Prediction and Control; The Ideal Pure Cycle and Probabilistic Indeterminacy

The central issues of this section are a) prediction and control in the economy, b) the non-systematic, probabilistic occurrence of conditional events, and c.) the discovery of “methods of attaining a sufficient accuracy for practical purposes.” [CWL 15, 72]

The theory of Functional Macroeconomics Dynamics is independent of human psychology.  It is a set of explanatory formulae; and it provides norms and precepts for human participants.  But humans often violate norms out of ignorance, malice, or innocent mistakes.  They can drive the economy off course.

The true aim of science is verification of understanding.

For Lonergan, prediction and control are not legitimate ends of science because they are not the same as verified understanding, which is the true aim of science.  [CWL 15, Editors’ Introduction, ftnt 32, xxxvii]

analysis may attain its goal without being able to predict, … [CWL 15, 11]

Moreover, prediction and control in the area of the so-called applied human sciences conflict with the very nature of the subject matter of human science: on the one hand, prediction and control depend upon and imply the policy of elimination of human freedom; on the other, human freedom is something that may just spring up even in situations in which people have managed practically to eliminate it. [CWL 15, Editors’ Introduction, ftnt 32, xxxvii]

Moreover, classical predictions are complemented by statistical predictions.  The possibility of variation and exception must be acknowledged.

Classical predictions can be exact within assignable limits, because relations between measurements converge on the functional relations that formulate classical laws. But because relative actual frequencies differ at random from probabilities, statistical predictions primarily regard the probabilities of events and only secondarily determine the corresponding frequencies that differ at random from probabilities.  Hence, even when numbers are very great and probabilities high, … the possibility of exceptions has to be acknowledged. [CWL 3, 66/88-9]

The development of economic dynamics within the present perspective will have its clusters of differential equations and probability functions.  [McShane, 2002-2, 68]

However, we want to discover methods of defining and measuring equilibrium or distortion in the economy with sufficient accuracy for the practical purpose of avoiding excesses and necessary corrections.

the analysis itself will provide rather convincing indicators, and as expertise develops the new tricks of a new trade, there well may be discovered methods of attaining a sufficient accuracy for practical purposes. [CWL 15, 72]

Human communities devise schemes of recurrence.  Events specified by classical laws recur over and over, ceteris paribus.  These schemes are intelligible and stated in classical laws.

Contemporary physics has established a distinction between classical and statistical laws.  Roughly, classical laws reveal that if A then B, provided other things are equal, while statistical laws tell us how often that proviso is met.  … A series of classical laws forms a chain when the consequent of each preceding law in the series is the condition of the next following law in the series.  Such a series becomes a scheme of recurrence when the consequent of the last is the condition of the first. [CWL 15, 3-4]

Human communities devise their own schemes of recurrence: the commonly understood and commonly accepted ways and means of cooperating.  Among them are the firms that keep producing goods and rendering services and no less the households that purchase the goods produced and the services rendered.  Such is the economy, which is a structure resting on the ecologies of nature and underpinning social and cultural structures. [CWL 15, 3-4]

Yet all schemes of recurrence are subject to a probability of not continuing to recur.  The prior conditions of recurrence form a diverging series.  With requisite information one could work backward from an event to grasp the intelligibility of the concrete pattern leading up to it. But one cannot go forward to predict with perfect accuracy which classical laws will combine and how they will combine to result in an event.

The following densely-packed paragraph is worth a slow read, or five slow reads:

Our analysis … acknowledged the existence of schemes of recurrence in which a happy combination of abstract laws and concrete circumstances makes typical, further determinations recurrent, and so brings them under the domination of intelligence.  Moreover, it acknowledged that concrete patterns of diverging series of conditions are intelligible; granted both the requisite information and mastery of systematic laws, it is possible in principle to work from any physical event, Z, (back) through as many prior stages of its diverging and scattering conditions as one pleases; and it is this intelligibility of concrete patterns that grounds the conviction of determinists, such as A. Einstein. … However, we agree with the indeterminists inasmuch as they deny in the general case the possibility of deduction and prediction.  For while each concrete pattern of diverging conditions is intelligible, still its intelligibility lies not on the level of the abstract understanding that grasps systems of laws but on the level of the concrete understanding that deals with particular situations.  Moreover such concrete patterns form an enormous manifold that cannot be handled by abstract systematizing intelligence for the excellent reason that their intelligibility in each case is concrete. There results the peculiar type of impossibility that arises from mutual conditioning. Granted complete information on a totality of events, one could work out from knowledge of all laws the concrete pattern in which the laws related the events in the totality.   Again, granted knowledge of the concrete pattern, one could use it as a guide to obtain information on a totality of relevant events.  But the proviso of the first statement is the conclusion of the second; the proviso of the second statement is the conclusion of the first; and so both conclusions are merely theoretical possibilities. For the concrete patterns form a non-systematic aggregate, and so it is only by appealing to the totality of relevant events that one can select the concrete pattern; on the other hand, the relevant totality of events is scattered, and so they can be selected for observation and measurement only if the relevant pattern is known already  [CWL 3, 650/672-3]

To resume the argument, deduction and prediction in the general case are impossible.  They are impossible for man’s limited understanding, because limited understanding could master the manifold of concrete patterns of diverging series of scattering conditions, only if that manifold could be systematized; and it cannot be systematized. [CWL 3, 651/672-3]

… even when the laws involved in the process are thoroughly understood, even when current and accurate reports from usually significant centres of information are available, still such slight differences in matters of fact can result  in such large differences in the subsequent course of events that deductions have to be restricted to the short run and predictions have to be content with indicating probabilities. So perhaps it is that astronomers can publish exact times of the eclipses of past and future centuries (using “classical laws”) but meteorologists need a constant supply of fresh and accurate information to tell us about tomorrow’s weather  [CWL 3, 51/74 ]

We have been considering the complementarity of classical and statistical investigations as forms of knowing.  We have found such complementarity to exist at each of the stages or components of the process of inquiry.  There is the classical heuristic anticipation of the systematic; there is the complementary statistical heuristic anticipation of the non-systematic, … classical and statistical laws pertain to a single complementary field, and to know either is to effect a mental separation between types of data that have to be accounted for and types that still remain to be explained. … the experiential and pure conjugates of classical laws can be verified only in events; the events occur only if other things are equal. … Inversely, as conjugates are verified only in events, so events are defined only by conjugates, …there is a complementarity in modes of abstraction; classical laws regard the systematic in abstraction from the non-systematic, the relations of things to one another in abstraction from their relations to our senses;  … the two types of laws are complementary in their verification: exact and complete knowledge of classical laws cannot successfully invade the field of statistical laws; and statistical investigations are confronted with regular recurrences that admit explanations of the classical type, … [CWL 3, ?/?]

The classical laws of the economic mechanism of expansion and contraction can be understood, though the laws of the current process do not determine a basis for making perfectly accurate predictions of the process’ future.

the present study will offer an analysis of the macroeconomy that accounts for its success and failures without attempting the historical and statistical research what would be necessary if any predictions were to be made.  How is this possible?  It is possible because knowledge of facts is one thing, and understanding known facts is another.  The facts of the macroeconomy are already well known.  What is lacking is a clear and precise understanding of the mechanism behind such obvious facts as the relations between expansion and contraction of the economy, employment and unemployment, inflation and deflation, and many other things that are just common knowledge. [CWL 15, 11-12]

While the rigidities of physics allow high probabilities in the predictions of planetary motions, other fields may not enjoy the same rigidities and the strong possibilities of precise prediction.

Again,

For Lonergan, prediction and control are not legitimate ends of science because they are not the same as verified understanding, which is the true aim of science.  Moreover, prediction and control in the area of the so-called applied human sciences conflict with the very nature of the subject matter of human science: on the one hand, prediction and control depend upon and imply the policy of elimination of human freedom; on the other, human freedom is something that may just spring up even in situations in which people have managed practically to eliminate it. [CWL 15, Editors’ Introduction, ftnt 32, xxxvii]

However, knowledge of the classical laws relating interdependent functional flows will provide approximations of equilibration or distortion.

the analysis itself will provide rather convincing indicators, and as expertise develops the new tricks of a new trade, there well may be discovered methods of attaining a sufficient accuracy for practical purposes. [CWL 15, 72]

In Functional Macroeconomic Dynamics we understand that the coincidental pricings and quantities are not basic, fundamental explanatory terms of scientific and systematic significance. We understand that of the particular pricings and quantities at any point in time are “further determinations that are contingent from the very fact that they have to be obtained from a non-systematic manifold.” [CWL 3, 492/516]  (In addition, read in the entirety CWL 3, 491-6/)

conjugate forms or terms ( such as [P’Q’], [p’a’Q’], and [p”a”Q”] FMDC) are defined implicitly by their explanatory and empirically verified relations to one another. …  Such relations (P’Q’ = p’a’Q’ + p”a”Q”Basic circuit R&MFMDC) are general laws; they hold in any number of instances; they admit application to the concrete only through the addition of further determinations (such as the indices and coefficients of price and quantity FMC), (however) such further determinations pertain to a non-systematic manifold.[1]  There is then, a primary relativity (correspondence of compensated factors of production with elements in the standard of living FMC) that is contained in the general law (P’Q’ = p’a’Q’ + p”a”Q”FMC); it is inseparable from its base in the conjugate form which implicitly it defines; and to reach the concrete relation that holds at a given place and time, it is not enough to think about the general law; one has to add further determinations (such as coincidental pricings and quantities) that are contingent from the very fact that they have to be obtained from a non-systematic manifold. [CWL 3, 492/516]  (In addition, read in the entirety CWL 3, 491-6/)

The development of economic dynamics within the present perspective will have its clusters of differential equations and probability functions.  [McShane, 2002-2, 68]

The scientific macroeconomist is not a bookkeeper recording the double-entry balance of inflows and outflows; nor is he an entrepreneur seeking to meet his estimated demand with a possible supply; he is a scientist seeking a law of circulation.

Now it is important to distinguish two different aspects of equations (39) and (42).[2]  Under a certain aspect these equations express a truism: if entrepreneurial receipts and payments equate, then they equate not only among entrepreneurs but also between entrepreneurs and the third party, demand.  But under another aspect the same equations, so far from expressing a necessary truth, express an almost unattainable ideal, namely a dynamic equilibrium to which any actual process continually attempts to approximate by varying prices and changing quantities of supply.  To study the truism is to study bookkeeping, to study the art of double entry, and to learn the magic of the variable items, profit and loss, which perforce make the books balance.  To study the ideal is to study equilibrium analysis.  The bookkeepers are wise after the event.  But if the entrepreneurs are to be wise, they have to be wise before the event, for their payments (outlays) precede their receipts, and the receipts may equal the payments (outlays) but they may also be greater or less, to give the entrepreneur a windfall profit or loss.  Such justification or condemnation of payments by receipts the bookkeeper records but the entrepreneur has to anticipate, and the grounds of his anticipations, their effects upon his decisions, and the interaction of all decisions form the staple topic of equilibrium analysis.  Now the viewpoint of the present discussion is neither that of the bookkeeper nor that of the equilibrium analyst.  Equations (39) to (42) are regarded not as a set of facts recorded by bookkeepers, nor as an ideal which entrepreneurs strive yet fail to attain, but as a first approximation to the law of circulation in the basic circuit.  The first approximation to the law of projectiles is the parabola: one might, if one chose, consider the projectiles as aiming at or tending towards the ideal of the parabola yet ever being frustrated by wind resistance; one might elaborately describe the trajectory of the projectile as an indefinite series of parabolas, each one in succession the goal of its tendency only to be deserted because adverse circumstance set it on another track.  In such a description of trajectories there is to be found at least a superficial resemblance with the statement that an economy is tending towards equilibrium at every instant, though towards a different equilibrium at every successive instant.  But whatever the resemblance, and however deep and significant the difference, we here propose to take a circuit and examine first the implications of this law and then the second approximations that are relevant to our inquiry.  [CWL 21, 142-43]

The analogy of a projectile and the economy veering off course:

Projectile Pure Cycle
Central Tendency or Ideal Model Parabola Crossover balance (equilibrated adjustment of savings) in all phases of the process to realization of full potential
Adverse Probabilistic External Event Wind gust Any Deviation in Any Monetary Channel
Adverse Result Veer off course Boom, Slump, Inflation, Deflation, Hyper employment, Unemployment, Excess Capital, Rusting Capital

The occurrence of possible events must be assigned a probability in the case where no system exists to be formulated in a classical law.  Indeterminacy is the nonsystematic probabilistic variation of events from the theoretical norm.  The prior conditions of the occurrence of the event diverge the more distant they are in space and time; the diverging series of conditions cannot be brought into a neat formulation.

A familiar example is the indeterminacy of the weather 30 days from now vs. tomorrow.

So perhaps it is that astronomers can publish exact times of the eclipses of past and future centuries (using “classical laws” and the rigidities of physics) but meteorologists need a constant supply of fresh and accurate information to tell us about tomorrow’s weather. [CWL 3, 51/74]

Objective process is not the realization of some blueprint but the cumulation of a conditioned series of things and schemes of recurrence in accord with successive schedules of probabilities. [CWL 3, 445/470]

Now, the economic process is an ecology consisting of schemes of recurrence following classical laws such as crop cycles and manufacturing cycles and transportation cycles which can be represented by classical formulas of rules and laws. But each of the recurrent economic schemes has a probability of emergence and a probability of survival.

The economic issue arises in an ecology in which abstract relationships are complemented by concrete probabilities. [CWL 15, 89]

one is led to think of schemes of recurrence, whose several carriers severally follow their own classical laws, whose assembly follows the probability of their emergence, and whose continued functioning follows the probability of their survival.  Such in a nutshell is the evolutionary view that in InsightI sketched out under the name of emergent probability and, earlier in this essay, I have applied to economics. [CWL 15,  92-93]

Thus it is that in the history of human societies there are halcyon periods of easy peace and tranquility that alternate with times of crisis and trouble. In the periods of relaxed tension, the good of order has come to terms with the intersubjective groups.  It commands their esteem by its palpable benefits; it has explained its intricate demands in some approximate yet sufficient fashion; it has adapted to its own requirements the play of imagination, the resonance of sentiment, the strength of habit, the ease of familiarity, the impetus of enthusiasm, the power of agreement and consent.  Then a man’s interest is in happy coincidence with his work; his country is also his homeland; its ways are the obviously right ways; its glory and peril are his own. [CWL 3, 216/241]

Clearly schemes of recurrence exist and function.  No less clearly, their functioning is not inevitable.  A population can decline, dwindle, vanish. A vast technological expansion, robbed of its technicians, would become a monument more intricate but no more useful than the pyramids.  An economy can falter, though resources and capital equipment abound, though skill cries for its opportunity and desire for skill’s product, though labour asks for work and industry is eager to employ it; then one can prime the pumps and make X occur; but because the schemes are not functioning properly, X fails to recur.  As the economy, so too the polity can fall apart. … much…in a twilight of straitened but gracious living men await the catalytic trifle that will reveal to a surprised world the end of a once brilliant day. [CWL 3, 209-210/235]

Functional Macroeconomic Dynamics explains to intersubjective groups its intricate demands in some approximate yet sufficient fashion.  It explains in terms of interrelated Gross Domestic Functional Flows.  But ignorance alone and of itself requires the assignment of probabilities in the economic process.  It is probable that unwitting human agents will not understand  the economic process; thus they will not be able consciously to adapt to the norms of the process.

relative to this system man is not an internal factor but an external agent, and that the present economic problems are peculiarly baffling because man as external agent has not the systematic guidance he needs to operate successfully the machine he controls. [CWL 21, 109]

Now the general theorem of continuity is that this (organic whole) has a nature that must be respected. … (otherwise there is a probability, however small, that human agents will) create the paradoxical situation of starvation in the midst of plenty, of workers eager for work and capable of finding none, of investors looking for opportunities to invest and being given no outlet, and of everyone’s inability to do what he wishes to do being the cause of everyone’s inability to remedy the situation.  Such is disorganization.  Continuity, on the other hand, is the maintenance of organization, the stability of the sets and patterns of dynamic relationships that constitute economic well-being in a society. [CWL 21, 74]

In addition to ignorance, there are possible independent variations in the flows of the channels.  In the monetary channels of the Diagram of Rates of Flow, some rates “may begin to vary independently of the others, and adjustment of the others may lag.”CWL 15, 144

The abstract classical relationships in Functional Macroeconomic Dynamics such as P’Q’ = p’a’Q’ + p”a”Q”and f = vw  are universal and valid.  They are general and hold in any number of instances. They are general and, barring disequilibrative borrowing or saving from the Redistributive Function, hold in both equilibrium and disequilibrium.  They constitute a formal cause.  Their validity is independent of human psychology. They are independent of the human psychology of the efficiently causal humans.  Though they cannot predict, they explain the current, purely-dynamic process and provide a guiding formulaic scheme to measure equilibrium and disequilibrium by application of secondary determinations.

relative to this system man is not an internal factor but an external agent, and that the present economic problems are peculiarly baffling because man as external agent has not the systematic guidance he needs to operate successfully the machine he controls. [CWL 21, 109]

Precise values at some distant point in time cannot be predicted.  The classical laws of the economic process are complemented by the probabilities of occurrence of understanding and cooperation, and by the vagaries of weather as it affects crops, the vagaries of politics as they affect institutional structures, etc.  Thus participants in the process are confronted with probabilistic risk.  Yet, we can understand the classical mechanism.

A condition of circuit acceleration was seen … to include the keeping in step of basic outlay, basic income, and basic expenditure, and on the other hand, the keeping in step of surplus outlay, surplus income, and surplus expenditure.  Any of these rates may begin to vary independently of the others, and adjustment of the others may lag. But any systematic divergence[3]brings automatic correctives to work.  The concomitance of outlay and expenditure follows from the interaction of supply and demand.  The concomitance of income with outlay and expenditure is identical with the adjustment of the rate of saving to the requirements of the productive process. [CWL 15, 144]

Entrepreneurs shoulder risk. Initial assumption of the risk of loss by being the doer doing the organizing, development, and managing of something that previously did not exist provides a right to own and manage property, to charge rent in the form of interest or dividends, and to donate wisely for the benefit of society.  But the occurrence of events beyond the entrepreneur’s control may cause the entrepreneur and his investors to go bankrupt and lose it all.

Still, entrepreneurs are not the only people shouldering risk.  Their employees also shoulder the risk of losing their employment because of technological change or the failure of their employer.

The economic process is fraught with indeterminacy.  But this admission is not to deny that a) classical laws exist, b) humans can understand the norms and precepts provided by these classical laws, and c) “the analysis itself will provide rather convincing indicators, and as expertise develops the new tricks of a new trade, there well may be discovered methods of attaining a sufficient accuracy for practical purposes.”CWL 15, 72

We set out to indicate the existence of an objective mechanical structure of economic activity, of something independent of human psychology, of something to which human psychology must adapt itself if economic activity is not to become a matter of standing in a tub and trying to lift it. [CWL 21, 56]

While the discovery of the classical laws of the economy is not the achievement of means of prediction and control of the macroeconomic mechanism, prediction is not the primary end and true aim of science.  The primary end of science is verification of understanding.

Again,

For Lonergan, prediction and control are not legitimate ends of science because they are not the same as verified understanding, which is the true aim of science.  Moreover, prediction and control in the area of the so-called applied human sciences conflict with the very nature of the subject matter of human science: on the one hand, prediction and control depend upon and imply the policy of elimination of human freedom; on the other, human freedom is something that may just spring up even in situations in which people have managed practically to eliminate it. [CWL 15, Editors’ Introduction, ftnt 32, xxxvii]

However, we can measure and relate functional flows so as to achieve norms, precepts, and a basis of goodwill.

It is true that the distinction between basic and surplus is functional (rather than profit and loss categorial), and that a number of activities may at one time be surplus and at another basic. So (the conventional accounts of) labor, services, power, transportation, materials can be known as contributions to the basic or surplus function only through further determinations and even special inquiries…….still the analysis itself will provide rather convincing indicators, and as expertise develops the new tricks of a new trade, there well may be discovered methods of attaining a sufficient accuracy for practical purposes. [CWL 15, 72]

Lonergan’s theoretical model of the pure cycle is an “idealization,” explaining and helping us to understand the phenomenon called the objective economic process in the real world.  It is a theoreticalmodel grounded in a macroeconomic theory.  It represents only one possible combination of flows forming a properly formed cycle in a manifold of possible properly formed cycles, plus possible deformed trade cycles.  However, the process has an exigence for a pure cycle and a model of a pure cycle serves to explain and set norms for the economic process.

Lonergan has introduced certain assumptions about rates of growth and acceleration.  These assumptions constitute something of a ‘model’ of a pure cycle.  That model is a four-phase cycle, … Such a model represents only one possible instance of a pure cycle; there are a manifold of other possible pure cycles, and a still larger possible aberrant ‘trade’ cycles. Lonergan’s use of this model at this point in the text merely illustrates his more general principles, … [CWL 15, 126, ftnt 165]

Lonergan’s aggregate, functional, and dynamic analysis of the pure cycle of the productive process of the economic good of order, like his idea of the good of order overall … may be thought of as a (theoretical) model, “an intelligible, interlocking set of terms and relations that it may be well to have about when it comes to describing reality or to forming hypotheses,” that he thought of as more than a model … , since it also would have the hypothetical normativity of any explanatory correlations empirically verifiable in data.  As explanatorily normative in this sense, it would manifest a trans-social and transcultural invariance, since it specifies the fundamental macroequilibria that “are the conditions of a properly functioning economy” (above p. 92).  They are the equilibria that have to be maintained if an economy chooses to remain in a stationary state, to embark on a long-term expansion, to distribute its benefits to the vast majority of its members, and so to return to a more affluent stationary state until such time as further expansion beckons.”….(the) analysis is relevant to any economy in anysociety or culture that has undergone a takeoff. [CWL 15 117 ftnt ]

This hypothetical normativity of the ideal system in the form of a mathematical model is critical.  Comparison with this hypothetical, scientific normativity reveals clearly the flaws in the economy and in other analyses of the economy.

I am on the edge of identifying accurately … the fundamental mess in Picketty’s work, as well as in a whole plethora of authors engaged with issues of income inequality.  The mess consists in the use of flawed characterizations in selecting and ordering data. … It is like a physicist searching data for traces of the Higgs particle without eyes laden with the standard model.  [McShane 2014, 62

In current physics there is a standard model used as an heuristic guide in discovery, selection of data, and empirical verification. Similarly in macroeconomics there is a set of equations comprising the standard model called Functional Macroeconomic Dynamics, which must be used in explanation of phenomena such as income inequality.

Abstract laws are complemented by concrete probabilities.

The exchange economy is fraught with indeterminacy.  While the economic process has classical laws of its own to which the economic community should adapt, the economic community is subject to ignorance, misinterpretation, poor judgment, mistaken anticipations, egoist bias, group bias, a bias to ad hoc, supposedly commonsense adjustments rather than to theory.  Drivers of the “economic motor car” include individual humans as consumers, individual humans as competing entrepreneurs, the collective in power[4]as taxer and spender, and the Central Bank as manager of the money supply and intervener in the market to manipulate the money supply and distort interest rates.

 

 

[1]CWL 3, 48 etc re non-systematic manifold

[2]

(39)

 

(40)

 

(41)

 

(42)

 

 

[3]See Strang for the mathematics and technical meaning of divergence.

[4]The “collective in power” is the government.