This year, I mustered up the courage to document the truth that, perhaps, up to 90% of formal theoretical models in Financial Economics do not, in fact, yield any credible mathematical insights, rather, merely are processes shown to provide a good fit to a story that accompanied, or perhaps better still, preceded the model.
Every Mathematician worth his or her salt knows you always can find a process that fits a story. There are constant processes (which of necessity embed fixed points), linear processes, strictly convex processes, concave processes, and strictly concave processes.
If a story precedes a model, typically it can be rationalized by a mathematical process.
Whenever a formal theoretical model produces an interior or corner analytic solution, as opposed to a process as output, a formal theoretical model always produces new insights.
This is the case, because absent parameterization of a specific and well specified mathematical space that is layered on a financial economics challenge for arrival at a Mathematical Financial Space — a mathematical space within which all of the elements in the space that admit mathematical operations have a financial economics, as opposed to a mathematical character — arrival at an interior or corner analytic solution virtually is impossible.
A mathematical space is a more robust mathematical concept than a mathematical process. Every mathematical process subsists in some mathematical space.
The difference between an interior or corner analytic solution, and a mathematical process?
In Mathematics, the real line, or the x-y plane, or the x-y-z plane, or N-dimensions already are shown to be mathematical spaces. Note, however, that these are generic mathematical spaces that are not customized to any specific modeling challenge.
If you switch from a study of Engineering to a study of Financial Economics, if your mathematical space was the x-y plane, and remains the x-y plane, the switch in context from Engineering to Financial Economics becomes redundant.
In this respect, consider that a vehicle’s acceleration can be modeled as a linear or convex mathematical process. But so also can the velocity of money. Note, however, that given a study of acceleration takes away a human’s cognitive capacity for choosing not to accelerate, there does not exist any room for human decision making.
But does this apply to a model of the velocity of money? In the test of a vehicle’s acceleration, the economic agent is a disinterested party — all of the output of the model relates, in entirety, to performance of the vehicle, not performance of the economic agent.
When it comes to modeling of the velocity of money, however, the economic agent is an ‘interested’, welfare maximizing agent. Given such agents can make choices that hamper multiplier effects of money within an economy, such as receipt of tax breaks by publicly quoted companies that are not fed into the economy in form of new investments, a model of velocity of money that does not allow for decision making on part of economic agents does exactly the opposite of what ought to make the model beneficial, that is, assumes all economic agents adopt a certain sort of behavior. But we already know what happens if everyone acts the same, meaning there merely is arrival at fitting of a process to a story. It is exactly these sorts of simplifications — non-modeling of behaviors of economic agents themselves— that are leading to breakdown of economic predictions all over the world.
If an MFS were applied to the velocity of money challenge, under conditions that feasibly could subsist, and that are of interest to a policy maker, the model would parameterize responses of economic agents to receipt of new monies. For one such application, check out this other study authored by myself that generates inferences about income multiplier effects within a society.
Qualitatively, a model of acceleration of a vehicle cannot be distinguished from a model of velocity of money, which already assumes money acquires a multiplier effect.
Given economic agents must be elements of an MFS, creation of an MFS, and arrival at an interior or corner analytic solution ensures uniqueness, relevance, and credibility of modeling outcomes.
Typically, laws of continuity, differentiation, and integration, all of which only require existence of some N-dimension are all that are required for generation of mathematical processes. Consistent with generic nature of such processes, laws of continuity, differentiation, and integration do not alter in context of applications in Car Manufacturing, or Monetary Theory, meaning solutions arrived at have a generic, non-customized, non-unique flavor.
You see then that any formal theoretical model whose output is a mathematical process produces a generic solution for any and all possible contexts, clearly, a stretch of the imagination.
An N-dimension made up of N real lines is not a Mathematical Financial Space (MFS), only is a Mathematical Space, as such ignores the human behavior that it set out to model.
Perhaps 90% of formal theoretical models in Financial Economics only produce processes as outputs, not analytical interior or corner solutions. In absence of analytical interior or corner solutions, the extent to which the accompanying stories are robust remains a matter of conjecture.
Consistent with all of the foregoing, the Financial Economics Literature has come under significant criticisms in recent times, both internally (Allen 2000; Farmer and Geanakoplos 2009) and from industry. All of the criticism questions practical relevance of most of the formal theoretical models generated by academics.
While practitioners seem not to have arrived at the realization that Econometrics, or crunching of numbers is not a substitute for formal theoretical models that are well done, the critiques in the academic literature are aware of necessity of arrival at better formal theoretical modeling of challenges of Financial Economics.
My studies not only point out essence of non-credibility of formal theoretical models of challenges that subsist in Financial Economics, more importantly, incorporate solutions to the problems.
But then, the Financial Economics Literature has been known to be slow to change.
Yet, the courageous work that I have done is gaining some attention, is gaining some traction.