Some background for this post (#1433202)
So, I've spent a stupid number of hours this week going back over notes from econometrics classes back in my university days and reading up on certain things. While arcane and technical, discussions of econometric results in economics or finance almost always came down to certain assumptions used in a model — or whether or not you could interpret the results in this or that way. It's much less rigorous than you at first suspect, much more subject to very-subjective interpretation, which is why I enjoyed it so much I think.
Econometric softwares are abundant, (hashtag AI economy, scarcity&abundance etc #1425743, #798342), meaning you can TECHNICALLY ask it to spit out numbers on absolutely anything.
The skill of an academic or data scientist is to understand what it's doing, why you're using which test to run a regression in what way, and CRUCIALLY interpreting the real-world meaningThe skill of an academic or data scientist is to understand what it's doing, why you're using which test to run a regression in what way, and CRUCIALLY interpreting the real-world meaning
So here's my little trouble. There are a ton of Bitcoiners running around with notions of The Power Law in their minds. The Bitcoin Power Law, from Mezinskis' Porkopolis website:
I first published a chart observing how Bitcoin’s price follows a trendline according to a power law in 2018. My thinking was inspired by famous posts on BitcoinTalk authored by Trolololo from 2014. In his early model, he observed Bitcoin’s price fitting to a logarithmic regression.
More examples:
https://www.youtube.com/watch?v=XW1GUeBe0Rs
https://www.youtube.com/watch?v=NaC3zGp6BSo
https://www.youtube.com/watch?v=vjwFusEnfiE&t=6s
- Giovanni Santostasi https://x.com/giovann35084111?s=21
- Fred Krueger https://x.com/dotkrueger?s=21
- Stephen Perrenod https://x.com/moneyordebt?s=21
My immediate observation comes from Fred Krueger and Ben Sigman's book Bitcoin One Million and their very neat associated website https://b1m.io/
- "You don't see relationships like this in financial data. Ever” (p. 7)
- “The mathematical relationship between time and price – the most robust pricing model in financial history – delivered exactly what the equation predicted.” (p. 299)
The devil is always in the details.
So hang on here, you
- took heavily smoothed-out...
- ...price levels...
- ...regressed that on time
- ...in log-log space
- ...which resulted in a stupidly high R-squared (0.997)
...AND YOU THINK YOU'VE DISCOVERED SOMETHING?!...AND YOU THINK YOU'VE DISCOVERED SOMETHING?!
Financial assets and their returns are not normally distributed. R-squares belong to linear regression and thus don't really work/mean anything in log-log space. You've smoothed out all the variation, whereas R-squares report the unexplained variation in a dependent variable. You take the levels of a financial asset, instead of its returns which absolutely every financial practitioner does, falling prey to nonstationary data problems. And you mechanically interpret your insane 0.997 result as evidence.
I dunno, man. The more I look at this, the more I think you can’t regress an asset’s (smoothed-out) level on time in log-log space, and think it means anything.
Poor Taleb would have a hizzyfit and collapse on the spot if he saw this. As would Granger and Newbold if they were still alive
So yeah, plenty of economists and econometrically savvy schtackers around. Happy to take some feedback here since it feels like I'm missing something... why are all these clever/respectable people pushing something that seems like such obvious gunk??
Not sure I follow, Padre...?
Young man, you don't follow for a very simple reason: these men are screwballs
Yeah, any model based on a simple time series is inherently flawed.
How can one construct a model when the unit of account ($) isn't a constant? This is particularly relevant for the 2020-21 era stimulus which saw 20-30% inflation across many assets.
How can you say that the model is useful if the predicted ranges are so large? For example, this model implies a current BTC price of anywhere between $52k and $528k:
https://charts.bitbo.io/long-term-power-law/
How can it possibly account for macro-scale events which aren't guaranteed to happen but completely change the price behavior of the asset (ETF approvals, MSTR, etc.)?
But to answer your question,
A few takes:
The truth is, even most highly respectable/smart people do not have a deep understanding of econometric modeling.
The subset of people who actually understand the math behind the models is extremely tiny. Including among people who have Masters in Econ/Finance. IMO learning it in a class, even getting an A in the class, is not really enough. Because the classes just teach you how to use the models, but you don't really spend time tinkering with the underlying assumptions or thinking too hard about what falsifies the models.
It kinda takes years of tinkering in the depths of the math, trying to build your own models, answering objections to them by other people, that builds your ability to deeply understand the models. Usually the only people who ever do that are people in PhD programs.
Guess that made me a bad student, then?? I basically did the opposite, focused on figuring out what was happening and the assumption, specify model etc, and then the exact commands in Stata later.
Quite a few of these people are PhDs, e.g. the physicist Giovanni-something. They usually have an astonishing grasp of math
No, that makes you a good student. Thinking about the underlying assumptions is what differentiates an "economist" from a "technician". When we were hiring for new faculty positions, sometimes people would say of a fresh grad, "That guy's just a technician," referencing the idea that they were good with the math, but they weren't thinking carefully about the underlying economics.
I remember sitting in ecmt labs with people just discussing with the TA or professor "what's the command for that? Do we have a test for that?" Having no idea what they were investigating or actually doing
Basically memorizing, if problem, then run y command
Indeed. That's 90% of students. Even the good ones.
Ah, yeah, another common problem with people who are good at math from other fields trying to comment on economics. Econometric theory isn't just math. It's a close connection between math, the underlying economics, and how your assumptions tie the underlying economics to the math. I find that people coming from a physics/engineering background often fail to grasp that. Because they are used to modeling physical systems where the underlying assumptions are natural law and (afaict) 100% accurate to how the world behaves. Not so for economics/finance.
As someone with both a physics and econ background, I like to offend physicists by saying econ is harder than physics. (Because of the assumptions issue, but also because of some self-referentiality in what we do. How people think about econ actually affects how the economy behaves. But how we think about physics doesn't affect how nature behaves.)
All very good explanations for what's going on, thank you
This is the part I'm most likely to disagree with. Did they actually test that against the price history of other assets?
I have a strong suspicion that you can find many 10-year windows of asset prices in which the log-log relationship between price and time is roughly linear with a high R2
I did some quick rudimentary check on the s&p, got 0.95-range. that's what first got me suspicious of this whole thing...
( But then again, low confidence that I did it well)
Sometimes you observe the empirical regularity before you understand its reason.
I don’t see any inherent reason why using log prices is inappropriate or why you can’t use R-squared, it’s just that you’re explaining the variation in the log-prices.
Mmm, noo? By compressing it, first by MA and then by log, you're stripping it of variation. So I suspect you get this stupidly high r-squared result pretty artificially
Perfect model
1 sat = 1 sat
Checks out