Sunday, June 7, 2015

A New/Old Theory of the Firm, Put to Use

There are two dominant theories of the firm in modern economics, one centered on transaction costs, the other viewing the firm as a nexus of contracts.  Both are premised on the notion that, absent any frictions, and especially those due to incentive problems, market coordination would always be superior to the coordination supplied by firms.  Hence firms are anomalies, and in the benchmark utopia of competitive general equilibrium they don’t exist at all except as accounting units.

There is a longstanding tradition that attempts to explain the existence and extent of firms according to their efficiencies rather than flaws in the market.  Such a view is implicit in Schumpeter, for whom entrepreneurship was a creative force that could not arise in markets composed of infinitely small players.  Chandler similarly tried to argue for efficiencies in coordination, especially in continuous process systems.  Neither succeeded in providing a formal explanation of what it was about the mechanisms that concerned them that indicated that firms rather than markets would house them, and their views have been largely banished from economic theorizing.  Nonetheless, the field of management, where questions of firm capacity and strategy are paramount, continues to draw on a conception of the firm in which administrative organization is capable of coordination that markets cannot supply.

In fact, there is a theory of the firm based on a single and, once it is laid out, rather obvious concept that provides a formal underpinning for management-centered approaches: the role of interactive nonconvexity in production systems.  Here are two explanations, one formal, the other intuitive.

Formal: The mono-equilibrium property of decentralized allocative methods depends on (quasi-) convex preference and production sets.  There are two potential sources of nonconvexity.  One is “wrongly” signed elements along the principal diagonal of matrices of cross-partial derivatives, especially as resulting from increasing returns in production.  The other is the presence of off-diagonal elements whose absolute value is sufficiently large to offset the effect of principal diagonal elements in determining the sign of the matrix of cross-partials.  The number of equilibria (local optima of an objective function encompassing this structure) is given by the degree of the underlying function.  Firms are instruments for selecting among (local) optima by direct specification of detailed quantities or processes.

Intuitive: Markets proceed through an adding-up process, where the collective result is the sum of many small transactions undertaken separately.  There exist situations, however, in which the outcome of taking an action depends on the action taken by others—this is the central problem in cooperative game theory, for instance.  Markets accommodate just one such interaction effect, the role that cumulative offers (demand and supply) plays in determining prices.  But there are many other types of interactions that markets are unable to coordinate.  Many arise in production, the effect that one person’s productive activity has on the productivity of another.  It is because of such interaction effects that it is necessary to draw up and implement a plan, a set of coordinated activities.  The firm is the organizational structure with the capacity to do this.

This view of the firm is based on an understanding of the limits of markets, but not on a presumption of market failure, as that term is understood by economists.  Specifically, the presence of externalities (missing markets) is neither necessary nor sufficient for the presence of interactive nonconvexities.  Thus there is no policy fix that can render the coordination of activities by firms unnecessary.  Also, the make-or-buy decision, which is central to any theory of the firm, is not governed solely by efficiency but depends also on the advantages of implementing plans that cannot be accomplished through contracting externally.

The value of this theory is demonstrated in a practical application: how do we explain the difference in the roles played by worker problem-solving in different kinds of firms?  In a recent paper, written with my coauthor Heike Nolte, we show that arguments based on nonconvex profit sets, along with institutional factors that influence strategic choice, can do this.

The central idea that links our coordinated activity theory of the firm to strategic differentiation is the profit landscape, as seen here, with an arbitrary starting point A.
In fact, this kind of landscape is familiar from evolutionary biology, where it is commonplace.  In biology the horizontal axes represent two particular traits genetically available to an organism, while the vertical axis represents evolutionary fitness.  The point is that natural selection, being nonpurposive, optimizes only locally, and there is no guarantee that organisms can adapt successfully as the landscape changes.  In our context, however, the horizontal axes represent a pair of activities the firm might undertake, and the vertical axis is profit.  Of course, this three-dimensional landscape is an immense simplification of the large-dimensional relationships analyzed by biologists or students of business.

The firm can navigate its profit landscape purposively, but it does so under conditions of uncertainty: the true hills and valleys are not known and can only be inferred.  The core tradeoff is between strategies that emphasize the generation and use of local knowledge to move readily toward hills adjacent to the one currently occupied, versus strategies that seek to minimize encumbrances that might interfere with movements toward more distant hills, less knowable but potentially more profitable.  The first is flexible in its existing operations, the second in its ability to exit and enter different operations.

In categorizing firms, we use two related distinctions, between stakeholder and shareholder enterprise models and between coordinated and liberal market environments.  The polar cases are stakeholder/coordinated and shareholder/liberal, but we are also interested in hybrids.  Our key assumption is that the shareholder firm seeks to maximize the present value of its profit stream, while the stakeholder firm wishes to maximize the likelihood of being profitable over a given time horizon.  Logically, this means that the shareholder firm is a “prospector” in the profit landscape, willing to take greater risks in order to maximize potential returns.  It makes fewer commitments, including fewer commitments to its workforce, that might interfere with its freedom to shed existing assets and acquire new ones.  The stakeholder firm, for which profit outliers are of less value, prefers to specialize in its local production space, taking less risk and maintaining its viability through operational flexibility.  The liberal/coordinated market distinction enters by altering the costs or feasibility of pursuing one strategy or the other.

These imputed preferences have implications for the role of workers within the firm.  The shareholder firm in a liberal environment will tend to recruit less qualified workers for routine tasks, make fewer commitments to them, invest less in their acquisition of new skills, accord them less autonomy in workplace decision-making, and utilize monetary incentives for performance.  It acquires less value from the locally-specific learning of workers who have the capacity and freedom to investigate their own operations.  The stakeholder firm in a coordinated environment will tend to recruit more qualified workers on the basis of long-term commitments, provide opportunities for skill-upgrading, permit much greater decision-making autonomy (as well as greater scope for autonomy), while relying to a greater extent on normative approaches to motivation.  It will implement more micro-innovations which can form the basis for navigation to adjacent profit hills.  If this schema is correct, we should observe these proclivities in the role of worker problem-solving in these different types of firms.

We have thus far conducted three intensive case studies, one with a stakeholder firm in a coordinated environment (Germany), another with a stakeholder firm in a liberal environment (the US), and a third with a shareholder firm in a coordinated environment (Germany again).  What we found are the patterns in worker problem-solving suggested by our theory, and informants describe institutional features, motivations and activities to which our theoretical explanations seem to apply.

We intend to continue case study research in worker problem-solving at additional firms.  The theoretical apparatus also lends itself to many other questions in economics and business.


Bruce Wilder said...

The mono-equilibrium property of decentralized allocative methods depends on (quasi-) convex preference and production sets. There are two potential sources of nonconvexity. One is “wrongly” signed elements along the principal diagonal of matrices of cross-partial derivatives, especially as resulting from increasing returns in production. The other is the presence of off-diagonal elements whose absolute value is sufficiently large to offset the effect of principal diagonal elements in determining the sign of the matrix of cross-partials. The number of equilibria (local optima of an objective function encompassing this structure) is given by the degree of the underlying function. Firms are instruments for selecting among (local) optima by direct specification of detailed quantities or processes.

Ha-ha-ha! That was very funny. ROFL

Peter Dorman said...

Bruce, I never said that firms actually succeed at this! More seriously, the nonconvexity approach raises issue of complexity that don't arise in models that assume that optimization can be achieved simply through marginal adjustment. You wouldn't know from the standard neoclassical approach why managing a firm is so damn hard.

Sandwichman said...

"Nine-tenths of the confusion and obscurity in which the doctrine of price has hitherto been involved has arisen from searching after the unsearchable, from seeking for some invariable rule for inevitable variations, from straining after precision where to be precise is necessarily to be wrong. Supply and demand are commonly spoken of as if they together formed some nicely fitting, well-balanced, self-adjusting piece of machinery, whose component parts could not alter their mutual relations without evolving, as the product of every change, a price exactly corresponding with that particular change. Price, and more especially the price of labor, is scarcely ever mentioned without provoking a reference to the 'inexorable' the ' immutable,' the 'eternal' laws by which it is governed; to laws which, according to my friend Professor Fawcett, 'are as certain in their operation as those which control physical nature.' It is no small gain to have discovered that no such despotic laws do or can exist; that, inasmuch as the sole function of scientific law is to predict the invariable recurrence of the same effect from the same causes, and as there can be no invariability where as in the case of price one of the most efficient causes is that ever-changing chameleon, human character or disposition, price cannot possibly be subjected to law." -- William Thomas Thornton, 1866.

Thornton Hall said...

It really does seem like Jane Goodall is a better scientist than Francis Bacon:

Thornton Hall said...

It's not at all clear to me that "demand" is a thing that even exists. It certainly doesn't exist out of time, given the fact that it is an action.

Sandwichman said...

"It's not at all clear to me that "demand" is a thing that even exists."

In the sense of an aggregate demand curve, no. This is where faith and make believe are so crucial to theory construction. said...

I imagine it is in the paper, but implicit and foundational to this is the Coase-Williamson transactions cost view that whether something gets done within a firm or gets outsourced to the market to be done outside the firm (that is, in another firm) depends on the transactions costs involved, with those guys, especially Williamson and his followers, having written gobs and gobs about the various things that go into determining those transactions costs.

Of course, it is perfectly relevant to bring in non-convexities and multiple equilibria and all that to what is determining those transactions costs, whose minimization is the dual of that profit max surface you showed, at least that is the view of this complexity-oriented economist.

Peter Dorman said...

Barkley, read the paper. There are *no* transaction costs identified or discussed. They are not relevant to the theory, at least on a first pass. Obviously transaction costs do exist, and there is nothing about the coordinated action approach that precludes incorporating them. But the best way to make sense of this theory is to clear your head of all the assumptions about transaction costs you would typically bring to institutional analysis.

john c. halasz said...

I'm probably a little bit more charitably disposed toward this one than Bruce Wilder, but the basic point is that the economy can't be reduced to a set of market transactions and that production systems have constraints and requirements of their own, which can't be reduced artificially to the math of markets and "equilibrium prices". But once you're making use of the formalism of biological fitness landscapes, why not go further and investigate general systems theory ("operations research") models of productive organization, since they too were originally developed for biological explanatory purposes?

Peter Dorman said...

I wonder why I have been so unsuccessful in communicating. Barkley thinks I'm describing transaction costs. You think I'm reducing the economy to markets without consideration for production systems. Weird.

Anyway, there are a couple of references in the paper to the OR literature where it leads to profit landscapes like the one we've developed. There are obvious OR linkages in our work -- and some that are less obvious. (A cybernetic model of the firm is the basis for our empirical work in worker problem-solving, but the theory portion of the paper was large enough as it was, so we left out that piece.)

Sandwichman said...

"I wonder why I have been so unsuccessful in communicating."

Not to worry, Peter. We're all monads now.

Peter Dorman said...

Yeah, sometimes blogging feels like, oh I don't know, talking to myself as I do the laundry. Or standing in the wrong line for something -- the line for people who have tickets when I don't or vice versa. Or something like that.

john c. halasz said...


I wasn't especially accusing you, nor your paper, (which I haven't read), but it's just a standard criticism of standard economics, and its demands for formalization, rather than merely "literary" and observational accounts. (Witness how long it took to get a formalized model of increasing returns to scale and scope, and how there is still no agreed formal model for oligopolies). You're to be at least congratulated on working against that grain, (though we blog-worms are the least you need to convince). I once tried to get Bruce Wilder to be interested in reading Niklas Luhmann, for all his perversities, (since that's one of the main sources of any familiarity with GST that I had), but he wouldn't take the bait.

Tom Geraghty said...

How is this notion related, if at all to the Milgrom/Roberts complementarity idea (for example, their 1990 AER paper on "The Economics of Modern Manufacturing"), where firms are needed to coordinate bundles of activities that are complementary in the profit function? It sounds fairly similar on the surface.

Peter Dorman said...

Good question! They are obviously cousins, but there are also differences. (1) M&R are at pains to differentiate supermodularity from nonconvexity (although they backtrack a bit at one point). Because of this, they don't generate a profit landscape, which for us is the central concept -- the point of the theory. I wonder why they didn't just opt for nonconvexity. (2) They define supermodularity over decisions and outcomes, not activities as we do. (3) Theirs is a theory of how particular production opportunities generate returns to coordination. Ours is a general theory of firms as entities through which returns to coordination, assumed to be widespread, are generated.

That's my take, but it would be interesting to get M&R's.

Incidentally, FWIW, I presented a precursor to the CA model, admittedly bare-bones, as a lowly grad student at the AEA meetings in 1981. I was chewed out by my discussant for proposing a theory of the firm when one wasn't needed, since Coase had already solved all our problems.

Anonymous said...

Nice graph---i didn't really many of these in econ (not my area) until zeeman (not an economist) and Rosser's book.
I wondered if that describes a system with multiple equilbria or rather just a system with a complex landscape with a unique one---on 2nd glance i see 3.

I don't think there is really and difference, except in words or terminology, between seeing these as some sort of nonconvex utility (or other ) function versus transaction costs. Its all about information---with perfect information, which only a few of us possess due to inheritance or hard work, there of course would be no firms---everything would be atoms, with no need to aggregate into different molecules to divide labor optimally (eg catalytic enzymes, structural proteins, etc.)

But because of imperfect information, there are 'search costs', a kind of transaction cost. Since these costs are on a budget constraint they have to be allocated non uniformally in general (eg preferential attachement, path dependence etc.) and hence mathematically lead to convexities.

(Of course since usually there are many ways to allocate them ---eg which aisle in a store do you pick first when filling up your basket with goods? which path does robert frost pick?---there are often many such 'landscapes' . (eg SMD, especially when choices are seen as endogenous---ie your search algorithm(s) changes depending on which aisle you pick first. You may end up with a vegetarian dish instead of a meat one, and next time because the store noticed that they will change the stocking of products etc., and when plotted on a computer the consumer/store system will look like a star/sun system and where it is in phase space will be highly dependent on initial conditions.

one can also then ask whether its ergodic but joesnt appear to be, or has kam or other properties.

Nick Rowe said...

Peter: you are not talking to yourself. You were at least partly successful in communicating this to me.

Nick Rowe said...

And I thank you for writing it, and found it worth reading, even though the theory of the firm is not really my area of interest.

kevin quinn said...

I agree with Nick, Peter; this is interesting stuff! I used to do a very baby version of something in the same general area, although obviously much less sophisticated, when I taught game theory to MBA students. I would contrast the Alchian/Demsetz theory of management, which sees managers/owners as resolving the prisoner's dilemma that characterizes teamwork with an agreement to split the proceeds equally (what some people call the "classical conception of the firm") with a view that would see management's role as selecting the best equilibrium in a coordination game, like the person who coordinates a rowing crew by calling out the pace.

Bruce Wilder said...

Peter Dorman: I never said that firms actually succeed at this!
You didn't, but the formal theory kind of does. It seems to me that you are using a formalization as a shibboleth, a signal to the profession that you are to be taken seriously, because you can talk "non-convexity" as if such a mathematical concept could substitute for knowledge of economic behaviors. I don't object to analysis, per se, or mathematics to clarify reasoning; I do object to letting the math become the master. I kind of thought you did as well.
Convexity in the theory is, as you say, a convenience, necessary to the conceit that an equilibrium price will resolve the conflict between super-independent producers and consumers. It is also a plausible consequence of assuming complete and perfect information -- everyone knows everything there is to know -- if you know all possible techniques, convexity of the production function is not such a stretch; anything else seems a bit arbitrary. The theory assumes that the technical problems are solved, leaving only the problem of allocation on the frontier. That's why the firm is left with the problem of navigating the frontier described by a convex function. So the theorist can think about the problem of allocative efficiency in isolation from the more varied and deeply problematic puzzles of technical efficiency.
In principle, I suppose economic theorists would love to be able to pose uncertainty as axiomatic, but that's not really feasible in a framework of deductive reason: you cannot get to a solution. So, instead, they look for ways to "relax" the assumptions of certainty in ways that still permit deductive reasoning to work its analytic magic. When economists assume non-convexity, I expect it usually is as a way of exploring one among many implications of an uncertainty that cannot be conveniently assumed in toto. In an uncertain world, limited knowledge and learning of production technologies would make production functions non-convex, so one way of introducing an aspect of uncertainty into theory is by arbitrarily asserting non-convexity and exploring the further implications.
Of course, when you confront the world as it is, and try to understand a specific factual case, you are confronting uncertainty in toto, not uncertainty in the form of single implication.
The point I would make about production possibilities as they appear in the world, with their non-convexity, is that that they are social constructions, the outcome of strategic behavior. If increasing returns are frequently observed, or sunk-cost investments are the rule, we should be thinking about the strategic behavior that gives that result. Why does that possibility survive strategic competition and other possibilities, maybe, do not? I am not saying that we should grab onto the Darwinian analogue, though maybe we should. What I am trying to say is that, in an uncertain world, it appears that one way of making what one does know about production technology, or what one can learn by doing, pay, is by making sunk cost investments that reduce variable costs, earn a rent and promise increasing returns across the relevant range of output. That's the intuition I would press to develop.

Peter Dorman said...

A few quick points, Bruce. (1) The relaxation of the convexity assumptions I'm urging are not about increasing returns or fixed vs variable costs. They are interactive nonconvexities, nonzero cross-partials of whatever function you're looking at. (2) These nonconvexities have immense social theoretic content. Some day I'd like to write a book about this. (I've been saying that for, oh, 30 years. (3) They are not the reason for uncertainty, but they greatly complicate it. If myopic decision rules are effective, the domain of relevant uncertainty is less, but hill-selection (as opposed to hill-climbing) enlarges that domain considerably. (4) Hill selection is equivalent to planning or strategy, depending on the context. (5) I am not assuming in general that firms (or anyone else) get to the precise tops of their hills, although I might make that assumption for heuristic purposes sometimes. (6) I am absolutely not opposed to the use of math as an aid to economic (or other) thinking. I am opposed to math whose assumptions have not be critically examined. Or: I am opposed to sneaking dubious assumptions about people, institutions, and their behavior through the back door via unreflected math.