Communicating Probability Margins in Economics

Economists spend a lot of time talking about some margins of adjustment, such as quantity, quality and price. Other margins are rarely discussed formally, such as the likelihood that a stock price will rise tomorrow (or next year) or the probability that a natural disaster is so bad that it causes a “hundred-year flood”. A recent survey offers some insights about how people talk about this margin.

Common marginal statements include “quantity demanded increased by 3%” or “productivity growth was 4%”. When making predictions or guesses in the absence of hard data, these kinds of statements are replaced by statements such as “quantity supplied next year will probably increase by 4%” or “productivity growth could exceed 5%” but no dictionary defines those words usefully.  

Risk vs. Uncertainty

Statisticians offer the precise language of “standard deviation”, “conditional probability” and “statistical significance”. This language is incredibly useful when something can be described as “risky”: i.e., numbers are available.

Ordinary people get confused by probabilistic statements even in relatively-simple situations. For example, doctors are often confused about how to interpret the results of a diagnostic test: e.g., Type I error vs. Type II error, should size of an effect be measured in absolute or relative terms.

Yet, the distinctions are critical. Consider predictions in professional sports such as “our team will win” or, to apply to comparative statics principle, “their team is more likely to win on a hot Tuesday”. There are (were and always will be) at most three possible outcomes: win, lose or tie and, famously, underdogs sometimes win. So, differences of opinion need to clarified by exploiting the probability margin, especially when people want to put their money where their mouth is.

When numbers are less reliable, because the interesting events are rare or hard to measure numerically, the adjective “uncertain” is often applied. This word is not very useful since not all uncertain situations are alike.

Meanings

Distinctions need to be made and people have trouble talking about uncertainty precisely. A large survey conducted online by Adam Kucharski offers some insights. Over 5000 people were asked to convert common English-language phrases. For most people talking about an event X such as “an increase in the unemployment rate”, stating that “X is almost certain” translates into a higher probability of happening than the phrase “X is likely”, and “X is probable” implies a higher probability of happening than the phrase “X could happen”. The debate about how much more probable is unresolved.

Not everybody uses the same phrase in the same way. Phrases such as “realistic possibility” or “might happen” were interpreted very differently by different individuals, while phases such as “about even”, “will happen” or “remote chance” had relatively similar meanings across individuals.  Younger people tended to give higher probability estimates for a given phrase. A second post extends some of these comparisons, with excellent examples of data visualization. I think that the comment on differences according to familiarity with English is very interesting.

Two Lessons

This work is important because, while formal economic analysis often uses the language of probability, communicating the results of that analysis relies on less precise language.

1/ Everybody should learn how to communicate precisely about risk and uncertainty. Some organizations give formal guidance on the terminology [IPCC, see p. 3] [CIA]. The benefits of this learning can be seen in the skill of “superforecasters”.

2/ Statisticians like to play with data concerning physical objects. Economic data involves behaviour. It often needs to be qualified by some measure of incentives and an understanding of the difference between “it can be done” and “it will be done”. This kind of “shirking” on the margin distinguishes “strategic risk” and “statistical risk” in an equilibrium.