Jousting with the Knightian knights: Uncertainty and entrepreneurship

On the one side, Sir Entrepreneur of Northkirznerland. On the other, Sir Ardee of the Order of the Knightian Knights, Master of the Uncertain. Which gallant contender will win in this duel? In the past, Sir Entrepreneur has defeated Sir Ardee’s younger brother, Sir Risk of Martingale. It turned out if you studied his past jousting activities you could predict his moves, and thus win. However, doing this with Sir Ardee has proven impossible, and thus he is a fearsome fellow.

Days before the jousting commences, Sir Entrepreneur has been studying some writings by Lord Knight, Ardee’s Master and in one of them we can read:


So risk is like playing roulette or flipping a coin, and uncertainty is not being able to know even the probability distribution of the event. Not even his friend Rev. Thomas Bayes could help him here like he was last time he had a problem of this sort. How will our hero defeat this mighty foe?

While he is pondering this questions, he learns of a book by an Italian sage, and there he finds out some useful things about Sir Ardee.

It is about the willingness and ability of economic agents to take on risk and real Knightian uncertainty: what is genuinely unknown. […]

They argue that in fact innovation is an example of true Knightian uncertainty, which cannot be modelled with a normal (or any other) probability distribution that is implicit in endogenous growth theory, where R&D is often modelled using game theory (Reinganum 1984). […]

What is less understood is the fact that public sector funding often ends up doing much more than fixing market failures. By being more willing to engage in the world of Knightian uncertainty, investing in early stage technology development, the public sector can in fact create new products and related markets. […]


This of course does not mean that innovation is based on luck, far from it. It is based on long-term strategies and targeted investments. But the returns from those investments are highly uncertain and thus cannot be understood through rational economic theory […]

In the face of such uncertainty, the business sector will not enter until the riskiest and most capital-intensive investments have been made, or until there are coherent and systematic policy signals in place. Mariana Mazzucato, The Entrepreneurial State (2013)

Apparently Sir Ardee isn’t a regular knight, but one that was only possible because of its powerful sponsor, the State. No one trusted in Sir Ardee’s uncertain jousting skills until the State did.

But why was this so?, Sir Entrepreneur asks himself. Why is this knight different from all the other knights in the Order of the Knightian Knights? It is known that other such members didn’t need such powerful backer to get started, and they also began from scratch.

The relation between uncertainty and entrepreneurship

We have now seen Frank Knight’s definition of risk and uncertainty, and how Mazzucato tries to wield the latter in defense of the Entrepreneurial State. However, when reading the book, I had some questions in my mind regarding this argument.

First, Knightian uncertainty applies to every entrepreneurial activity. Opening a bakery in your neighborhood is making an uncertain choice, as is investing in R&D. However, we intuitively think that the former is less risky than the latter. So there are degrees of uncertainty, and R&D would sit at the top. If one would argue that Knightian uncertainty is a reason for R&D underinvestment, one would also be commited to thinking that it is a cause for undersupply of entrepreneurship across all areas. This is why it isn’t a very strong argument, unless you want to be prepared to defend that the leading force in entrepreneuership in general has been and ought to be the government. And no.

What is interesting, though, is Mazzucato’s claim that entrepreneurship under Knightian conditions defy rational economic theory, because you can’t calculate expected utilities here.

Accepting this whole framework, this would not be an argument for State intervention similar to the classical market failure one. There are different levels of uncertainty tolerance one can have, and this will modulate the degree of entrepreneurial activity one will undertake. Attempting to justify State intervention on Knightian grounds is equivalent to saying “Well, society has some risk preferences, but they are too much averse, so the State has to invest in riskier things”. But this is incompatible with saying that this defies rational action: if there is no rational uncertainty tolerance, what reason does the State give to justify saying that societal preferences regarding uncertainty are wrong? None!

Of course, the framework is incomplete. Bakeries open, and R&D happens without there being a State doing it, and firms don’t seem to randomly crash when doing R&D, nor bakeries suffer the same fate. It seems Knightian risk can be tamed up to a certain point.

To understand why, we rely on a paper by Vlad Tarko titled Can Probability Theory Deal with Entrepreneurship? (2013). Knight’s, Mazzucato’s, Keynes’ and others answer would be that no, entrepreneurship lies beyond probability theory. The two latter would also put forward that since there is no rational reason for investing under such conditions, they will be driven by irrational passions: animal spirits. This issue could quickly overflow the topic of this post, and seep into issues of the meaning of rationality and epistemology. Suffice to say, for now, that I don’t buy this.

Entrepreneurship and rationality

Tarko begins his paper addressing the same concern we just saw here. Is entrepreneurship irrational?

On average, about 25 percent of new firms don’t survive the first year, less than half survive past the third year, and less than 30 percent survive past ten years (Headd, 2003; Knaup, 2005; Shane 2008: p. 99). Similarly, less than half of self-employed persons remain self-employed past the 6 years mark, with a long term success rate of about 40 percent (Shane 2008: p. 99). Nonetheless, one in four entrepreneurs who close their business try again another venture (Schutjens & Stam, 2006). Given this rather high rate of closures and perseverance in what, at least at first glance, seems like error, we are lead to ask: Are people starting new businesses overconfident and deluding themselves about their chances of success (Wu & Knott, 2006)? In other words, does the entrepreneurial engine of our economy depend in some fundamental way on the irrational urge of some people?

Take into account that entrepreneurs are doing far better than chance. The space of possible business plans you could undertake is unbounded, and picking one at random would yield a zero probability of success. Yet entrepreneurs achieve a long term success rate of 40%.

From a naive conception of economics, entrepreneurs would work in ths funny way:

From a neoclassical rational expectations point of view, a rational entrepreneur would take the observed frequency of successful new firms as an estimate of one’s own success probability. However, the high closure rate is not necessarily evidence of failure (Headd, 2003). On one hand, (a) a business may be closed because investment has reached its optimum end time, i.e. the diminishing returns point beyond which expected profits are lower than the interest rate (Hirshleifer, 1970: pp. 81-7), and, on the other hand, (b) entrepreneurship can also be understood as a consumption good rather than as an investment good, with entrepreneurs drawing significant utility from the activity itself, regardless of whether it is profitable or not (Sarasvathy, 2001; 2003; Sarasvathy & Dew, 2007). Form this neoclassical perspective, whatever heterogeneity exists among entrepreneurs, it is entirely due to preferences heterogeneity with respect to the consumption good aspect of entrepreneurship.

So according to Tarko, neoclassical economics way of grappling with the existence of entrepreneurship is not by saying entrepreneurs are irrational, but that entrepreneurship is also a consumption good, and so doing it is enjoyable by itself, and also that the high rate of apparent closure should not lead us to expect really low rates of entrepreneurship. On the consumption good aspect of entrepreneurship, and why profit maximization does not fully explain entrepreneurship or even business in general, see Manish and Sutter 2015.

The second view presented in the paper is the Austrian School view:

The classic Austrian view, based on the uncertainty-risk distinction proposed by Knight (1921), is diametrically opposed to the neoclassical perspective (Kirzner, 1997). The most important objection Austrians have to rational expectations regards the assumption of common knowledge. They note that entrepreneurship essentially depends on epistemic heterogeneity, i.e. on the fact that various people, due to their different ways of understanding and interpreting the world around them, see different opportunities for profit (Kirzner, 1973; 1976; 1980; 1997; Lachmann, 1976; O’Driscoll & Rizzo, 1985; Boettke, 1998; Klein, 2012). Their position is to deny that one can have a meaningful statistical estimate of the risk of starting a new business. Due to the high heterogeneity of the contexts in which any new business starts, the uncertainty involved in such a decision is unquantifiable and, thus, entrepreneurship lies outside the scope of cost-benefit analysis – it is neither rational nor irrational. As Knight put it (1921: III.VII.47), “[b]usiness decisions … deal with situations which are far too unique, generally speaking, for any sort of statistical tabulation to have any value for guidance. The conception of an objectively measurable probability or chance is simply inapplicable.”

Mazzucato would probably agree with this, but I don’t quite like saying entrepreneurship lies beyond the realm of the rational, altough it depends on how you want to define rational. The Austrian view seems more plausible than the neoclassical one. (This view does not exclude the consumption good aspect)

So far we have entrepreneurship as irrationality (Keynes), entrepreneurship as a rational activity (neoclassical economics) and entrepreneuership as neither rational or irrational (Austrians).

Finally, Tarko presents us with a Bayesian view of entrepreneurship, that attempts to justify entrepreneurship as rational like the neoclassicals, taking the Austrian view seriously. This is nice, because the neoclassical justification for entrepreneurial rationality seems flimsy to me. For the multiple conceptions of entrepreneurship available in the literature, see Foss and Klein 2008

Finally, the Bayesian perspective, advocated by this paper, is situated in-between the other two extremes. On one hand, it agrees with the Austrians about the importance of epistemic heterogeneity and imagination for understanding entrepreneurship. On the other hand, it agrees with the neoclassical perspective that the probability of success is quantifiable, and thus that cost-benefit analysis is possible even in the case of a decision to start a new business in a novel context or a decision to introduce a new product or service on the market. However, the Bayesian perspective is not a compromise between the other two. Instead, it stems from rejecting a common assumption about the objectivity of probability estimations that the rational expectations approach and the Knightian-Austrian approach both share. From the Bayesian perspective, a probability distribution is not an objective feature (or property) of the outside reality which one tries to “measure”; probability distributions are quantitative descriptions of the state of knowledge that one has – i.e. they describe the existing epistemic relation between an observer and his or her environment, rather than just the objective state of affairs in which the observer is situated (Jaynes 5 2003: chapters 1 and 2; Samuelson, 2004: section 3).

What this means in technical terms is that all probabilities are conditional probabilities. It is this relativity of all probability estimations to specified conditions (which can be either hypothetical assumptions or empirical information) that creates the analytical ability to deal with epistemic heterogeneity, as different agents and make different probability estimates of the same event due to their different background assumptions: (p |A )≠( p| B). From this perspective, entrepreneurial action is a combination of two tasks: (1) the task of selecting one’s assumptions about the world (the imagination part), and (2) the standard constrained maximization process of cost-benefit analysis (the mechanical part). The reason why different people are not as good at detecting opportunities (of being “alert”) is that they have different background assumptions, which lead them to different probability estimations of the likelihood of success of a particular type of action. Thus, understanding differences in alertness amounts to nothing more but understanding that people make probability estimations conditional on different assumptions.

Cool, isn’t it?

There is a further thing to be said here to close this section without falling into the realm of epistemology: there is Objective and Subjective Bayesianism, and this paper takes the Subjective view. Objective Bayesianism imposes certain contraints on what you are allowed to believe (what priors you ought to have). This, however, isn’t that much relevant to the present discussion, but could be to a discussion of what is rational and what is not. For some remarks on that see Huemer 2009.

Risk and uncertainty under Bayesianism

Bayesianism says the title of this section is repetitive. Risk and uncertainty are not that different:

There is an important sense in which the Bayesian approach to probability (Jaynes, 1988; 2003) undermines the Knightian original distinction between risk and uncertainty (Knight, 1921). From a Bayesian point of view, Knight had understood risk – the measurable side of uncertainty – in an overly restrictive manner. […]

According to this alternative perspective, there are numerous other ways in which one can measure probability, apart from repeated experiments under homogenous conditions. These involve everything from the principle of indifference and symmetry considerations (which allow one to determine an event’s probability even before making a single sampling experiment) to entropy maximization

So it turns out you can measure the unmeasurable after all!

Given this background about the way in which the distinction between risk and uncertainty has been originally made, and the realization that the original concept of risk itself has been defined based on an overly-restrictive method of assigning probabilities, there is a legitimate suspicion that perhaps the riskuncertainty distinction itself is mistaken (Caplan, 1999; 2001). In other words, perhaps that, if we take into consideration the more general Bayesian perspective, everything that was once thought to be unmeasurable will turn out to be measurable. One should take “guesstimation” methods much more seriously and recognize the fact that one’s ability to measure something often depends only on how ingenious one manages to be (Hubbard, 2010): apparently “intangible” variables often turn out to be quite measurable if one corners the matter from enough empirically available directions.

… or maybe not

This conclusion would be premature. Far from undermining the distinction between risk and uncertainty, the basic Bayesian insight that all probabilities are conditional probabilities leads unavoidably to it. The idea that all probabilities are conditional means that there is no such thing as p(x ) but only ( p|X ), where X is the background information used to compute the numeric value of x the probability of – the set of hypotheses on which we are relying when we assign a probability estimation to the truth of a statement. At a minimum, X is the assumption about the set of possible values x that can take, but it may include much more complex assumptions as well.

So what is the difference?

Once we take into consideration the conditional nature of all probabilities, the distinction between risk and uncertainty can be restated without relying in any way on the contentious requirement of repeated experiments under homogenous conditions. The risk of x is the value of its probability computed for a given set X of assumptions (hypotheses): risk(x)=p(x|X)

The uncertainty of x refers to the possibility that the background information X , on which we are relying in order to compute risk, might not actually be correct. In other words, we must consider all possible versions (be they infinitely many) of the background information: uncertainty(x )={p (x |X1 ) ,p(x |X2 ),…}

This approach seems to favor a radically relativist perspective. If we’re basing our predictions on some estimate of risk, dependent on the hypotheses set X, we may turn out to be completely off-track if X is actually false. What is missing is the recognition that, after all, there exists a Bayesian model selection method (Bretthorst 1996). The set uncertainty(x ) is thus somewhat deceptive because its components, the probability distributions p( x| Xi), don’t have an equal standing – some are more plausible than others. However, this cannot solve the problem entirely. The question arises: They are more plausible conditional on what assumptions? We can nonetheless push the issue one step further, considering the probability of each hypotheses set Xi: uncertainty(x|B)=SUM(p(x|,Xi,B)p(Xi|B))

That is, different models lead to different probability estimates, but then, different background model assumptions B lead to different estimates about how plausible one model is. The above equation tries to capture this. Of course, if your mind works as mine, you will now be wondering “But what about the probability that the background assumptions for model selection themelves?? How yo you pick B?” Answer: Yes, it is what you are thinking. B turn into Bi, that depend on further assumptions C. Or, you can just subsume all meta-meta-hypothesis, meta-meta-meta-hypothesis and so on under the simple banner of the meta-hypothetical: B.

This obviously does not fully reduce the concept of uncertainty to risk, because it still depends on the meta-hypotheses B about how to construct the set of all possible hypotheses Xi . What this shows is that it is impossible to completely get rid of uncertainty.

So summing up

Importantly, the connection between this distinction and entrepreneurship is preserved: entrepreneurship involves differences between peoples’ hypothesis spaces, i.e. stems from differences between their representations of the world (including the social world). Kirznerian alertness exists because, thanks to one’s different background assumptions, one assigns a higher probability to some opportunity for profit as compared to other people who use some other hypothesis spaces. Similarly, Kirznerian error reflects the fact that one’s subjective probability estimations (i.e. risk estimations) may lead to completely mistaken predictions as a result of the fact that they are computed on the basis of some mistaken assumptions. To put it differently, one’s ability to identify “opportunities”, to be “alert”, is a consequence of one’s representation of the world. Uncertainty exists because one may misidentify the set of possibilities (i.e. fail to identify one’s opportunities), and one’s models may be flawed.

Now, after a discussion on mathematical measures of surprise, Tarko says that the rational choice framework can accomodate empirical reality and explain entrepreneurial activity, by doing without the common knowledge (or priors) assumption:

The philosophical consequence is that one can now explain away within the rational choice framework various puzzling and apparently irrational decisions of entrepreneurs. This is harder or impossible to do in the rational expectations model or in any model that works under the common knowledge assumption. Take for example Mark Zuckerberg’s decision to refuse to sell his business even for sums of money that seem extremely large to outside (and perhaps less informed) observers. One interpretation of such refusal is that he is absurdly vain. However, another interpretation is that his refusal to sell is a signal that he considers Facebook to be far more disruptive than the potential buyers have estimated it to be (this is how some commentators have indeed interpreted his refusal). This rational choice explanation thus repeats at a deeper level the same line of thinking that lies behind the no-trade theorem (Milgrom & Stokey, 1982; Samuelson, 2004), without however leading to the same no-trade conclusion, because the assumption that all agents share the same priors is no longer part of the story.

He then talks about something I mentioned: that the things you may do are infinite and in many cases, singular enough. You can’t list every business plan, analyse it, and execute the one that maximises expected utility.

“The most important features of genuine uncertainty are the inherent unlistability of all possible outcomes resulting from a course of action, and the complete endogeneity of the uncertainty. The first feature … is the basis of novelty or true surprise. This is in sharp contrast to the mere arrangement (or weighting) of known possibilities characteristic of neoclassical uncertainty. The second feature … is the origin of an ongoing market process that itself produces changes to which the system must adapt”

This quote captures well the essential problem of uncertainty and why it is important for economic science. The question for present purposes is whether Bayesian theory relies on the assumption that we know and can list all the possible outcomes. In other words, while the Bayesian theory might be better than the simple rational expectations model, it might still not fit all the intricacies highlighted by the Austrian theory of entrepreneurship.[…]

This problem of unlistability is far less serious than O’Driscoll & Rizzo make it out to be. First on all, the real problem is not unlistability per se, but the fact that different people conceive of different (listable) sets of possibilities. In other words, the task of a theory of entrepreneurship is not to describe the mind of  God from whose perspective the entire unlistable set of possibilities is contemplated, but to describe human beings who, for better or worse, only take small sets of possibilities into account at any given moment in time. To put it differently, one can deal with the important issue of epistemic heterogeneity without framing the entire matter from a “view from nowhere” perspective, in which epistemic heterogeneity no longer exists because all possible perspectives of human entrepreneurs (real or possible) have been merged into a single, all-encompassing, and “unbounded” perspective. The issue is thus simply to allow the list of possibilities to change over time, but at every moment it will be a “bounded” list.

Secondly, Bayesian theory actually deals explicitly with the problem of unknown unknowns (see for instance Bretthorst 1988: section 5.1; 1990; Jensen & Nielsen 2007: chapter 6). Bayesian theory deals with this issue by simply adding to the set of possibilities an additional “unknown” item. As Bretthorst put it (1988: pp. 55-6): “To say that we confine ourselves to the set [ ] is not to assert dogmatically that there are no other possibilities; we may assign prior probabilities … which do not add up to one. … Then we are assigning a prior probability … to some unknown proposition, SE = Something Else not yet thought of.” By taking this path we can show why the problem of unlistability is not that serious. It can be easily proved that, by adding SE to the set of possibilities, the relative probabilities of the known alternatives remain unchanged. This means that the rational decision made by taking the unknown unknowns into consideration will always be the same as the one made without taking them into consideration. In other words, as long as one keeps an open mind that one may be missing something, the issue of objective unlistability has no behavioral effects.


Gull (1988) notes that [t]he real art it to choose an appropriate “space of possibilities”, and to date we have no systematic way of generating it. … [I]n many problems one has no guarantee that our choice is right in any final sense, and this feeling of ambiguity has led to much soul-searching. I feel (along with Jaynes, 1986) that our aims should be different. We should not seek a “final truth” in our hypothesis space, but use our common sense to capture enough structure of the real problem being solved so that we can make useful predictions. If the predictions are useful, then that is an indication that the hypothesis space is good enough for now, without prejudice to the possibility of revising it later. If the predictions are not good, this is not a disaster, for we then have learnt that the hypotheses have to be reformulated and the ways in which our predictions are wrong may help us to do this.

I stipulate that this is exactly how entrepreneurs, as well as managers of established businesses, think as well. If one applies this search “algorithm” not to the process of discovering and correcting scientific models of nature (as Jaynes and Gull do in the quoted papers), but to the process of discovering new profit opportunities, one ends up precisely with Kirzner’s concept of entrepreneurship and with the 16 Kirznerian view of the market process. In the economic case, the hypothesis space refers to assumptions one makes about consumer demand and about the various possibilities of combining existing resources in novel ways (of creating new “recipes” [Romer, 1993]). Entrepreneurship thus involves a process of updating one’s representations about the world (including the social world), an update which leads one to make different estimations of risk as compared to one’s competitors who rely on different representations. Entrepreneurship does not thus involve merely a search within an objectively given, unique structure of probabilities, known and accepted by all, and within which actors move mechanically driven by maximizing expected profit. While it is true that we can model all actors as maximizing expected profit, each of them acts based upon a slightly different representation of the world, and thus on different subjective probability distributions.

And is using the common sense assumptions to choose a plausible set of background conditions rational, as Gull says? Yes, see Huemer 2001 for that.

So, entrepreneurship is generally rational, after all. Different agents will have different hypothesis spaces, and will act on them. Knowledge of the actions of one agent will change others’ ideas about their own planes, and this whole process is what lies at heart of the free market itself, and why central planning will generally underperform it: There is not always a way to convince some manager an idea is good, even if it looks very clear in the entrepreneur’s head. I’ll leave this here, on risk of this devolving into a critical discussion of Aumann’s Theorem.

The reason uncertainty is not a reason for government intervention similar to the one present  in the market failure argument is that the market failure fix just tries to implement what people would do if the profits accruing from their discoveries and diffusing through the economy went back to them, thus equalising social and private returns. The idea there is that there is in theory an agent that in theory can capture all such rents: the government via taxation. With uncertainty, this is not so, especially on the light of the above discussion. The government can provide an environment with increased predictability via rule of law, or can botch it via regime uncertainty, but investing in particularly uncertain activities does nothing to solve coordination problems the people have. If one argues R&D investment will be low because it is uncertain, the obvious reply is that “low compared to what?”. To some measure of lower uncertainty, I suppose. But why should it be supposed that people who are out there, in the market, trying to foresee events, will have worse hypothesis carving capabilities (and thus worse performance under uncertainty) than government officials? If there were an objectively true and rational ex ante known optimal level of uncertainty that has to be beared, and market participants are being more risk averse than that, there would be a market failure because of that. But there isn’t.


So how does rational entrepreneurship and action under uncertainty in general work? First, the entrepreneur thinks about the problem she wants to address, because she likes solving that problem itself and/or because of a profit opportunity. She will gather all relevant information she thinks necessary. With this information, she will think of possible courses of action, basing her predictions on assumptions derived from the initial step. There is a tradeoff between speed of implementation of a business plan, and amount of information gathered, so she will take that into account. As more information comes in, models and assumptions will vary. When she thinks a given action is proper, she will implement it. There is no more mistery to it.

It is true that, if the cost of failure is reduced, it will be easier to perform risky actions and there will be more of them. But this would only be some reason for government investment in the case public servants were better at the entrepreneurial job than entrepreneurs, and if this is true, it is true in general, not only for R&D, and this leads one straight into central planning, which we know doesn’t work. The way a market solves this is allowing people to bet, so to speak, on their business plans and make into an intersubjective fact (a price) what was a subjective fact (knowledge), and allow anyone to challenge any businessplan. This objection cannot be surpassed even within a Langean market socialist scheme. See here (in Spanish). It can be argued, that given some preferences, arrangements different to the spontaneous ones will be better (the usual argument), but you would need additional argumentation to say the problem is with the preferences on uncertainty themselves, and this argumentation has not been supplied by Mazzucato, or others.

Once we have disabled the Knightian objection, we can focus in the future in the real meat of the justification for public R&D: the market failure argument.

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