Rational Estimation and Price Under Uncertainty

• John Vandivier

This article talks about ways to deal with uncertainty, and I will also briefly define the concept in contrast with simple risk.

  1. Definitions: Uncertainty vs Risk
  2. Rational Estimation without Uncertainty
  3. Rational Estimation with Uncertainty

1 - Definitions: Uncertainty vs Risk

  1. Uncertainty and risk are both not simple economic phenomena. They are generic elements of complex systems.
  2. They are both represented as error in a forward-tested model, but only risk is captured in a backward-tested model.
  3. Risk
    1. A probability of some event
    2. Sometimes, the expected value of some event: The probability multiplied by the payoff
    3. Think of your budget: You have a line item for gas, but there is some risk you will go a bit above or below that amount.
    4. You are familiar with the kind of event
    5. You may have bought insurance for this thing because you knew beforehand it might happen
  4. Uncertainty
    1. Synonyms
      1. Knightian Uncertainty
      2. Wicked Problem
      3. Kirzner's sheer ignorance
      4. Donald Rumsfeld's Unknown unknowns
      5. Mises' Case Probability
    2. Think of your budget: You have a category for \"Other\" or \"Unexpected Expenditure\"
    3. You probably didn't buy insurance for this thing because you don't know what it is and no one sells \"Other Stuff Insurance\" (yet...?)

2 - Rational Estimation without Uncertainty

Before we go on to estimating the costs of uncertainty (which I argue can be done), what are some principles of estimation when uncertainty is not the case?
  1. If you have lots of data, do a regression. If you don't, take an average. You never have no data.
    1. The regression should be linear by default unless you have some reason for another approach.
  2. Direction-ambiguous bias doesn't invalidate or prevent estimation; it preserves the point estimate.
    1. If I could spend more, less, or the same on gas as I budgeted, should I throw out the budget? No! It means I budgeted the optimal estimate.
    2. Obviously, if you have some reason to think the weight one way is bigger then you can apply some correction. But if you just don't know the errors offset in either direction.
    3. More error in both directions will reduce our confidence in our point-estimate, but it doesn't shift the value of the point estimate.
  3. Direction-specified bias can be corrected using ordinal logic
    1. If I know I will spend more on gas next month, how should I proceed?
      1. Ask yourself, \"How much more?\" Based on your answer:
        1. \"I don't know.\" Assume no change. This is also an axiomatic way to justify the default usage of the linear regression.
        2. \"A small amount more.\" Small relative to what? The original value. New budgeted value = 1.5(Original)
        3. \"An even amount.\" New budgeted value = Original
        4. \"A large amount more.\" New budgeted value = 2(Original)
      2. I have a long personal literature on ordinal modelling for more detail including the maths:
        1. Ordinal Modelling Applied to Connoisseurship
        2. A Priori Probability: Larger Values
        3. An Example of Quantified Opinion
        4. Quantified Ordinal Modelling of Action
  4. Abstraction reduces the accuracy of estimation, but doesn't prevent the possibility of estimation
    1. Corollary: The accuracy of a forecast is roughly commensurate with the number of observable input or input properties
      1. This is why micro-founded economic models are more accurate than aggregate models. Eg, including individual level characteristics improve accuracy
      2. You can do a bit of handling for unobserved heterogeneity, but not much. You pretty much get 1 extra parameter in addition to observable data.
    2. Any set of observations, events, or items can be abstracted to some level such that they belong to a common class.
    3. Any item belonging to a common class can be estimated on the grounds of the other items belonging to the class.
    4. So a maximum-likelihood estimate of any item can be obtained. The tricky part is reducing the error such that substantial confidence or usefulness is gained.
  5. Information contained in the model is represented in the portion of variation explained.
    1. Corollary: Ignorance is represented as a smaller share of variation explained, more error in forecasting, and/or less confidence in estimation of various parameters.

3 - Rational Estimation with Uncertainty

I argue that case probability estimation is possible, contrary to what Mises has said, for two reasons:
  1. Everything can be classified at some level of abstraction, even if it is a retrospective category for \"Unforeseen costs\" or \"Other\"
    1. If you have never suffered an unforeseen cost then you:
      1. Probably shouldn't budget for it, or
      2. Budget for it at the rate of a foreseen cost since this is your only rational focal point / Schelling point
    2. If you have some data, even if it is small-n but definitely for large-n, on the frequency and payoff of unexpected events then use that.
  2. It is possible to demand surprise
    1. Or, exert effort or money to influence the own-rate of surprise or the rate of discovery
    2. There are things I know alot about and things I don't know alot about
      1. If I engage in an activity I know very little about it is easy for me to be surprised
        1. Eg visiting China: Known unknown = I have to learn Mandarin.
        2. Unknown unknown = I don't know!
          1. But I can set aside some cash for it just in case
          2. More cash set aside reduces the potential negative consequence
          3. At the cost of foregoing known rewards
      2. If I engage in an activity I know alot about it is hard for me to be surprised
        1. Eg talking about economics: I have probably already heard it and even if it's new I doubt it's highly surprising
        2. Or, getting a desk job and never doing new things. The same tasks over and over. No learning, no discovery.
    3. A friend suggested that things I know alot about actually increase my ability to be surprised: Fine, it's possible, but I was still able to influence the own-rate of surprise
  3. Tangentially, it should be possible to estimate the rate of innovation whether such rate is endogenous or totally random.
Here are some applications:
  1. Budget for unknown expenditures
  2. Include an \"Other\" category in surveys
  3. In Agile planning, you can plan using points which are associated with unknown requirements
  4. Give Rumsfeld extra money even though he doesn't have a specific thing to spend it on (I'm not really recommending this, but it's the conclusion of his remark)
  5. When investing, double the risk premium to include a rational estimate of Knightian Uncertainty
    1. Note: Don't assume an increase to risk unless you have a reason. Knightian Uncertainty could reduce you risk.
    2. Another Note: Rational doesn't actually mean true or accurate. It just means you got nothing better. It's definitely better than the idea that estimation is impossible.
    3. A Third Note: But like, what are you going to do, allow for infinite uncertainty? That's not rational or solvable, but we assume uncertainty all the time. Uncertainty is solvable.
  6. Key point: It is possible to estimate the frequency and cost (or benefit) of a surprise, but it is not possible to precisely identify the kind or content of a surprise.
    1. In that case it wouldn't be a surprise; the precise content is revealed in the moment of discovery.
    2. But, it may be possible to estimate the broad nature of a surprise.
      1. Eg there is an emerging field of medicine likely to bring more inventions compared to legacy fields.
      2. Very hard to do at a social level as it stands; maybe not too hard for a self-reflecting individual to recognize high potential areas of personal discovery or surprise.