Distinguishing Risk, Uncertainty, and Non-Ergodicity

In response to yesterday's post, LK asks: "non-e[rgodicity] is a subset within uncertainty, right?"

A good heuristic I keep handy to avoid looking like a fool is to be cautious when answering what seems like an obvious question when posed by someone clearly smarter than me. Here, we've got a few minor semantic issues and at least one problem of application. As I attempt to clarify, please bear in mind that I'm combining a brief survey of what others have done with what I think is useful. Out of an abundance of caution, I'll use a bit of technical jargon from statistics, but I'll do my best to illustrate what I mean with metaphors. If you're a casual reader, please don't let mentions of probability density functions throw you.

For the difference between risk and uncertainty, I turn to Frank Knight (who was the professor of James Buchanan, sort of making him my intellectual great-grandfather). In chapter VII of Risk, Uncertainty, and Profit (alas, I can find no electronic copy worth a pig's knuckle—even my paper copy is a photocopied, semi-legible disaster), Knight distinguishes risk arising from a defined, known probability distribution from uncertainty arising from an inscrutable, unknown probability distribution. Importantly, he takes a Cartesian, empirical approach to the question. Since he's an economist looking at real world phenomena—he mentions life and fire hazard insurance—he's leery of a priori probability reckoning. From p.225:

It must be emphasized that any high degree of confidence that the proportions found in the past will hold in the future is still based on an a priori judgment of indeterminateness. Two complications are to be kept separate: first, the impossibility of eliminating all factors not really indeterminate; and, second, the impossibility of enumerating the equally probable alternatives involved determining their mode of combination so as to evaluate the probability by a priori calculation.

Knight is saying here that careful analysis must not ignore what Nassim Taleb calls "fat-tail" events, or "black swans", to be alert for the financial profession's maxim "past performance does not guarantee future returns." The rapid summary is found in the opening sentence to the next chapter (p.233): "[t]o preserve the distinction which has been drawn in the last chapter between the measurable uncertainty and an unmeasurable one we may use the term "risk" to designate the former and the term "uncertainty" for the latter." That's more than 140 characters, but it's about as pithy as one might hope. Risk is governed by a defined, known probability distribution. Uncertainty is not.

For ergodicity (and the lack thereof), I turn to Douglass North. In Understanding the Process of Economic Change, Chapter 2, Section II (p.19) opens with a dictionary definition of ergocity:

"involving or relating to the probability that any state will recur, especially having zero probability that any state will never recur." Therefore, "an ergodic stochastic process simply means that averages calculated from past observations cannot be persistently different from the time average of future outcomes." For Samuelson the ergodic hypothesis was essential for a scientific economics.

Obviously, Knight disagreed with Samuelson. For Knight, the challenge faced by firms was to deal with uncertainty and the role of the economist was to catalog and observe rather than to predict and manage. For more on these (and more) intellectual traditions in economics, I strongly recommend Pete Boettke's Living Economics. At any rate, North continues:

To an economic historian surveying the ten millennia of human history from the onset of the Neolithic revolution, however, the ergodic hypothesis is a-historical. Further, the extraordinary changes in every facet of present-day society are evident all around us; and it is evident that we have been and are creating societies that are unique in comparison to anything in the past.

Non-ergodicity concerns novelty. Adding North to the Schumpeter-Knight-Kirzner synthesis isn't a matter of managing shocks within industries, it's how institutions (and to sprinkle a dash of McCloskey on top, rhetoric and moral sentiment as well) respond to system-wide disruptions. The commercial viability of the steam engine sounded the death knell of the stagecoach industry. Ditto the reversion of the purse strings to parliament in the Orange Revolution, ditto the moldboard plough, cooking meat over a fire, or fore-and-aft rigging on sailboats. Some developments kill entire industries, entire ways of life. These are not problems of the firm, but of society.

So to answer Lynne's question: both Northian non-ergodicity and Knightian uncertainty deal with inscrutable outcomes that arise from processes that we can only roughly and imprecisely model using historical evidence. But the way I understand uncertainty from Knight is that outcomes are still basically in the same ballpark as before: we've still got the same basic rule of law, the same basic patterns of production and exchange, the same bourgeois rhetoric, and the same types of relationships. The way I understand non-ergodicity from North is that when something big hits, all bets are off. Whole social orders, entire nation-states, entrenched ways of life, broad political coalitions are threatened by non-ergodic developments. The two are related in type, but not in scale.

To close, picture three urns, labeled "risk", "uncertainty", and "non-ergodicity".

In the risk urn, there are 50 white balls and 50 black balls. You know a priori the odds of what you're going to draw.

In the uncertainty urn, there are 50 white balls and some other balls. You know a priori that you could draw a white ball, but you can't calculate the odds beyond what you've seen other people do in the past.

In the non-ergodicity urn, there are 50 white balls and some other things. They could be balls, but as far as you know, they could be snapping turtles or vinyl copies of Fleetwood Mac's classic album Rumours. You can't calculate the odds, and you might not even have a very good idea of what the downside risks could be.

To recap, this is simply my understanding of the differences. Much like the "political kayfabe" meme, distinguishing the three is a little personal pet project. As you might imagine, the boundaries between risk, uncertainty, and non-ergodicity are hazy. And the implications for ensuring an environment where peaceful, mutually-beneficial voluntary exchange aren't always perfectly clear. But I am of the opinion that distinguishing these three helps clarify how and why some societies seem to be robust against minor change and major upheaval while others collapse. I hope this helps.

Kirznerian vs Schumpeterian Entrepreneurship, a Review of Knightian Uncertainty: in Which I Pick a Bone with One of My Favorite People

The always-excellent Lynne K reviews Jill Lepore's critique of Clayton Christensen's The Innovator's Dilemma. She delves quite the rabbit hole. I'll do my best to parse the arguments as I see them.

Schumpeter: the entrepreneur advances the possibility frontier of economic production by introducing novel products, new methods of production, or changes to how products are bought and sold. Entrepreneurs disrupt, in other words, existing patterns of production and exchange. [okay, I snuck in a little Arnold Kling in there. I'll cop to it] Entrepreneurs create even as they destroy. This creative destruction ultimately leads to greater abundance as firms are able to produce more output using fewer inputs. [SLW: these are paraphrases, not actual quotes]

Christensen: firms that refrain from sustained disruption, even to their own business models risk ossification and decline. Disruptive innovation is The Spice: it must flow. Try to imagine what the roadways would look like if automobile manufacturers refused to update model specifications year after year. We'd all still be driving the Model A.

It's worse than that, of course. We'd still be going blind in droves from handwashing our clothes using raw lye, frittering hours each week mending (relatively) expensive clothes, and dying early after a short, rough life of backbreaking toil.

Kirzner: saying that the role of the entrepreneur is simply 'to disrupt' misses the whole point of production. The point is mutually beneficial, peaceful, voluntary exchange. The entrepreneur busies himself with the task of discovering new opportunities for exchange. If destruction happens, that's merely a consequence, a side-effect of people finding better ways to enrich each others' lives. This important task of discovering new channels for mutual service is obfuscated by pointing to the aftermath and claiming that it, rather than the action that gave rise to it, is the purpose of entrepreneurial discovery. [SLW: again, these aren't quotes, they are merely my interpretation]

Josh Gans: Kirzner, ftw. Customers ultimately test whether or not an innovation is any good. Disruption on its own tells us nothing about if a new product or service is any good. Firms must take calculated risks under conditions of uncertainty. Ex ante, it could have seemed possible that Crystal Pepsi was a good idea. You don't know till you try. The customers have to sort it out. And even with careful study, risk management, and attentive marketing teams, your customers are almost always sure to surprise you.

Furthermore, what counts as "important" today may not be important tomorrow. Metrics are a locus of attention. Attention shifts.

Frank Knight: the difference between "risk" and "uncertainty" is crucial to understanding the nature of the problem of the firm. Risk governs a probabilistic relationship over a known domain of outcomes. When you randomly draw a single playing card from a standard poker deck, you can calculate the odds that the card will be the Queen of Spades because you know how many cards are in the deck and what each of their values are. If, contrarily, you randomly draw a card from a pile of business cards dropped in an urn by passersby, you lack the ability to calculate the odds, as you don't know what the underlying distribution is. I submit to you that the challenge of productive activity deals far more often in an environment of uncertainty than of risk.

North: when discussing large-scale upheaval, the problems of knowing the underlying distribution are worse than those offered by Professor Knight. To extend the business card-and-urn metaphor, imagine that passersby could drop anything into the urn. Not only does the forecaster lack knowledge of the probability distribution, but the entire domain itself is obscure. The system is non-ergodic. This is to say that if there are patterns in the system, they are incomprehensible thanks to small sampling problems, timing inconsistencies, and the difficulty, if not impossibility of consistently outperforming other actors. Institutional or regime change is best modeled as non-ergodic, meaning that hopes for reliable predictions are futile.

Kiesling: "My epistemic/knowledge problem take on the innovator’s dilemma is that both risk and uncertainty are at play in the dynamics of innovation, and they are hard to disentangle, both epistemologically and as a matter of strategy. Successful innovation will arise from combining awareness of profit opportunities and taking action along with the disruption (the Schumpeter-Knight-Kirzner synthesis)." [SLW: that one is actually a quote]

The economics of energy delivery are particularly salient here. Every now and again, there are big, non-ergodic disruptions to how humans convert heat and light into something useful. The rest of the time, clever folks, ever alert to the importance of mutual, (eu)voluntary production and exchange work to improve, refine, distill this conversion. Prediction is cheap talk (and perhaps impossible). Action is better.

Me: Adam Smith was right. Euvoluntary exchange expands when the entrepreneur retains dignity in an environment of peace, easy taxes, and a tolerable administration of justice. I find rhetoric concentrating on the mutually beneficial nature of entrepreneurship more natural, more accurate, more important than a narrow focus on mere disruption. Side effects are worth acknowledging, but it is the chief effect, that innovation results in mutually beneficial cooperation, that is the real story, the one worth telling loudly and often.

The APEEmath vol 1: Giberson and Kiesling Unbundle the Grid

The Association of Private Enterprise Education concluded its annual meeting this past Tuesday. I attended a generous abundance of fine panels, rubbed elbows with a generous abundance of fine scholars, and enjoyed a generous abundance of excruciating back pain. My back has largely recovered, so I find my mental satchel full of puzzles, questions, conundrums, pleas for clarification, and challenges to much of what I witnessed in (relative) peace and quiet. So for the next few days, I'll be sifting through the aftermath of APEE 2014. The APEEmath, if you will forgive me some bad dad humor.

And since it is often advised to start at the beginning, let's start with Session M1. The session I attended featured Michael Giberson and Lynne Kiesling, our friends at Knowledge Problem. Combined, their presentations told a story that I think we've all felt shimmering in the air since the 70s: decentralized energy production is a matter of when, not if. However, it is far less sure that energy distribution faces a similar threat, or if it does, it's certainly not clear that the grid will share the same time schedule as the power plants.

Please indulge me a brief digression here. My firsthand experience is in Naval nuclear propulsion. There are three and a half distinct divisions in the nuclear side of a submarine's engineering department (the Sailors charged with monitoring and maintenance of primary plant chemistry are, strictly speaking, part of Machinery Division, but they boast specialized skills and training that set them apart from the ordinary knuckle-draggers; they are the half division, but the ones I know personally also count among some of the finest men it has been my honor to have ever met, so don't let this imply that I think any less of them). We, the gaunt twidgets, the reactor operators, pasty from lack of sunlight, fine-and-brittle-boned from the many months spent hunched over Byzantine mazes of electronic components, yapping discontentedly in our odd tongue of resistance, capacitance, induction, and reduction—our eyes filled with cascading arcs of ionizing radiation detection, our ears stuffed with the harsh syllables of a routine critical checkoff, our sinuses subverted by the penetrating aroma of the loved-and-hated chemical that unceremoniously replaces the roiling breath and fart of 160 of our fellow shipmates into something vaguely resembling a breathable atmosphere, it is we who wrangle, harness, command the broken soul wrought from the enraged heart of uranium-23X, bending its fury to the diligent task of whispering life and vigor into the cold, coiled copper snaking arterial ardor up and down the stubborn corpse of the underwater pig, grunting and snuffling beneath the dismissive swell of an indifferent father ocean. The Electrical Division is responsible for shipboard load distribution and maintenance of generators, batteries, and the interface of the AC and DC portions of the network. Why do I mention this? Well, in the mind of a Sailor serving in an engineering department (again, many apologies to A-gang for not including you in my reindeer games), there is a perfectly natural cleavage between the generation and distribution functions in the quest to turn fuel and fire into warmth and comfort.

So here's the thing: rooftop solar is becoming not only more technologically efficient, but more economically efficient. This implies that legacy utility plants are rapidly advancing towards obsolescence. They are soon to be the twinkling phylacteries in which dwell the souls of the dear departed wizards of Thomas Edison's coven. But the grid? The grid is a thing alive, pulsing with the lifeblood of shared electricity. When its vitality can be sustained by bough and twig alone, the Big Capital power plants (with all the attendant costs) will end up clinging, vestigial, to the undercarriage of a sprightly distribution network. They are and shall be an unseemly legacy cost that threaten to burden a critically important component of ye moderne œconomy.

So why not split the utilities along their production and distribution seams? Might we get a jump on the inevitable transitional gains trap by half a league onward? Sure, there might be some negotiation costs for the intermediate bits, but determining who gets the line item for a decoupling station seems a lot more tractable (from the point of view of the end customer) than worrying about how to resolve the inevitable problem of how to keep rooftop solar providers from getting sucked under the waves when the pod of power rorquals go belly up and burst under the unforgiving gaze of the sun.

Power generation is not euvoluntary. Neither is power distribution. Keeping them bundled multiplies the risk without providing much extra reward. It's time to cut the cord, people.