Uncertainty, Competence and the Theory of the Firm
(Some crucial omissions and misunderstandings of the current debate)
by Angelo Fusari
Istituto di Studi e Analisi Economica (ISAE)
Piazza dell’Indipendenza, 4, 00185 Roma, Italy
Email a.fusari@Isae.it Tel. 06 44482877
Paper presented at the
second meeting of the European Network on the Economics of the Firm (ENEF), Erasmus
University, Rotterdam, 8-9 September 2005
Abstract: This essay aims in particular at remedying one of the major failing of the current state of
the analysis on uncertainty, competences and innovation: the lack of a measure of radical
uncertainty and of tension in the use of entrepreneurial skill. It shows the possibility of those
measures and their importance for the explanation of investment, innovation and some other crucial
variables. The shaped model of the firm also flanks transaction costs with productive expenses and
emphasizes the monitoring role of profit rate as expression of the firm’s results. Some FIML
estimates at the industry level are provided.
Keywords: Entrepreneurship, Competence, Uncertainty, Innovation, Decision-making, Estimations
Introduction
This paper considers the problem of the firm in the perspective of general
economics much more than in that of business schools. In fact, it seems to us that a
major shortcoming of the good deal of work performed by those schools is the lack of
coordination with general economics. In an earlier essay1, we treated
entrepreneurship and economic process at length. The present paper complements it
by adding a treatment of the firm. Despite the incessant transformations of the
economic background, which produce parallel changes in the organization of the
firm, some basic features preserve substantial stability. Unfortunately, their meaning
is obscured by various misunderstandings; some clarification is accordingly required.
A main feature of modern economies is the central and growing role that
creativity and innovation play in the context of the process of dynamic competition.
They generate uncertainty that makes entrepreneurship, decentralization and market
institutions indispensable, being bureaucratic decision making no congenial to
uncertainty. Therefore, the treatment of creativity, innovation and entrepreneurship
requires a parallel and accurate treatment of uncertainty and a tight theoretical
interaction amongst them.
At present, economics is afflicted by a sharp division between a line that
presumes perfect knowledge, also including known probability distributions, and
another emphasizing true or radical uncertainty, i. e. incomplete knowledge and the
connected notion of bounded rationality. Unfortunately, the second and more realistic
line unanimously supposes, as far as I know, that radical uncertainty is unmeasurable
by definition. We shall see, both from a theoretical and empirical perspective, that
1
See A. Fusari (2005)
1
this assumption is wrong, that it deviates attention from the level of uncertainty and
its variation and that this condemns in a state of theoretical vagueness some important
variables, such as entrepreneurship and innovation as well as decisional criteria.
Besides, it prevents a coherent formalization of the dynamic competition process,
which is indispensable to encapsulate the theory of the firm in general economics.
It will also be shown the way of measuring the degree of radical uncertainty and
discussed the importance of such measure for the explanation of innovation,
investment, the formation and use of (hence the tension in) entrepreneurial capability.
Moreover, it will be pointed out that the refusal of optimization because it would
require the irrealistic hypothesis of perfect knowledge is due to the wrong assumption
of non measurableness of radical uncertainty; in the presence of that measure, it is
perfectly possible to arrange optimization with radical uncertainty and hence to use
the approach in decision-making.
The paper is organized as follows:
Section 1 expounds some very general consideration on organization, capabilities
and uncertainty. Section 2 briefly discusses a number of significant aspects of the
present debate on the firm. Section 3 is specifically dedicated to the controversy on
optimization, relevant for its links with the notions of entrepreneurship and
uncertainty. Section 4 presents some developments that give a special importance to
uncertainty, entrepreneurial capabilities, innovation, the role of the firm and its
decision-making. Section 5 sets out a formalization of the entire theory, and Section 6
presents some estimations of the model.
1. Organization, capabilities and uncertainty
The question of the firm is part of the more general topic of organizational and
institutional forms and may opportunely be hinged on such a general framework.
Man needs organizational forms, as a consequence of his skill limitations that
make necessary co-operation and hence its organization. Social systems cannot limit
themselves to the establishment of some general rules aimed at allowing common
life, trusting for the remainder on individual action. Some more specifical and
involving organizational problems must also be faced; otherwise not even the
accomplishment of general regulations will be warranted.
Human societies have known, in the course of history, two main types of
organizations that profoundly differ each other for both contents and implications:
a)
Closed organizational forms, the nature of which is conservative and
bureaucratic; they dominated in tribal societies based on relatives and strongly
characterized the administrative structures of ancient great empires. These
organizational forms are suitable to face repetitive processes and to operate in
the presence of perfect knowledge. Accordingly, they thwart innovation and
uncertainty that disconcert them and paralyse their ability to take decisions. In
parallel lines, they tend to preserve and perfect the repetitivity of processes,
which is congenial to them.
b) Open organizational forms, driven by entrepreneurial behavior. They
characterize the social systems inclined to innovate and distinguished by high
2
uncertainty. This kind of organization requires and feeds on some decisional
skills that are the opposite of those sub a and are characterized by versatility,
ability to meet unknown and to engender new situations, in sum, to meet and
feed uncertainty.
Open organizational forms remained marginal for a long historical time. In the
beginning, they came forth in the presence of natural contexts that promoted
uncertainty or very aleatory activities (e.g. commercial relations) and/or as part of
civilizations that stimulated critical behavior, adventure and evolutionary process.
This kind of organization emphasizes, beside the limitation of skills, a more troubling
kind of limitation concerning knowledge.
Open and entrepreneurial organization has vigorously spread in Western world;
the economy has represented the most fertile soil of its development. The firm is a
main entrepreneurial organization (sub b) devoted to produce goods or services.
Therefore, the problem of its nature and existence is part of the wider field of
dynamic and entrepreneurial organizational forms and the growing need of these
caused by the acceleration of evolutionary process. In some sense, the firm has
accentuated the peculiar traits of open organizations, first of all, the pattern of
capabilities requested by true uncertainty. Therefore, in the study of the firm, the
insistence on administrative organization may cause some serious misunderstandings,
since it is mainly typical of non entrepreneurial forms (sub a) that often show a very
sophisticated and well specified administrative organization. It is important to not
forget that the firm derives its very nature of entrepreneurial agent from uncertainty.
For one side, it causes uncertainty through innovation in a more direct and insistent
way than other open organizational forms; for the other side, it is obliged to meet
uncertainty caused by other innovators or exogenous accidents. Profit, the main target
of the firm, is the result of uncertainty, i.e. the limitations of knowledge and the
connected differentials in capabilities; as a matter of fact, only limited and hence
differentiated skills can evolve and produce gains. In the absence of exogenous
shocks or innovation, the opportunities for profit would disappear.
If considered in the perspective of general economics, the firm is the engine of the
dynamic competition process, which characterizes the functioning of modern
economies. For that process is the result of the entrepreneurial activity of search and
discovery of profit opportunities based both on innovation and arbitrage over time
and space, with the aim to extract gain from the disequilibria and darkness
characterizing evolutionary processes. Therefore, dynamic competition seems to be
the most appropriate tool for inserting the theory of the firm in general economics.
So, the skills, knowledge, innovation and, more in general, the role of the firm
must be considered in relation to uncertainty since in the absence of this one there
would be no need of entrepreneurial decisions and organization. But the simple
reference to uncertainty is not enough. It is necessary to measure and verify its level
that, as we shall see, assumes a central role for the formation and use of capabilities
and hence for determining the tension in that use, as well as for explaining
innovation, investment and, last but not least, representing dynamic competition,
indispensable to conjugate the theory of the firm to general economics.
3
2. Some significant aspects of the debate on the firm
Uncertainty is a dominating trait of the human societies where the economy
holds a central position and hence strongly pushes growth and development.
Notwithstanding, uncertainty has been turned round by mainstream economics
through the hypothesis of perfect knowledge and competition that brings out play
entrepreneurial skills. Upon this hypothesis (that includes the case of known
probability distribution, i. e. probabilistic certainty)) has grown a theoretical system
extremely coherent in the appearance but in effect undermined by a fundamental
inconsistency: it is qualified for bureaucratic-conservative organizations typical of
repetitive societies or, more in general, of societies that have less to do with
uncertainty; nevertheless, it pretends to explain the behavior of open entrepreneurial
economies.
The perception of the fundamental role that play uncertainty and the limitation
of knowledge has progressively entered economics. A number of theoretical
approaches have grown on this perception and may be unified under the
denomination of “heterodox economics”.
In a seminal contribution of many years ago, E. Penrose reacted to the
hypothesis of perfect knowledge, which erases entrepreneurial capabilities, through a
“Theory of the growth of the firm” that is founded upon the availability and evolution
of its managerial capabilities and knowledge and the ability to diversify production.
She says: «Thus the availability of ‘inherited managers’ with such experience limits
the amount of expansion that can be planned and undertaken in any period of time…
Once a substantial increment of growth is completed, however, the managerial
services devoted to it become available for further expansions» 2 A shortcoming of
this development is the omission that such availability depends on the level of
uncertainty, which markedly influences both the formation of entrepreneurship and
the quantity of entrepreneurial knowledge used in ordinary activities and to manage
the achieved expansion.
Penrose attributes great importance to versatility, which avoid that “the market for
those products will restrict the firms opportunities of expansion”, and adds: «a
versatile type of executive service is needed if expansion requires major efforts on the
part of the firm to develop new markets or entail branching out into new lines of
production»3. The author insists in depicting the firm as an administrative and
planning organization. She does not consider that this kind of organization is mainly
typical of bureaucratic-conservative forms sub a. The lack of caution in this matter is
an effect of the minor role she attributes to uncertainty. This one is considered as:
«the entrepreneur’s confidence in his estimates of expectations», i.e. as a subjective
and not an objective fact that influences the firm’s behavior. She adds: «Risk, on the
other hand, refers to the possible outcomes of action, specifically to the loss that may
2
3
See E. Penrose (1999), p. xii
See E. Penrose (1999), p. 37
4
be incurred if a given action is taken».4 These peculiar notions of risk and uncertainty
are useful to Penrose’s analytical purposes, but they are deceitful if considered in a
more general sense. She is concerned about the role of information in reducing
subjective uncertainty and in the resources necessary to get information, and
concludes that risk and uncertainty are final limiting factors only if managerial
services are fully used. Again, she forgets to consider that the use and the need of
managerial services depend on the level of uncertainty. This level is never
considered; uncertainty is simply treated as a subjective entity, rather than an
objective one influencing both demand and supply of entrepreneurship. A main
shortcoming of Penrose’s analysis seems to be the marginality of the role she
attributes to uncertainty. This marginalisation of uncertainty persists in all the
theories of the firm that attribute a central role to capabilities; the reason of that is the
usual way to intend uncertainty makes difficult to treat capabilities. In order to clarify
this aspect, some considerations on the way economics consider uncertainty is
required.
As is well known, a pioneeristic treatment of uncertainty was provided by F. H.
Knight. But his analysis is afflicted by two main errors:
First, the idea that uncertainty only implies some deviation from the results of
Neoclassical economics of perfect knowledge, but without substantial prejudice for
its teaching.
Second, the idea that uncertainty is unmeasurable.
Heterodox economics that, polemically with mainstream economics of perfect
knowledge, underlines the importance of uncertainty, plainly overcomes the first
Knight’s error. But it completely shares the second one. In addition, its right
perception of the qualitative jump with respect to Neoclassical economics that the
introduction of true uncertainty in the analysis implies, has strongly accentuated the
consequences of the second Knight’s mistake.
Neoaustrian economics gives a clear expression of some misunderstandings
caused by this equivocation. Its sharp criticism against Neoclassical economics is
hinged on uncertainty. But the assumption of unmeasurableness and impalpability of
uncertainty has imprinted on Neoaustrian students an extreme hostility towards
organization, leading them to erase the problem of the firm from the agenda of their
work. More precisely, the emphasis on unknown and unintentional events has pushed
their analysis, mainly in Hayek’s version, toward a prejudicial preference for
spontaneous order over organization and command considered as arbitrary
interferences obstructing the tendency of social events toward self adjustment.
According to this school of thought, general rules, mainly market laws, are enough to
allow the harmonization of spontaneous actions and unintentional events. But the
emphasis on individual initiative ignores the simple fact that the limitation of skills
requires organization.
Another main obstacle to a neo-Austrian theory of the firm is that this school sees
entrepreneurial capability as an evanescent, non-measurable entity and, as such, not
4
See E. Penrose, ibidem, p. 56
5
liable to rational evaluation and impossible to specify. But skills do exist, and the
firm has the duty of evaluating its capabilities with a reliable degree of approximation
so as to use them properly. Neo-Austrians’ work on market process, uncertainty,
search and discovery can make an important contribution to the theory of the firm.
Unfortunately, their prejudice against organization has deprived the analysis of the
firm by these neo-Austrians deepenings.
J. A. Schumpeter made an opposite error: his attention for entrepreneurial
capabilities disregarded uncertainty, notwithstanding this one springs out copiously
from his “creative destruction”. This omission, that confirms the difficulty to
conjugate capabilities to the usual way to consider uncertainty, induced him to
emphasize, in “Capitalism, socialism and democracy”, the role of managerial services
and in the absolute error to predict the end of capitalism as a consequence of
bureaucratization. It is illuminating on the importance of a proper consideration of
uncertainty the fact that the Schumpeterian theoretical effort, full of lightings and
contradictions, gives space, in the end, to bureaucratic aspect (sub a) at the expense of
the entrepreneurial one (sub b). As a consequence, the building of a general theory of
the firm has also been deprived by the support of the branch of dynamic competition
process represented by creative destruction, in addition to neo-Austrian (the other
branch) refusal of the question of the firm.
The effects of these misunderstandings have partially affected evolutionary
economics, that has accomplished an interesting analysis on the microfoundations of
innovation along Schumpeterian lines. Nelson and Winter’s explanatory models of
technical change, search and selection within the firm have represented an interesting
starting point. But an important aspect differentiates this school of thought from
Schumpeter: the remark it attributes to uncertainty, mainly under the notion of
bounded rationality that, as we shall see, is an ambiguous way to call up incomplete
knowledge. In a theoretical context marked by the notion of bounded rationality
clearly appears the difficulty to treat entrepreneurial capabilities, being uncertainty
considered as an unmeasurable, subjective, impalpable entity. In point of fact,
evolutionary economics has performed some interesting researches on capabilities
that stress the power of learning and tacit knowledge for explaining the behavior,
internal organization, boundaries and results of the firm. But significantly, it insists in
the identification of capabilities through the notion of decisional routine, as a partial
remedy to the analytical vacuity deriving from the idea of unmeasurableness and
impalpability of uncertainty. This insistence is coherent with the importance that
Schumpeter attributed to managerial bureaucracy and with Penrose’s insistence on
capabilities independently on uncertainty. In fact, decisional routines are concerned
with the bureaucratic-conservative aspect of organizations. They refer to repetition
and hence not to entrepreneurial decision-making since this requires versatility and
some skills able to face uncertainty.
It must be underlined that a fundamental ambivalence characterizes evolutionary
social thought, which is well reflected by evolutionary economics: for one side, this
school is inclined to disregard the problem of the firm as a consequence of its
tendency to exaggerate the limits in human knowledge and hence to distrust of
6
organization at the advantage of spontaneous behavior; but, for the other side, a
branch of evolutionary social thought is greatly attracted by the evolution of
institutions, not only in the sense of Menger’s theory of the emergence of money as a
result of unintentional events. In economics, this attraction is mainly concerned with
the firm and the connected analysis was initially fertilized by Coase’s seminal article
on “The Nature of the Firm”. He wrote «The main reason why it is profitable to
establish a firm would seem to be that there is a cost of using the price mechanism…
It is true that contracts are not eliminated when there is a firm but they are greatly
reduced»5. Here the firm appears to be an organization that substitutes command for
the price and market mechanism in the allocation of resources. This Coasian
perspective has promoted useful investigations on the firm. Precisely, it has
stimulated two lines of research directed towards explaining the nature and the role of
the firm as an organization, now unified as the “contractual perspective”. One is
derived from O. Williamson, who has developed Coase’s intuition on transaction
costs and hence emphasized the distinction between “markets and hierarchies”; the
other is Alchian and Demsetz’s approach on the “nexus of contracts”.
Williamson writes: «The two behavioral assumptions on which transaction costs
analysis relies –and without which the study of economic organization is pointless are bounded rationality and opportunism»6. The incompleteness of contracts due to
the limits of human knowledge, in conjunction with asset specificity (site, physical
and human specificity), is said to permit opportunism in market contracting, mainly
the threat of a unilateral termination of contract that will reduce the value of specific
assets. This would generate costs depending on the frequency of transactions,
uncertainty and the specificity of investment. So the key role of the firm, it is held, is
reducing those costs by substituting a command mechanism to contracts and the
market.
The consideration of transaction costs, in addition to production expenses, permits
significant analytical improvement on the boundaries of the firm and its governance
structure; but these ones mainly depend on the availability of capabilities and
uncertainty, that limits the degree of understanding and hence the potential of skills.
Therefore, uncertainty limits the impact of transaction costs in stimulating the size of
the firm. In fact, it requires versatility, flexibility and promptness that large firm
usually lack and that only partly may be stimulated by setting up a decentralized
structure. However, transaction costs are not essential for explaining the firm’s
existence and nature, which can be referred to some more general consideration on
organization, as we saw in the previous section. Of course Williamson’s
developments centered on bounded rationality are inconsistent with Neoclassical
economics that neverthless Williamson prefers, while are coherent with our previous
considerations on entrepreneurial open organizations.
Alchian and Demsetz considered contracts from a different point of view. Their
work on the firm signalled the benefits that input owners may achieve through
contractual cooperation and hence the need of monitoring of costs. Moreover, they
5
See R. H. Coase (1937), p. 390
See O. E. Williamson (1981), p. 154
6
7
argued that cooperation necessitates of measuring the productive contribution of each
member of the “team” (to avoid free riding and shirking). They accordingly focused
on the consequent organizational problems, mainly concerning monitoring and
incentives. Probably, the most important insight here is the acknowledgement that the
monitoring of the monitor requires that the overseer has a residual claimant status.
Actually, though, it is inappropriate to treat the firm as a “team” of entrepreneursresource owners. The firm is a unitary structure, and its results must refer to that
structure as a whole. It is the task of the responsible for the firm’s performance, who
is therefore entitled to a control power, to monitor the productive contribution of
every component of the organization, through incentives or otherwise, in order to
improve efficiency. But to make accountability effective one needs a precise
indicator of the firm’s success. This indicator can only be the profit rate, as all others
are partial and misleading.
Some insights on the problem of incentives have been provided by the principalagent approach. However, the strong insistence on the crucial role of property rights,
and hence of private ownership7, as indispensable to the efficient use of resources and
hence to long-term economic growth, appears misplaced. Monitoring based on the
last-claimer principle does not require private ownership but only a clear and precise
attribution of responsibility for results (profits). True in small firms, with their serious
problems of accountability, efficiency may require private ownership with its implicit
automatic monitoring, reflecting an immediate interest in economic results. But in
larger ones efficiency does not require property rights; all that is needed is the clear
and inescapable attribution of responsibility for the results (in terms of profit rate),
accompanied by appropriate powers of control. This does not necessarily mean the
ownership of resources.
In conclusion, contractual approach has provided important results on the internal
organization of the firm. Besides, it attributes to uncertainty, or incomplete
knowledge, an important role, mainly through the notions of transaction costs and
residual claimant. But the computations it proposes express an evident ambiguity as
long as uncertainty is considered an unmeasurable entity. Another most serious
limitation of contractarian theories is their disregard for the firm’s competence and
skills and, more precisely, the lack of an interest in one key task of firms: searching
for and discovering profit opportunities, which is the principal driving force of
innovation and hence development and growth. On this front the contractual theories,
in both the versions sketched out here, have made no advance.
There is now a growing perception among students of the necessity to consider
capabilities as a key explanatory factor of the firm’s boundaries, behaviour and
organization. N. J. Foss and R. N. Langlois have focused on this aspect. Against the
dominant theory centered on contracts and incentives, they contend that: «the
7
See, for instance, O. Hart and J. Moore (1990). The one-sidedness of this position is well stated by Holmström and
Roberts, who write :«But this approach also needs to expand its horizon and recognize that power derives from other
sources than asset ownership and that other incentive instruments than ownership are available to deal with the joint
problems of motivation and coordination» See B. Holmström and J. Roberts (1998) p. 92
8
capabilities perspective is much more conscious of the production side of the firm
and represents the nature of production in a way that is potentially complementary to
the transaction cost approach»8. An important characteristic of their approach is their
insistence on the need to integrate the capability and transaction cost perspectives
into a unitary approach, indispensable to the analytical revitalization of the
production costs side. But the main flaw is, again, an undervaluation of uncertainty
and its links with capabilities. Probably, this is mainly due to the supposed non
measurableness of uncertainty, implying a theoretical vacuity that makes
embarrassing the reference to this variable
In my own opinion, some main, most paralyzing shortcomings of the current
theories of the firm are rooted in the way the key notion of uncertainty is considered
and used, mainly in the mistaken idea that by definition uncertainty does not admit of
quantification but is a sort of impalpable entity. The consideration of the level of
uncertainty and its variations is indispensable to appropriately consider
entrepreneurial capabilities and to conjugate innovation and adaptation and hence to
the specification of dynamic competition process9. On the contrary, the disregard in
principle of the level of uncertainty and its variations precludes proper specification
of the formation and use of entrepreneurial capabilities and hence the enunciation of
the important notion of excess (or tension in the use) of entrepreneurial skills, as well
as the explanation of innovation and investment. Sections 4 and 5 seek to remedy this
defect.
3. Optimization in the presence of true uncertainty
The controversy on optimization is important for our topic, in that can help clarify
the rather similar notions of bounded rationality, true uncertainty, limits to knowledge
and other aspects of heterodox economics. As is well known, the success of the
notion of bounded rationality is mainly due to its help to the criticism to the principle
of rational behavior and optimization. But this critique may result misleading. Man is
limited by nature; a variety of bounds are always inherent in any kind of decision;
under this respect, the notion of bounded rationality is little more than a truism.
Within the boundaries of his knowledge, though, man is obliged, mainly by
competition, to do his best to implement the efficiency of decisions. Man and society
need to act rationally; a task of science is to stimulate rationality in decision making.
The critique of the postulate of rational behavior, and in particular of the optimization
principle, does not take this need fully into account.
Probably the terms “uncertainty” and “incomplete knowledge” would be
preferable to “bounded rationality”. But this terminological change does not provide
decisive clarification; in fact, the growing hostility to optimization and some major
impediments to a stringent formalization of an alternative to the Neoclassical theory
of the firm spring from ambiguities in the notion of uncertainty that have precluded,
as previously seen, a more satisfactory elaboration on capabilities and other
theoretical advances. The exposition of some of the main objections to the optimum
8
9
See R. N. Langlois and N. J. Foss (1999) p. 202
See A. Fusari (2005)
9
principle may illuminate this subject. Kirzner writes: «The decision, in the framework
of the human-action approach, is not arrived at merely by mechanical computation of
the solution to the maximization problem implicit in the configuration of the given
ends and means». Later he adds:«In other words, where the circumstances of a
decision are believed to be certainly known to the decision-maker, we can “predict”
what form that decision will take merely by identifying the optimum course of action
relevant to the known circumstances. Now this “mechanical” interpretation of
decision-making would be entirely acceptable for a world of perfect knowledge and
prediction».10
Kirzner’s reasoning is referable to Neoclassical approach, which excludes
uncertainty; but it cannot be generalized. The optimum principle is a mathematical
tool that may be applied to various theoretical contexts. It is mistaken to presume that
it is not applicable in the presence of limited knowledge; such a mistake derives from
the presumption that uncertainty cannot be measured by definition. But we shall see
soon that the distinction of uncertainty from measurable probability does not imply
the non measurability of the degree of uncertainty. As a consequence of the absence
of a measure of that degree, various authors have pretended to place uncertainty in
the optimization approaches in the form of some known distribution of probabilities,
which as such do not express uncertainty; this defect has strengthen the propensity of
heterodox economists to refuse optimization.
A different and more cautious critique to the application of the optimization
principle has been expressed by Nelson and Winter. They write: «Orthodoxy treats
the skilful behavior of the businessman as maximizing choice, and “choice” carries
connotation of “deliberation”. We, on the other hand, emphasize the automaticity of
skillful behavior and the suppression of choice that this involves». And later: «Formal
orthodox theory, on the other hand, does not rate solutions as maximizing because
they are better than some other observed solutions, but because they are the best
feasible solutions. It thus premises a standard of performance that is independent of
the characteristics of performers; the attribution “skilled driver” involves no such
premises»11. This critique does not express a radical refusal of optimization in
economics; simply maintains that decision making is based on tacit knowledge and
automaticity instead of deliberate choice. Nelson and Winter’s reprimand to
Neoclassical pretention to define the best feasible solution ignoring the skills of
performers is by itself unexceptionable; and it has strongly influenced the
evolutionary economics refusal of optimization.
In our opinion, even though many decisions are based on non-optimizing methods,
it is mistaken and excessively limiting to exclude optimization for improving
decision-making and theoretical formalization. However, the appropriate use of
optimization requires a joint specification of the degree of true uncertainty and the
associated entrepreneurial skills, as in the absence of uncertainty entrepreneurial skill
is inconceivable. Such a specification would allow us to express entrepreneurial
capabilities and the related notion of incomplete knowledge as the constraints of
10
11
See I. M. Kirzner (1973), pp. 33 and 35
See R. R. Nelson and S. G. Winter (1982), p. 94
10
optimization approach, thus removing the bounded rationality criticism to
optimisation. This seems to be a major challenge for the theory of the firm. But it is
crucial, for that specification, to define some indicator of the lack of knowledge and
to express it in quantitative terms.
At the end of a review on optimization and evolution, G. Hodgson writes:
«Usefully, modern evolutionary theory immediately suggests a variety of
circumstances in which the validity of the maximization idea is under strain. Only
further detailed theoretical investigation can tell us more»12. In this stage, it may be
said that the perceived strain is, for a large part, a result of misunderstandings. As far
as I know, nobody has pointed out the great importance of a measure of the degree of
true uncertainty that can be broken down according to firm, sector, area, at global
level and over time. A central purpose of this essay is to demonstrate the importance,
both theoretically and empirically, of such measure. Among other things, it would
enable us to formalize optimization in a realistic non-orthodox way and to represent
the natural inclination and interest of the firm to choose the best among different
opportunities.
It is not correct to counter that the existence of a measure of the degree of
uncertainty would imply the possibility of taking out an insurance policy against bad
economic results, hence the negation of entrepreneurship. In fact, that measure is not
a risk estimation, giving a probabilistic certainty, but just a measure of the lack of
knowledge, i.e. of ones distance from a state of complete knowledge. On the other
hand, uncertainty implies the strong influence of entrepreneurial skills on results, and
it is impossible for insurance companies to measure those skills and results from
outside. Finally, the insurance of entrepreneurial results would stimulate
inconsiderate entrepreneurial decision-making, thus increasing insurance costs and
jeopardizing entrepreneurial role
4. Preliminaries for a model of the firm in the perspective of general
economics
a) The close link between the firm’s capabilities and uncertainty
The firm without entrepreneurship typical of mainstream economics is pointless.
Probably, the lack of consideration by economics for entrepreneurial capabilities
depends on the difficulty of quantifying the firm’s skills from outside. They are known
only to the firm, and always in highly approximate manner. But this inconvenience
does not warrant relegating capabilities to a secondary role as an evanescent entity. In
fact, one of the most important prerequisites for the firm’s success is the knowledge of
its capabilities, even if approximate, which allows one to consider available
opportunities accurately. This essay shows that in the absence of a clear formalization
on capabilities it is impossible to model a realistic theory of the firm, and that such
formalization needs a gauge of the degree of uncertainty; in fact, one characteristic of
the firm is the daily confrontation with uncertainty, understood as lack of knowledge.
12
See G. M. Hodgson (1999), p. 195
11
Truth to tell, uncertainty permeates every aspect of human life; but with respect to
the firm’s activity the situation is special, not only because the level of uncertainty is
particularly high but also because firms professionally and insistently generate
uncertainty through innovation. This implies the existence of an unbreakable link
between capabilities and uncertainty, so that they simply cannot be treated separately.
Knight has shown that in repetitive processes, and hence in the absence of limitations
to knowledge, there would be no space either for entrepreneurs or for profit, since
entrepreneurial capability is mainly skill in coping with uncertainty. It is precisely this
distinctive mark of entrepreneurship that makes the related capabilities evanescent,
unless a measure of the degree of radical uncertainty can be defined. Unfortunately, all
the schools of thought (e.g. the Keynesian and neo-Austrian) that emphasize the role of
uncertainty, and such leading economists in this field as Shackle, Lawson and
Davidson, have neglected the crucial importance of a measure of the lack of
knowledge. The non measurability of uncertainty is presumed on the grounds that the
definition of some probabilistic distribution of uncertainty would imply a probabilistic
certainty. But it is quite natural to try to measure the degree of absence of knowledge
(or the Keynesian state of confidence), i.e. the distance from a complete state of
knowledge; this is, after all, what the entrepreneur does in his daily confrontation with
uncertainty. At any rate, we can define some indicators of the degree of uncertainty for
industries, geographical areas and the whole system.
A natural choice as indicator of the sectoral, global or territorial degree of
uncertainty is the variance (or standard deviation) of profit rates across firms. As a
matter of fact, in the absence of uncertainty, profit (and hence its variance) would be
zero. It is the existence of limits to knowledge (uncertainty) that allows differentials in
capabilities and the associated profits to arise. This seems to imply that the variance of
profit rates across firms gives an expression of the limits to knowledge, i.e. of
uncertainty. Another way to specify a proxy of the degree of uncertainty by industry
may consist in some appropriate survey for a sample of firms, asking them to assess
their degree of “ignorance”. Another method is discussed in Section 6 on estimation.
b) On the role, behavior and decision-making of the firm
However important or unimportant the role attributed to individual initiative,
social life needs organization. The main organizational entity concerning economic
life is the firm. Many economists have insisted on the explanation of the existence of
the firm. As previously seen, this insistence is mainly attributable to the celebrated
virtue of market rules in coordinating and hence giving full value to the autonomous
initiative and creativity of individuals, which induces many to dislike organization, as
well as to the increasing role of uncertainty in economic life and therefore of trial and
error, reinforcing the focus on spontaneous order and processes. But even if the trial
and error method is unavoidable given the limits to human skills and knowledge, it is
still necessary to reduce the dimension of error by appropriate organization. And the
cornerstone of an open economic organization is the firm. The importance of
studying its behaviour, dimension and some other peculiarities is clear. But there is
not much to explain about its existence, it is almost self evident.
12
This paper will not insist on the internal organization of the firm. It is enough, for
the present study, to show that those important fields can be perfectly and coherently
integrated in general economics. But this integration appears to have been well
accomplished only by mainstream economics, while it is a main shortcoming of
heterodox economics.
Every organization needs some clear, well-defined term of reference for its action.
For the firm, this term is profit. At the top of the firm’s concerns there is (and there
must be) the profit rate. More specifically, the main engagement of the firm is to
discover available and new opportunities for profit, as well as to determine which
commodities to produce and how much, with the objective of profit. In the absence of
institutional monopoly, the profit rate is the only reliable and meaningful expression
of a firm’s success, and hence the best indicator for determining responsibility (and
accountability). This implies that the importance of profit goes well beyond private
initiative. In public firms, however, the role of profit as a gauge of success must be
strongly stated, since in this case profit is not automatically pursued as an effect of
private interest. In sum, the most effective monitoring instrument for the firm’s
activity is the last-claimer principle. Only by placing profit at the top of the firm’s
objectives, it is possible to explain the firm’s behavior: its search and discovery, its
size, organizational form, activity levels and some other minor questions.
A concise representation of the firm’s decision-making must concentrate on:
First, the choice of investment (and hence of activity levels), that may be based on the
maximization of total profit.
Second, the search for profit opportunities, mainly through the introduction of new
techniques
With reference to the optimization model used to explain investment, it must be
made clear, mainly for the benefit of heterodox economists, that it is not a mere
mechanical computable tool, disregarding human creativity, as it includes available
entrepreneurship that incorporates, among other things, the stock of “creativity” of
each firm. On the other hand, the firm’s optimizing behavior represented in the next
section depicts a part of entrepreneurial process, while a non optimizing decisional
procedure will be utilized to represent the technological search.
Many authors have pointed out that firms’ decisions follow much simpler rules
than profit optimization (see the pioneeristic study of R. M. Cyert and S. C. March
1963). M. Polanyi’s (1962) teaching on tacit knowledge has added some powerful
weapons to this argument. Neverthless, the hypothesis that the firm optimizes the
distribution of its initiative among different profit opportunities seems to express a
rigorous and general interpretation of its behaviour, irrespectively from the various
decisional routines characterizing each firm organization. In fact, it is quite natural
for the firm to use its limited skills and other resources in such a way to get the
maximum benefit, even more than a similar attitude is natural in consumer’s
spending. In point of fact, consumers that do not like worldly delights will disregard
such a maximization; instead, the firm is obliged to maximize by competition and
13
uncertainty on the potentialities of its rivals, otherwise it will be defeated by
optimizing firms13.
With reference to the search for profit opportunities based on technological
search, we explain this search (and technical progress) as a decreasing function of
uncertainty, and an increasing function of the excess of entrepreneurial skill (as
defined below). The former discourages the introduction of new techniques and
makes it difficult to see some better solution to imitate, while the latter represents the
talent that the firm may dedicate to search. This makes immediately evident the great
importance of uncertainty, entrepreneurial skill and the links between them. For
completeness, “technology” is intended as inclusive of all aspects of the firm’s
organization.
5. The formalization of the model
Now a synthetic model of the firm is set out14.
The prominent importance of profit both in private and public firms, as an
indicator of their degree of success, suggests to derive investment from profit
optimization of firms:
∞T
Max j ∫ ∫s=t {1je-s-ujsrj (t,s) Ij (t,s) + 2Ē (t,s) }ds
(Ut)
t=0
Ē (the part of entrepreneurial skill depending, as we shall see soon, on the firm’s
policy) acts as control variable in the above objective function, while I stays for gross
investment. The integral over the life period of investment ∫ Ts=t {1je-s-ujsrj (t,s) Ij
(t,s)}ds expresses expected profit as discounted by uncertainty indicated by u (that in
this case may consist in a subjective evaluation operated by the firm plus an objective
sectoral indicator determined in the way we shall see in section 6) and interest rate
().  indicates the impact of other factors influencing expected profitability. 
represent weights.
This objective function assumes that the firm distributes its skills and resources
among sectors with the aim of exploiting at the best the market opportunities of
profit. One of the weakest aspects of economics is the way it considers investment
that, when is not simply represented as exogenous, is explained for the most through
the accelerator principle, i.e. as a consequence of the decisions on output level. Our
development overturns the terms of the question: we start from the explanation of
investment, that represents a major challenge for the firm and may be deduced by the
above objective function, and hence derives output, as we shall see soon.
I agree with Hodgson’s criticism of the idea that evolution implies maximization and to some other aspects of the
optimization principle ; but this author would not deny that, for instance, the participants to an examination for, say, a
limited number of grants are induced by their ignorance of the worth of rivals to do their best to pass the examination.
14
The empirical analysis that will follow obliges to consider uncertainty as exogenous. This precludes the formulation of
dynamic competition process. That was done in A. Fusari (2005) along with some simulation experiments.
13
14
Now we need a survey of the system of motion of the optimum problem. All
equations will be expressed in explicit form, as an anticipation of the formalization
for estimation.
The specification of an indicator of uncertainty allows us to overcome the present
vacuous stage of the analysis of entrepreneurial capabilities. More precisely, it
permits to endogenize both the formation and use of the firm’s skills, as tightly linked
to uncertainty. As is well known, these skills constitute, for the major part, a kind of
tacit knowledge (in the sense of M. Polanyi), resulting from learning by doing, by
watching, using etc. Therefore, their accumulation over time may be expressed by the
integral below:
0
E = ∫-∞ (jgsjujXj1 + 1jDj - E)ds
that, by taking the derivative, may be written as:
DE = jgsjujXj1 + 1jDj - E
(1)
giving the increase in entrepreneurial capabilities at time t. E stays for entrepreneurial
skill and u for uncertainty. D is an expression of technical progress (see the equation
3 below); uX indicates output weighted with uncertainty (remember that, in the
absence of uncertainty, no entrepreneurial skill is requested and hence no
entrepreneurial learning is possible); gs is a parameter of the learning. D is a
differential operator d/dt and j indicates industry. It is presumed that entrepreneurial
skill grows at a decreasing rate with the increase in the activity level, mainly because
this increase causes a reduction in adaptive skills (0 < 1 < 1). The term E refers to
the decay of skill due to the “obsolescence” over time of knowledge, with 
indicating the rate of obsolescence.
Some increases in the firm’s capabilities may also be achieved through
restructuring: for instance, the building of a managerial organization or merger. This
kind of capability is considered as a control variable in the optimum problem
specified above, and indicated by Ē
Various types of the firm’s skills may be defined, simply through the
specification of more than one explanatory equation15. Some sort of semientrepreneurial capabilities may be considered as a part of the organizational
structure of the firm: the trade-off between incentives and insurances, as in the
principal-agent theory, gives an example of semi-entrepreneurial role. More
drastically, P. F. Drucker has written «The most important caveat is not to mix
managerial units and entrepreneurial ones. Do not ever put the entrepreneurial into
the existing managerial component. Do not make innovation an objective for people
charged with running, exploiting, optimizing what already exists»16.
Now an explanation of the use of entrepreneurial capabilities must be set out. It
may be expressed as an increasing function of the product of uncertainty by the
activity level i.e. u*X2 (remember that, in the absence of uncertainty, no
15
For instance, evolutionary economics insists on the distinction of innovative skill, as the result of the cumulation of
successful R&D. See U. Cantner, H. Hanusch and A. Pyka (1998). Also the skills deriving from the so called network
relationships among firms should be taken into account.
16
See P. F. Drucker, 1985.
15
entrepreneurial skill would be required), with 0 < 2< 1, indicating that the use of
skills grows at a decreasing rate with the activity level (a kind of scale economy in
that use). This gives the entrepreneurship absorbed by the firm’s ordinary activity. Its
knowledge permits to get, by difference with respect to the availability of
entrepreneurial skill, an excess of skill to be dedicated to innovation if that be the
case. So an excess of entrepreneurial skill may be expressed as the difference
between the capability formation and the skill used in ordinary activity:
Ec = E + Ē – jgjdujXj2
(2)
c
This notion of excess (E ) expresses the link between uncertainty and
entrepreneurial skill or, more precisely, the variation with uncertainty in the tension
in the use of skills; it plays a crucial role in the theory that will follow. gd is a
parameter of the use of entrepreneurial skills to produce X units of output in the
presence of uncertainty. Of course, the entrepreneurship employed is, as a rule, much
higher than the learning due to the corresponding use of entrepreneurship, i.e. gd > gs
For the sake of simplicity, an equation explaining technical progress may refer to
the variation in labor productivity and expressed as follows:
Dj/j = 2e3(1-uj)Ij/Kj +4e5EcjIj/Kj -6uj + 7Ecj
(3)
where  is the productivity of labor per standard unit, e indicates exponential, I
gross investment and K the capital stock. D is a differential operator d/d t, so that
Dj/j is a variation rate. In this peculiar function of technical progress, the
exponentials of u (uncertainty) and Ec (the excess of entrepreneurial skill), both
weighted with the share of gross investment in capital stock I/K (or the share of R&D
expenditure in GNP), express the innovative effect of investment as dependent on the
excess of entrepreneurial skill (which encourages innovation) and uncertainty (which
discourages innovation). The exponentials express the fact that, as a rule, innovation
cannot cause a decrease in productivity since a worse technique than the one in use
will not be adopted. The third and fourth terms, u and Ec, refer respectively to the
negative and positive effect that uncertainty and the excess of entrepreneurial skill
may have on productivity through their influence on the efficiency of factor
combinations, management and the accuracy of decision-making.
Capital stock may be expressed by the following identity:
DKj/Kj = Ij/Kj - 
(4)
K indicates capital stock, I is gross investment and  a rate of capital
depreciation.
Activity levels may be broadly understood as a consequence of investment. More
precisely, the rate of variation in output by firm and industry (DX j/Xj) may be
indicated as proportional to the variation in capital stock. But we must also consider
the influence of uncertainty, which discourages output17. Besides, in the case of noncompetitive market, one must also consider the influence of demand on output, which
may cause a variation in the capital/output ratio. Therefore, the equation for the
firm’s output may be written as follows:
17
Variations in profit rate may encourage, (if positive) or discourage (if negative) production through larger (or smaller)
use of variable factors; so that also those variations should appear in the right hand side of equation 5.
16
DXj/Xj = 8DKj/Kj - 9uj + 10 log(Xdj/Xj)
(5)
d
d
with X j indicating industry demand. Both u and X j/Xj are referred to the sector, not
the firm, while the other variables refer both to firm i and industry j.
Transaction costs per unit of output may be explained by: the size of the firm, as
expressed by its total output, which reduces the frequency of transactions (this
implies that transaction costs stimulate the scale of production); the degree of
uncertainty; and an indicator of the degree of specificity of assets. So the equation
may be written as follows:
TCj = - 11jXj + 12uj + 13j
(6)
where TCj indicates transaction costs per unit of output and  asset specificity.
What is evident, in all the equations specified, is the great importance of an
indicator of the degree of uncertainty. This clearly shows the limitations that
heterodox economics suffers due to its concept of uncertainty as a generic
atmosphere permeating reality and resistant to any quantification. It also appears
evident, from equation 3, the great importance of an indicator of the tension in
entrepreneurial capabilities, as expressed by the notion of excess of entrepreneurial
skill.
Finally, profit rate is given by the following identity
rj = {[1 – wj/(pjj) –TCj]Xj/Kjpkj}– ( -Dpkj/pkj)
(7)
Where wj is the industry money wage. wj/pjj gives the unit labor cost that also
includes the cost of independent labor. TCj indicates transaction costs per unit of
output, pj indicates industry price, pk capital price and  interest rate. To simplify
notations, the above identity intends X as value added (but this affects the
appropriateness of jXj in equation 6 for transaction costs) that implies the
elimination of intermediate goods. Interest rate has been expressed in real terms with
respect to pk and indicated as  -Dpkj/pkj
The compact formulation of the proposed maximization problem is:
∞T
Max j ∫ ∫s=t {1je-s-ujsrj (t,s) Ij (t,s) + 2Ē (t,s) }ds
(Ut)
DKj/Kj
DXj/Xj
Dj/j
TCj
rj
DE
Ec
t=0
= Ij/Kj - 
= 1DKj/Kj - 2uj + 3(Xjd/Xj)
= 4e5(1-uj)Ij/Kj + 6 e7logEcIj/Kj - 8uj + 9Ec
= - 10jXj + 11uj + 12j
= {[1 – wj/(pjj)-TCj]Xj/Kjpkj}– (-Dpki/pkj)
= jgsjuj Xj1 + 12jDj - E
= E + Ē – jgdjujXj2
The above intertemporal objective function allows us to derive an expression for
gross investment.
The crucial variables of the model are the available skill and the associated
degree of uncertainty, which influence productivity and profit and hence investment.
The very low skill and competence (high gdj) of each firm in many activities reduces
17
its area of interest. Schumpeter pointed out that a successful (a skilful) firm may
obtain all the capital it needs from the banking system18 and hence buy on the market
all the other resources requested by production. This statement is exaggerated. Each
firm knows the difficulty of raising capital but this should be considered neither as a
constraint nor as unlimited. A natural way of expressing capital limitation is to refer
to profit rate in investment (and hence production) decisions so that the resulting
profit implies the capital requirements. Clearly, the boundaries of the firm depend on
available capabilities, the dimension of transaction costs and the possible presence of
scale economies.
6. Econometric estimations
The model has been estimated at the industry level.
It would be possible to derive an expression for the growth of capital by
optimization of the above intertemporal objective function, interpreted in the light of
the motion system. At any rate, the objective function implies that I = f(r ,u, ,, Ē).
The solution of this expression for r gives r*=f(I,u, , , Ē). r* may be intended as
the profit rate required to invest I units of capital for given values of u, , , Ē. So, an
expression for the rate of variation in gross investment may be written as follows:
DIj/Ij = (rj - rj*). This equation explains the variation rate in investment through the
adjustment of actual profit rate towards the desired profit rate. If the first exceeds the
profit rate (r*) required to invest I units of capital, investment grows, and vice versa.
 may be interpreted as the entrepreneurial alertness in taking advantage of the
market opportunities. So, the compact formalization of the model, in the version for
estimation, is:
DlogI
= (r – r*) with r* = 1I + 2u +3 +4logEc + 1
DlogK
= I/K - 
Dlog
= 5e6(1-u) I/K + 7 e8logEcI/K - 9u + 10logEc + 2
DlogX
= 11DlogK - 12u + 13 log(Xd/Xj) + 3
Dri= (Xp/Kpk)(DlogX+Dlogp-DlogK-Dlogpk)–(wL/ Kpk )(Dlogw+DlogL
-DlogK-Dlogpk) – D(-Dlogpk)
DlogL
= DlogX - Dlog
c
E
= Z/uX
(1)
(2)
(3)
(4)
(5)
(6)
(7)
The equation for transaction costs has been eliminated, since it has no meaning at
industry level.
D indicates the differential operator (d/dt) and log natural logarithms. Therefore Dlog
indicates the rate of variation of the corresponding variable.  stays for intercept. X
indicates value added at factor costs and Z is the trend (calculated outside the model)
of value added. L indicates total employment, expressed in standard labor units. All
the remaining variables preserve the previous notations. The identity for the profit
rate has been expressed as a first derivative.
18
See J. A. Schumpeter (1934)
18
The model remedies the lack of a data series on entrepreneurial skill (E) through
identity 7 defining the excess of skill. Bear in mind, in interpreting this identity, that
uncertainty (u) has been expressed as the ratio to its average over the estimation
period, i. e. as a deviation from the average. Thus, in identity 7, uncertainty does not
appear in the numerator (this should be multiplied by the average of uncertainty that,
divided by itself, gives one). The deviation of ordinary activity and the relative
uncertainty (in the denominator) with respect to their trend (Z), gives the strain on
entrepreneurial skill. If X and u grow, the strain on entrepreneurial skill rises; if the
two variables diminish, it decreases.
The data series on uncertainty have been obtained through the elaboration of the
answers to a monthly survey of business conditions for a sample of firms
representative of all industrial sectors and Italian geographical areas by ISAE 19. The
answers refer to expectations over the next three or four months, are discounted by all
seasonal factors and concern the probable behavior of: delivery orders, production,
prices, cost of financing and liquidity assets. These variables are defined by three
modalities: modality 1 expresses “increase” (in the rate of change in the variables),
modality 2 indicates “no change”, modality 3 indicates “decrease”. The answers of
two consecutive months have been compared, taking the number of those that differ
from the previous month’s and dividing them by the total answers available. This
expression of firms’ “secondthoughts” can be taken as a measure of the industry
degree of uncertainty. The data series run from 1986 to 2003.
A FIML estimator has been used. The estimates are derived by an asymptotically
exact Gaussian estimator of a differential equation system using discrete data. As there
is no equivalent of a just-identified model for non-linear systems, there is no systemwide test such as the Carter-Nagar R2 or likelihood-ratio. In order to give an idea of the
efficiency of estimations, also the means and standard deviations of the estimated
endogenous variables are reported. But firstly it is indispensable to expose some
warning on the use of econometric methods.
Social reality, being the product of human action and creativity, and hence
characterized by qualitative jumps, can be understood and explained with difficulty
simply on the basis of observation. In general, econometric estimations may be
referred to the past, to the observation period, not to the future. But their extension to
the future may have some foundation if there exists some a priori knowledge on the
durability over time of the considered phenomena. One possibility to assess such
durability may consist in the verification that the observed phenomena reflect some
organizational necessity of social systems that derives from long lasting aspects of
the considered reality, for instance, from the general conditions of development.
Well, dynamic competition and its constituent elements represented by
entrepreneurship, uncertainty and innovation embody some fundamental and long
lasting aspects of the modern dynamic economies. This justifies, at the aggregate and
industry level, some econometric estimation on the matter.
19
Institute of Studies and Economic Analysis
19
Table 1 Manufacturing industry. Estimated parameters, their asymptotic standard errors,
endogenous variables and residuals.
Parameters
 0.207
1 0.070
 2 0.107
3 0.473
4 0.899
5 0.023
6 -4.349
7 0,077
8 15.140
9 0.025
10 0.105
11 0.914
12 0.006
1 0.060
2 0.492
3 -0.111
Asympt. Stand. Error
0.0373
0.0013
0.0022
0.0119
0.0461
logI
0.0310
logK
0.0149
log
0.0305
logX
2.6537
r
0.00006
logL
0.0076
0.0741
0.0031
0.0111
0.0069
0.0206
Endogenous variables
Estimated
Observed
Mean
10.751
13.012
3.683
12.264
0.103
8.584
Stand. Deviation
0.092
0.071
0.079
0.054
0.022
0.036
Mean
10.748
13.012
3.680
12.260
0.102
8.583
Stand. Deviat.
0.096
0.072
0.082
0.062
0.024
0.035
Errors in estimation
Mean
0.003
0.0005
0.0029
0.0038
0.0010
0.0005
Stand. Deviat
0.041
0.004
0.016
0.026
0.010
0.019
All parameters have reasonable values and are significantly different from zero at the
1 per cent level.
Table 2 Food staff industry Estimated parameters, their asymptotic standard errors,
endogenous variables and residuals.
Parameters
 0.992
1 0.061
 2 -0.003
3 0.445
4 1.515
5 0.0273
6 9.347
7 0,0229
8 10.443
9 0.045
10 0.0112
11 1.807
12 0.074
1 0.060
2 0.492
3 -0.111
Asympt. Stand. Error
0.0038
0.0078
0.0512
0.0198
0.0631
logI
0.0011
logK
5.0455
log
0.0013
logX
0.3592
r
0.0084
logL
0.0008
1.5971
0.0347
0.0111
0.0069
0.0206
Endogenous variables
Estimated
Observed
Mean
8.338
10.412
3.649
9.829
0.144
6.180
Stand. Deviation
0.128
0.107
0.063
0.059
0.023
0.024
Mean
8.346
10.412
3.652
9.833
0.146
6.181
Errors in estimation
Stand. Deviat.
Mean
0.137
0.110
0.080
0.076
0.021
0.026
-0.008
-0.0004
-0.0033
-0.0043
-0.0020
-0.0007
Stand. Deviat
0.015
0.009
0.028
0.031
0.019
0.027
The results are no worse than in manufacturing industry, but the parameter 2 has
wrong sign and is not significant.
The estimations over other 13 industrial sectors, giving results no worse than the
previous, have been excluded for space reasons.
20
More extensive comments (and comparisons) on and among the above results
have been omitted for space constraints.
6. Dynamic competition, development and growth: specification and
econometric estimation
The elements that this paper notes as essential to a realistic theory of the firm are
also central to the analysis of the entire economic system. In particular, the interaction
between innovation and uncertainty is at the heart of the mechanism of growth and
development and may be intended as expressive of the process of dynamic competition,
i. e. the competition based both on innovation and the opportunities deriving from
market disequilibria (Schumpeterian and neo-Austrian competition). Therefore, it will
be interesting to specify a formalization to represent that interaction and subject it to
econometric testing. So that, this section goes beyond the theory of the firm and, unlike
previous sections, considers uncertainty as endogenous and expressed as the standard
deviation of profit rates across firms, which also gives an expression of market
disequilibria.
Section 4 has shown that uncertainty reduces innovation, both directly and
because of its negative influence on the excess of entrepreneurship. This stimulates the
concentration of entrepreneurs’ search for profit on adaptive strategies (the search
according to neo-Austrians), since innovation feeds the standard deviation of profit rates
across firms (as a proxy of market disequilibria and uncertainty). But the reduction in
that standard deviation, as a consequence of adaptive competition, causes a rise in
innovation, both directly and because of the increase in the excess of entrepreneurship;
and so on, with a cyclical behaviour and alternation between innovation and adaptation
(or structural organization). This suggests representing, at the aggregate level, the
relation between innovation and adaptation through a Lotka-Volterra predator-prey
system, with innovation acting as the prey and the standard deviation of profit rates
across firms as the predator. The estimated differential system is, therefore, the
following:
DPA = b1PA - b2VR*PA
(1)
DVR = -b3VR + b4PA*VR
(2)
where:
PA = Patent applications (intended as an indicator of innovation).
VR = Standard deviation of profit rates across firms.
D = Derivative d/dt.
Equation 1 may also include a term DE for the variation of entrepreneurial skill
displaying on innovation (the prey) a propulsive role similar to that of stocking in the
predator-prey models used by studies on food chains20.
The parameter b1 is a constant exponential rate of growth of innovation,
expressing the autonomous push to innovate due to entrepreneurial aggressiveness;
its impact on DPA is reduced by the increase in the standard deviation of profit rates
20
Alternatively, a three equation predator-predator-prey model could be specified, with innovation that preys
entrepreneurial skill and is preyed by uncertainty, that also preys entrepreneurial skill
21
across firms (according to parameter b2). b3 is an exponential rate of growth of the
standard deviation of profit rates across firms; the negative sign on b 3 expresses the
compressing effect coming from adaptive competition on the standard deviation of
profit rates. Innovation is the field of pasture of the standard deviation of profit rates
across firms (the proxy of uncertainty): in the absence of innovation, the term with b 4
would disappear and such a standard deviation would become null because of the
adaptive search for profit. When innovation intensifies, the standard deviation of
profit rates across firms (predator) grows, thus causing the contraction in innovation
(the prey), and hence the predator, with a cyclical alternation. The system parameters
give the dimension of the disequilibrating (b1 and b4) and equilibrating (b2 and b3)
push expressed by dynamic competition (the combination between innovative and
adaptive competition).21 It may be useful to underline in this regard that the measures
of dynamic competition based on the rapidity of contraction of the standard deviation
of profit rates across firms (as, for instance, in D.C. Mueller and others or H.
Odagiri22), only consider adaptive competition or, more precisely, parameter b 3 of the
above system. They ignore the other parameters, giving a poor approximation to the
intensity of competition and economic dynamism, as dynamic competition consists
both in innovation and adaptation.
The estimation below refers to three main European industrial countries: The United
Kingdom, France and Germany. The data on patent applications and grants come from
the USA Department of Commerce. The data on the standard deviation of profit rates
across firms come from D.C. Mueller (1990) for France and Germany; while those for
the United Kingdom come from H. Odagiri (1994). The data for France give pre tax
profit, those for the United Kingdom and Germany give after tax profit. Their
reliabilities are affected by their derivation from some firms’ balance sheet based on
dissimilar and not well-established procedure.
The results shown below must be judged in the light of the deficiencies of the
appropriate data series. Nevertheless, confirmation of the theory is encouraging. But the
improvement of quantitative analysis in the crucial fields of innovation and dynamic
competition needs a great deal of statistical research.
A FIML estimator was used to preserve the tight interaction between (1) and (2)
above, i.e. innovation and adaptation, which is a crucial point of the theory of dynamic
competition presented in this essay.
A system which differs from Volterra in that the second equation uses only PA
instead of the term PA*VR in the right hand side, has also been estimated. As a matter
of fact, it may be assumed that the “reproduction” hypothesis typical of Volterra’s study
on population plainly operates only in the equation of innovation in that each innovation
is strongly influenced by the state of knowledge resulting from previous innovations. In
the equation of the standard deviation of profit rates, however, it may operate only
backwards as large disequilibria stimulate adaptation. This means that in equation 2 the
21
A ponderous author's research on social and historical process, from primitive ages to the beginning of modern dynamic society,
shows the important role played by the binomial innovation-adaptation in historical evolution. (See A. Fusari, Human adventure; an
inquiry on the way of people and civilizations, Ed. SEAM, Roma 2000, pages 760.
22
See D. C. Mueller (1990); H. Odagiri (1994)
22
cross product term of Volterra, the encounter between predator and prey, may be
replaced by the prey (innovation) only.
Data on patent have been divided by thousand, for uniformity of their scale with
respect to VR.
UNITED KINGDOM.
Table 3. Model in the Volterra form.
b1
b2
b3
b4
PAt
VRt
Estimate of parameters
0.519
0.082
1.716
0.367
Mean
4.7876
6.4006
Asymptotic standard errors
0.099
0.016
0.504
0.105
Endogenous variables
Observed
Standard deviation Mean
0.2189
4.7925
0.7898
6.3773
t values
5.25
5.19
3.41
3.48
Estimated
Standard deviation
0.2982
0.9747
The model with the term PA in equation (2), instead of PA*VR, does not converge.
FRANCE.
The data series of the standard deviation of profit rates for France has two out-lying
observations in 1974 and 1977. The first has no justification and is probably due to
inaccuracy of the data; the second is largely determined by the revaluations, in 1977, of
the assets of mergers that consistently depressed profit rates. We have substituted to
those anomalous data an interpolation with the contiguous data23.
“Take in Table 4”
Table 4. Model in the Volterra form.
b1
b2
b3
b4
Estimate of parameters
0.318
0.048
0.558
0.192
Asymptotic standard errors
0.121
0.019
0.244
0.080
PAt
VRt
Endogenous variables
Observed
Estimated
Mean
Standard deviation Mean
Standard deviation
3.0316
0.2261
3.0295
0.2302
6.3311
0.7627
6.3183
0.8061
23
t values
2.61
2.46
2.29
2.40
The fact that only two observations were out liers, that the model is dynamic, and that there is no reason to assume
that the cause, if any, of these anomalies were the same, suggested that the use of a dummy variable was inappropriate
23
Table 5. Model with the term PA in equation (2), instead of PA*VR.
b1
b2
b3
b4
Estimate of parameters
0.252
0.037
0.608
1.320
Asymptotic standard errors
0.158
0.252
0.348
0.722
t values
1.59
1.48
1.75
1.83
PAt
VRt
Endogenous variables
Observed
Estimated
Mean
Standard deviation Mean
Standard deviation
3.0316
0.2261
3.0263
0.2418
6.2933
0.7637
6.3072
0.5024
GERMANY
Table 6. Model in the Volterra form.
b1
b2
b3
b4
Estimate of parameters
0.316
0.090
0.089
0.128
Asymptotic standard errors
0.115
0.037
0.177
0.023
t values
2.74
2.45
0.50
0.56
PAt
VRt
Endogenous variables
Observed
Estimated
Mean
Standard deviation Mean
Standard deviation
7.7933
1.4829
7.7608
1.6193
3.1622
0.3524
3.1554
0.3401
Table 7. Model with the term PA in equation (2), instead of PA*VR.
b1
b2
b3
b4
Estimate of parameters
0.333
0.096
0.221
0.095
Asymptotic standard errors
0.124
0.039
0.164
0.066
PAt
VRt
Endogenous variables
Observed
Estimated
Mean
Standard deviation Mean
Standard deviation
7.7933
1.4829
7.7603
1.5898
3.1622
0.3524
3.1588
0.2810
24
t values
2.69
2.43
1.35
1.43
For Germany, the model in the Volterra form provides a worse estimate of the
equation of the standard deviation than the model where the term PA is substituted to
PA*VR in (2); the contrary happens for France and the United Kingdom. It would
seem, therefore, that in the first country disequilibria do not generate disequilibria,
while a self-reinforcing tendency of disequilibria appears in the United Kingdom and
France, i.e. VR contributes to stimulate its own growth through the term PA*VR.
All parameters have the correct signs, have reasonable values and are significantly
different from zero around the 1 percent level in the estimation of the model in the
Volterra form for the United Kingdom and France, and in the pseudo Volterra form for
Germany.
The models were also estimated utilizing data on patent grants instead of patent
applications but the results have not been presented as, in all cases, patent applications
gave better estimates. This is not surprising since patent applications provide a better
expression of the innovative propensity of firms, i. e. their intention to innovate.
It may be interesting to compare the estimated parameters relative to various
countries, taking present that parameter b1 gives the innovative dash, parameter b3 the
adaptive push, while parameters b1 and b4 represent the disequilibrating forces and
parameters b2 and b3 express the equilibrating ones.
The United Kingdom shows the highest innovative dash (b1) and also the highest
adaptive push (b3), i.e. the strongest dynamic competition. Germany shows a strong
innovative dash and a low adaptive push, while France presents an innovative dash a
little lower than Germany, but a much higher adaptive push. Relatively to Germany,
France has a lower parameter on the term in equation (1) braking innovative dash and a
higher parameter on the term in equation (2) braking adaptive push. These offsetting
values of b1 and b3, and b2 and b4 tend to partly compensate the differences in the
innovative dash and the adaptive push, making the disequilibrating-equilibrating
process closer in those two countries. The United Kingdom shows such offsetting
behavior only with reference to the adaptive push (but the difference between b3 and b4
is large), while the parameter b2, braking the innovative dash, appears higher than
France and lower than Germany, implying for this aspect a widening of the
disequilibrating forces relatively to this country.
Conclusion
This research points out the close relation between entrepreneurship and
uncertainty, their crucial and opposite influence on growth and development, the
importance of a measure of the degree of radical uncertainty. A large part of
economics, precisely the so called mainstream economics, ignores uncertainty and
pretend to hide this omission through the inclusion in its analysis of known
probability distributions that, as such, only express probabilistic certainty. But the
modern dynamic economies, characterised by growing endogenous uncertainty, fully
contradicts the economics of perfect knowledge and stimulate a more and more
diffuse perception among economists of the crucial role of uncertainty properly
understood in the representation of economic process. Unfortunately, some
fundamental misunderstandings afflict the way true uncertainty is considered and
25
treated by heterodox students. It is our opinion that an improvement of heterodox
theories requires an accurate criticism of their current state. One main
misunderstanding seems to be represented by what I call the postulate of
unmeasurability, that is, the general assumption that true uncertainty is, by its nature,
an unmeasurable entity. This greatly damages the possibility to explain some crucial
economic variables such as entrepreneurship, innovation, investment and the
specification of the theory of the firm.
In particular, the consideration of uncertainty as a subjective, unmeasurable and
hence evanescent phenomenon makes entrepreneurial capabilities an evanescent
entity, as strictly linked to evanescent uncertainty. This has engendered a propensity
of the theories of the firm that give importance to entrepreneurial capabilities, from E.
Penrose to the present time, to dedicate little consideration to uncertainty and hence
to consider the firm as a bureaucratic, managerial structure much more than an
entrepreneurial one. Significantly, an important example of this propensity is given
by a father of entrepreneurship, J. A. Schumpeter. His well known lack of
consideration for uncertainty, notwithstanding this one springs out copiously from the
Schumpeterian notion of “creative destruction”, downrightly induced this author in
the absolute error to foresee the disappearance of entrepreneurship in favour of
bureaucratic organisation.
Some other students strongly concerned about true uncertainty have been
induced, by the consideration of this one as an unmeasurable result of a flow of
unintentional events, to prefer spontaneous order to organisation and hence to
disregard the theory of the firm, as is typical of the neo-Austrian school of thought.
A growing number of heterodox economists have eluded the difficulty to deal
with uncertainty intended as a fleeting, subjective, unmeasurable variable by putting
it under the notion of bounded rationality. Accordingly, they have put forward a
notion of capabilities amended by uncertainty: the notion of decisional routine that,
as implying repetition, may be referred to managerial bureaucratic structures, not to
entrepreneurial decision-making, having to do with uncertainty. A main aspect of
bounded rationality economics’ is the analysis of entrepreneurial behaviour drawn by
this school of thought and, in particular, its critique of optimisation. This gives a clear
example of some serious misunderstanding caused by the assumption of
unmeasurability and impalpability of uncertainty. In effect, in the absence of a
measure of uncertainty and consequently of a quantification of entrepreneurial
capabilities properly understood, that is, the capabilities to meet uncertainty, it is
impossible to specify some sensible optimisation model at the service of the theory of
the firm and it remains to appeal to some other more vague decisional criteria, for
instance, the Simonian satisfying behaviour, or more stringent decisional routines
that, however, deny, as just seen, entrepreneurial versatility. On the contrary, if the
bound to rationality, as represented by the level of uncertainty and capabilities, is
specified in the constraints of an optimisation problem, the bounded rationality
criticism against optimisation drops out and the theory of the firm may preserve
optimisation tool.
26
In the contemporary studies on the firm, uncertainty frequently emerges through
the explanation of “transaction costs”. But this reference to uncertainty, even if
interesting, is not so much important as it is sometimes considered to be. In fact, the
explanation of the existence of the firm does not need transaction costs; it may be
based on some more general organisational necessities consequent to the limitations
in human skills. Besides, it seems important to take present that the stimulus of
uncertainty to the firm dimension through transaction costs is flanked by the opposite
effect of uncertainty to favour little firms, with their versatility and flexibility. In
effect, a main cause of the boundaries of the firm is probably represented by the
availability of entrepreneurial capabilities and the associated level of uncertainty, that
limits the degree of understanding and hence the power force of capabilities
Finally, it is our firm belief that a major deepening of the coordination between
the theory of the firm and general economics is indispensable to make heterodox
economics more attractive. In fact, a main reason of the survival of the Neoclassical
theory of the firm and its large number of followers (notwithstanding its complete
inability to consider some crucial aspects of the economy such as innovation,
entrepreneurship and uncertainty) is its perfect coordination with general economics.
Unfortunately, the current idea of true uncertainty as an unmeasurable entity prevents
the coordination of the heterodox theories of the firm with general economics, for
instance, through a specification of dynamic competition, representing economic
process with entrepreneurship, innovation and uncertainty. As a matter of fact,
dynamic competition may be expressed as a result of entrepreneurial search for profit
based both on innovation and the exploitation of market disequilibria, that is, the
combination of neo-Austrian market process and Schumpeterian creative destruction.
But this combination needs the consideration of the level of uncertainty and its
variation, as indispensable to explain the rise of innovation when uncertainty falls,
and the intensification of market adaptive process when disequilibria and uncertainty
rise. The unmeasurable uncertainty of neo-Austrians and the Schumpeterian lack of
consideration of uncertainty have prevented the combination of the two approaches
and hence the formalisation of dynamic competition, so that an important frame for
the insertion of the theory of the firm in general economics has got lost.
The paper presents a formulation of the theory of the firm that has some
substantial differences with respect to usual formulations, mainly on the explanation
of capital accumulation, the role of the profit rate and technical progress. In
particular, it points out the close relation between entrepreneurship and uncertainty,
their crucial and opposite influence on growth and development, the importance of a
measure of the degree of radical uncertainty. A FIML econometric testing at industry
level of the equations derived at the firm level has been provided. Moreover, a short
formalization and estimation on the whole economic system has been added, which
stresses the importance of uncertainty and its measure. Since uncertainty is largely
endogenous to the economic process (mainly as an effect of creative destruction) and
requires the use of entrepreneurship, it follows that the promotion of growth mainly
needs the stimulus of entrepreneurial skills.
27
Starting from this approach, a more complete model of the economy may be
specified simply by adding equations for demand, wages, interest rates, prices, and so
on. But this is beyond the scope of the present essay, which concerns the theory of
the firm. The introduction into the model of new products is a further, unavoidable
challenge because, in the end, it is product innovation that prevents stagnation.
Another planned extension will be the presentation of estimates at firm level, on the
basis of panel data.
28
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