially more precise before you had fuzzy sets. As it is you just have fuzzy informal concepts. Is it really worth trying to find an appropriate mathematical formalism for fuzzy informal concepts? Unless you’re interested in how fuzziness itself works, I don’t think so; for any particular problem of fuzziness, the solution is instead to get in there and make things less fuzzy.
[Thing]
Sep 30 2018 at 10:23pm
Heh. Maybe “fuzzy set” will be the next “epistemic closure.” Still, there should be a word for abstract concepts that clearly point to something real but lack crisp intensional definitions. Maybe philosophers have already invented one and I just haven’t heard of it? I remember years ago seeing Matt Yglesias use the term “cluster concept” for something like that, while vaguely alluding to Wittgenstein. It was just an offhand remark in a political essay, but I have remembered that passage ever since, because it’s actually pretty handy to have a cluster concept to denote the cluster of concepts which denote clusters.
But there’s a more specific thing that Scott S. and Scott A. both refer to, which is concepts that refer to clusters of traits that are usually, but not always, correlated. Then you get a specific kind of especially troublesome boundary case: outliers which are high in some of the defining traits but low in others. An example would be idiot-savants, in relation to the concept of “intelligence.”
Scott Sumner
Sep 30 2018 at 6:27pm
Sniffnoy, You said:
“Is it really worth trying to find an appropriate mathematical formalism for fuzzy informal concepts? Is it really worth trying to find an appropriate mathematical formalism for fuzzy informal concepts?”
Actually, I’m not trying to find an appropriate mathematical formalism, just a useful analogy.
Philo
Sep 30 2018 at 8:03pm
As you write: “Most people believe Fed policy is gradually becoming less accommodative. I believe the Fed is now becoming more accommodative.” But this does not imply that there is any ambiguity in the concept of the stance of monetary policy: perhaps it is just a factual disagreement. Because you have a different theory about how the economy works from that of most people (you have a different “model”), you and other people come up with different answers to the question, “How accommodative is current policy,” even though the concept of monetary accommodation itself is understood the same by you all.
The scandal is that so many people, including important, powerful people, have not embraced your (correct) model, even though you have explained it and defended it very clearly.
As for “fuzzy sets”: fuhgeddaboudit!
Benjamin Cole
Sep 30 2018 at 9:17pm
Great post.
On the Cato and Heritage Foundation rankings of Singapore and Hong Kong: those two cities are prosperous, so I suspect right-wing leaning organizations bent over backwards to find that they were also free enterprise oriented.
In fact, all the land in Singapore is owned by the state. It is perhaps the most highly regulated and managed economy on the planet— that is the assessment of Singapore economists published in the Singapore Economic Review.
I think Singapore succeeds as it is only a city state and probably pretty well managed. Indeed, real per capita GDP PPP is 50% higher in Singapore than in the United States.
The interesting case going forward will be mainland China. Can such a large nation be managed by central planning and extensive Chinese Communist Party involvement in every business?
Can ongoing macroeconomic success coexist with total repression of free speech abnd all political and legal rights?
As a Westerner, I want to say “no.” But then I thought greater material prosperity in China would lead to greater political freedoms. We have seen exactly the opposite course over the past 30 years.
Mark Z
Sep 30 2018 at 10:09pm
Perhaps the appropriate concept here – much simpler than fuzzy sets – is the principle of relativity in physics. Certainly in the case of monetary policy this seems to be the confusion. May people habitually think of interest rates in absolute terms rather than relative terms: the fed lowering its target seems like an easing of monetary policy in ‘absolute’ terms; but if the natural rate is falling faster than the rate at which the fed is lowering its target, it is tightening policy in relative terms. So you might argue that people thinking in the former manner rather than the latter are using the wrong (or an entirely arbitrary) reference point, because what really matters is the velocity of one thing relative to the other, nor relative to some reference point.
I don’t think this analogy is informative on happiness though. With happiness, it seems more that different countries speak different languages, even on a more ‘meta’ level, and mere translation doesn’t control for this, because the same word may have different connotations or its meaning may vary depending on context in different ways from one language to another. For example, if you were to survey different nationalities about, say, love, you would likely find Germans are comparatively unloving toward friends and family members relative to English speakers, simply because in German, to say you “love” someone is far more restricted (mainly to a romantic context) unlike in English speaking cultures where the same phrase (“I love you”) can be applied to family members and even friends as well as romantic partners. So unless two groups speak the same language and share the same idioms, simply transliterating the survey from one language into the other doesn’t properly control for differences in language.
Benjamin Cole
Sep 30 2018 at 10:59pm
Speaking of freedom, how does anyone like this one:
“It’s high time.’ Public companies required to have women on boards under new California law
BY BRYAN ANDERSON
September 30, 2018 02:10 PM
Updated 5 hours 13 minutes ago
With Gov. Jerry Brown’s signature on Sunday, California public companies will soon expand female representation on their boards.
Senate Bill 826, introduced by Democrats Hannah Beth-Jackson and Toni Atkins, requires public companies to have at least one female director on their board by the end of next year. By the end of 2021, companies with five directors must have two women on their boards, and companies with six or more board members must have at least three women.
In a signing statement, Brown acknowledged concerns that “may prove fatal” to the bill’s implementation, but said “it’s high time corporate boards include the people who constitute more than half the ‘persons’ in America.”
I wish I was making this up.
Scott Sumner
Oct 1 2018 at 2:34am
Philo, No, I’m making a much more extreme claim. I’m not saying the profession has a bad definition of the “stance of monetary policy”. I’m saying they completely lack any coherent definition at all. It’s all nonsense. Gibberish.
I could live with a simple disagreement. This is much worse.
Ben, You said:
“On the Cato and Heritage Foundation rankings of Singapore and Hong Kong: those two cities are prosperous, so I suspect right-wing leaning organizations bent over backwards to find that they were also free enterprise oriented.”
Nice try, but Hong Kong was rated number one long before it became prosperous.
Here’s my question for you. Do you characterize countries in a way that best matches your ideological policy preferences? If not, why assume that others do?
Mark, It’s not just interest rates. Some people look at the money supply, or the exchange rate, or the inflation rate. There are many different ways of characterizing the stance of monetary policy.
Philo
Oct 1 2018 at 9:02am
Well, my suggestion is that it *is* just a factual disagreement, and, as I see it, you have given us no reason to think otherwise.
Scott Sumner
Oct 1 2018 at 2:55pm
Philo, So how do mainstream economists define the stance of monetary policy?
Philo
Oct 1 2018 at 11:10pm
The proper question is not, What do mainstream economists say when asked to define ‘stance of monetary policy’? but, What definition would a wise observer of the discourse of mainstream economists, heterodox economists, journalists, pundits, and sophisticated amateurs offer? Unfortunately, I am not a very wise observer, but I would say that ‘more accommodative’ means something like more stimulative of employment and production in the short run. For a complete definition we would need, in addition, to specify what counts as neutral monetary policy. I must admit that that is quite beyond me, but I suggest that there is such a specification, capturing (at a high level of abstraction) the usage of almost everybody, even though I cannot produce it. I am confident that you have not shown this suggestion to be wrong.
Scott Sumner
Oct 2 2018 at 11:54am
I believe my last 10 years of blogging constitutes a very persuasive argument that you are wrong. Time and time again I showed that both individual and consensus views of “stance of monetary policy” (by professional economists) are not even internally consistent.
Miguel Madeira
Oct 1 2018 at 5:48am
“Nice try, but Hong Kong was rated number one long before it became prosperous.”
There was even indexs of economic freedom before HK was prosperous?
Scott Sumner
Oct 1 2018 at 2:56pm
Miguel, These indices go back to at least 1975, when Singapore and HK were much less developed.
stoneybatter
Oct 1 2018 at 10:35pm
Scott, nice thought-provoking post.
Previously, you have argued that fiscal policy does not have a macro impact due to the Fed’s offset. In this post, you said that Fed policy has become more accommodative this year, what with NGDP accelerating. Is this not evidence that the monetary offset is not working properly, i.e. policy is not tight enough to balance out the fiscal boost? If not, why not?
Benjamin Cole
Oct 1 2018 at 11:07pm
Here’s my question for you. Do you characterize countries in a way that best matches your ideological policy preferences? If not, why assume that others do?–Scott Sumner
Well, the short cynical answer is, “My time is not worth enough for anyone to pay me to have an opinion.” Also, I am not much an an ideologue.
In short, I can say what I want, which is also what I believe. I have no academic track record, or reputation, and no financial connections related to opinions or observations I express here.
Surely, you have noticed when “liberal” or “conservative” or other ideologues present their studies, they inevitably come to foregone conclusions.
I could also ask you: Why do you believe in rational man, and that people respond to economic incentives, but then also believe that liberal or conservative think tanks present anything than what is expected by sponsors?
Please show me a link to the Heritage Foundation calling Hong Kong No. 1, before the ity-state was prosperous.
Add on: Does anyone ever ponder property zoning when rating a nation or city-state? Why or why not? Seems like a rather large omission….property zoning allows a club of property developers and lenders to use government to extract rents, and for running decades at a time….see Kevin Erdmann’s excellent analysis of California, and that applies double to Hong Kong….
So is the No 1 economic freedom rating like asking “Are you happy?”
In large part, yes. Depends on what you are rating.
In Thailand, almost anyone can become a street vendor. Almost no one can in the US. So, for the average guy, which nation has the most economic freedom?
Scott Sumner
Oct 2 2018 at 12:07pm
stoneybatter, I’ve argued that fiscal policy does not have a demand side impact, due to monetary offset. The corporate tax cut likely had a supply side impact, which explains the faster RGDP growth. Having said that, I’ve never claimed that monetary offset worked perfectly, and it’s possible that (unlike in 2013) the Fed erred in not fully offsetting the demand side impact of fiscal stimulus. Some of the current inflation is due to oil, inflation forecasts are still around 2%.
Ben, To me, you seem like one of my more ideological commenters. You stubbornly insist that Singapore has widespread tariffs, when we repeatedly point out that you have simply misunderstood a domestic sales tax. It seems like you are trying to have the facts fit your preconceptions about the usefulness of economic nationalism. You’d be better off just accepting that Singapore is an extremely market-oriented economy.
I don’t know about Heritage, but the first Fraser/Cato ranking I could find was 1975, and Hong Kong was already ranked the most economically free country. At that time, its per capita income was far lower than lots of other places, such as Europe. Since then, it’s moved well ahead of most European countries.
Comments are closed.