Weekly Philo economics (with more on modal economics): "Assume that we can make an exhaustive list of all the uncertain events that might take place in the future."

Last year I called attention to how economists introduced mathematical technicalities to model randomness in order to dispense with uncertainty (recall here, here, here, here, and here among others). I have called special attention to the non trivial modal assumptions built into these formalisms (recall my writing about the modal properties of a so-called martingale.) But while there is a lot more to be said about the displacement of uncertainty by (supposed) randomness that is only one half of the story. As my informant on High Theory in economics, M. Ali Khan, taught me there is another path by which we can trace the effacement of uncertainty: so-called contingent commodities, or an Arrow security (named after Kenneth Arrow). (In what follows the mistakes are mine!)

The post title is a quote from the following paragraph: “There is also uncertainty. Economically important events that we cannot clearly foresee include the weather, our health, and technical change. It is formally possible fully to take account of uncertainty…through a very clever reinterpretation of the model we have already have in place…Uncertainty means that we don’t know what’s going to happen in the future. But we do know what might happen. Assume that we can make an exhaustive list of all the uncertain events that might take place in the future…At each date there is assumed to be a finite list of events that describes the condition of the economy in terms of all the economically relevant uncertain events that may occur…A state of the world will be defined by the current condition (in terms of uncertain events) of the economy and history of the past realizations of uncertain events that leads to it…to accommodate uncertainty by defining a commodity to include specification of a state of the world. A commodity is now characterized By what it is (its description), By where it is available (its location), By when it is available (its date), and By its state of the world (the uncertain event in which it is deliverable)" (R. Starr, 233; emphasis in orginal [this link should give the whole passage that I am discussing. Starr was trained by Arrow.]

That is to say, every possible moment in this universe has a unique so-called 'contingent commodity' connected to it. And a contract can be devised that promises to pay a unit of a numeraire good [there is no money in the main model of a capitalist economy!] if a particular state in a particular time period occurs and nothing otherwise; this is an "Arrow security". Arrow argued that in order to transfer purchasing power across all states in a general equilibrium model, we really only need a single "Arrow security" for each such state. "Thus, if we have S possible states in any time period and n physically-differentiated commodities, we merely necessitate S securities for each time period.” In this world, each moment is covered by some contingent commodity that can have an arrow security assigned to it. (Often these terms are used interchangeably.)

In this world all the possible moments are really possibly. It pretends to eliminate uncertainty -- unknown unknowns -- entirely. But, of course, the assumption that we can make an exhaustive list begs the question. (This is also an empirical matter: YOU try getting insurance coverage for terrorism, acts of war, or nuclear accidents!) So, the economist's main conceptual-mathematical-workhorse-machinery is unable to handle genuine uncertainty in a fruitful way.

But...I leave with you three very interesting interesting philosophical-technical-historical questions. From the 1950s onward, economists "handled" uncertainty either by treating it as something random or in terms of contingent commodities. 1) Are the modal properties of moments in a world with contingent commodities and randomness as defined by a martingale identical? (Hint: NO WAY!) 2) When did the move "randomness = contingent commodity" get made within economics [Hint: in the wake of Paul Samuelson's Capital Asset Pricing Model); 3) Did anybody notice the problem? [Hint: probably Mandelbrot did, but that awaits further research]