Saturday, June 19, 2021

On My Research Program

"I know not how I may seem to the world, but as to myself I seem to have been only like a boy playing on the sea-shore and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me." -- Isaac Newton (apocryphal?)

For the past couple of years, I have been pursuing a research program that I seem to have stumbled upon. I am looking for fluke switch points, where these fluke switch points partition certain parameter spaces. The analysis of the choice of technique is supposed to be qualitatively invariant, in some sense, in each region formed by these partitions, but varies among regions.

I have tried to define a taxonomy for such fluke switch points. Using an example, I have explored structural dynamics. Analyzing fluke switch points in models of fixed capital lets me see maybe more deeply into the incoherence of Austrian and marginalist approaches. Lately, I have been considering a parameter space of relative markups. Even more recently, I have been considering models of extensive rent.

Mathematically, these post-Sraffian models I have been exploring are open. Given parameters characterizing the technology and relative markups among industries, the distribution of income can vary with one degree of freedom. But if the wage, for example, and the size and composition of the net product is given, the rate of profits and the price of each commodity is determined. This is a matter of mathematics, close to accounting. Is my approach compatible with Ajit Sinha's reading of Sraffa's work as an approach akin to geometrical reasoning?

I do not know that Tony Lawson would accept that these models are ontologically open in his sense. Similarly, Nicholas Georgescu-Roegen made a distinction between what he called arithmorphic and dialetic reasoning. In my approach, I emphasize how quantitative perturbations of parameters leads to qualitative change in admittedly static models. I limit myself to discovering structures at the level of mesoeconomics, not visible at the level of individual transactions or an individual (non-vertically integrated) industry.

I rarely comment on whether or not I am taking an empirical economy as given. My approach certainly relates to Leontief input-output matrices, which can be constructed or approximated from National Income and Product Accounts (NIPAs). The econometrician would probably also want prices indices for individual industries. At a given point of time, one might say a process is dominant in each industry. But some firms might be still operating old processes, and others might be introducing new processes with which they hope to make super normal profits for a time. This observation provides some justification for considering the choice of technique. I often postulate continuous declines in coefficients of production, following Pasinetti's lead, or variations in relative markups. Is this a matter of counter-factual reasoning that Sraffa would reject?

I am aware that my models are not set in historical time. This is a point of contention for some Post Keynesian, such as Lars Syll. Do at least some of my partitions have implications for the dynamics of how or whether market prices approach prices of production? This is a question that I will continue not to address. I found intriguing this talk by Ian Wright, with accompanying handout.

Research in flukes may lead to more acceptance of possibility of reswitching, capital reversing, reverse substitution of labor, recurrence of processes. I wonder if somebody that understands something about algebraic geometry could summarize my approach more shortly, but even more abstractly. I hope and wish that I can read sometime somebody extending this research. Some sort of structures definitely seem to exist in these parameter spaces.


Blissex said...

«you seem to focused on marginalism as a justification for an ideology about income distribution.»

There is another point here that I am trying to make, that a lot of academic work is not serendipitous, but teleogical, as in driven by an intrinsic or extrinsic goal:

* Many academics don't just have curiosity about interesting random stuff, they have goals to pursue, and want to achieve them, conclusions that they want to prove, and try to find ways to achieve. Whether it is JB Clark trying to justify the rents of asset owners, or K Marx doing cost accounting to show that if "value" is defined as the labor of free people, those who don't contribute labor extract a chunk of it from those who do, or R Vienneau trying to find patterns in re-switching.

* Even more often, whether a result was serendipitous or driven by some goal, some "emergent" purpose is retrofitted to that result, not necessarily the one that drove it.

This happens even in natural sciences like physics or mathematics. I am sure you abstractly know this, but I am reminding you because pointing out the design purpose, or the emergent purpose, of something usually is very illuminating: there are several results in sciences like physics and disciplines like engineering or political economy that to me seemed incomprehensible or weird until I figured out what was their original or emergent purpose.

Blissex said...

After a couple of attempt to send the previous comment "There is another point here" it has ended up on this post, but it was meant as a reply to a comment on another post:

But it is fairly apposite here too, as you seem to have developed a serendipitous interet, as in “a research program that I seem to have stumbled upon”.

«Some sort of structures definitely seem to exist in these parameter spaces.»

Thom's "catastrophes"? Starting with saddle points for example? Just guessing wildly. The underlying problem is variational in "bumpy" topologies as in like "simulated annealing" (being deliberately hand-waving here...), so there must some stuff about stability and instability regions in operations research literature that might be adapted.

The big question here is: if such literature exists, are economic models constrained enough that profiling them is easier? Neoclassicists constrain them *too much* for ideological reasons, are less constrained models still somewhat tractable?

Anonymous said...

Robert Vienneau said...

I developed the ideas I talk about in my post from thinking about dynamical systems and bifurcation theory. To connect them up, though, I would need some definitive way to connect dynamical paths of market prices to the way I partition the parameters in models of prices of production. I think that will always be beyond me.

I must remember to look up that Bidard paper.