Introduction, Diagrams, and Framework

Preliminary note: Recently there’s been increased interest in Paul Romer’s “Endogenous Technological Change” in Bernard Lonergan’s Framework. In this subsection entitled Introduction, Diagrams, and Framework , the software didn’t pick up every aspect of the main spreadsheet entitled  The Structure of Romer’s “Endogenous Technological Change” as Rendered in Lonergan’s General, Universal, and Always Current Framework.  I’d be happy to send a good copy via an email attachment or the postal service to anyone who requests it. Please use the Contact Us form accessible on this Home Page. Thanks.
John Costello

The current, purely dynamic, economic process should always exhibit potential for growth; but, depending upon concrete circumstances and human agency, it may actually be a) dynamically growing, b) dynamically stationary, or c) dynamically contracting.

Herein we are comparing two essays treating the immanent intelligibility of the economic process:

Romer, Paul, (1990) Endogenous Technological Change, Journal of Political Economy, Vol. 98, No. 5, Part 2, The Problem of Development: A Conference of the Institute for the Study of Free Enterprise Systems, October., 1990 pp. S71-S102 [Romer, 1990]

Lonergan, Bernard, (1999), Macroeconomic Dynamics: An Essay in Circulation Analysis, ed. Frederick G. Lawrence, Patrick H. Byrne, and Charles Hefling, Jr., vol 15 of Collected Works of Bernard Lonergan, (Toronto: University of Toronto Press) [CWL 15]

There are formal similarities in the two treatments, which justify comparison and contrast within a single framework.  Both posit a hierarchical and sequential productive process of interdependent functional flows.

First, we’ll show, Lonergan’s double-circuited, credit-centered Diagram of Rates of Flow representing and explaining the always current, purely dynamic process; second, we’ll run quickly through Lonergan’s diagrams of how the always current process plays out in transitions over the longer term; third, to compare and contrast  Romer’s and Lonergan’s formal similarities, we’ll rotate Lonergan’s double-circuited schematic 45 degrees counterclockwise, add a third level-circuit of R&D, and demonstrate how Romer’s three hierarchical sectors-circuits, explanatory conjugates, and formulae fit neatly into that three-leveled Lonerganian form.

Romer’s goal is to explain Endogenous Technological Change effected over the very long run by profit-motivated human talent working in firms. Lonergan’s goals ,on the other hand, are, first, to discover the immanent intelligibility, i.e. the general laws, of the current, dynamic process prior to and independent of human psychology, and, second, to demonstrate the laws of a normative, equilibrated transitional expansion implied by Lonergan’s general and universal theory.  And, because Lonergan’s two-part, purely functional and purely relational treatment is a)  encompassing of intrinsic productive cyclicality and of the correlated real monetary circulation, b) at a higher level of abstraction, and c) completely general and universal, his theory is more detailed, more comprehensive, and more explanatory than Romer’s – especially in his treatment of a) the structure of the hierarchical and intrinsically-cyclical productive process, b) the normative circulatory flows of money meeting, in a congruence at the point of sale, rectilinear flows of products in the sequential productive order, and c) the rhythmicality of accumulative “revolutions” in the longer term.

Our major title announces a “framework,”  i.e. a “diagram” or “image” or “form.”  Now, forms and formulae are grasped by insight into image, therefore an image suggesting and leading to insight is worth a thousand words; also, a single formula – both isomorphic with and explanatory of the actual process – is worth a ton of prose.  In a diagram or image

Image and question, insight and concepts, all combine. The function of the symbolism is to supply the relevant image, and the symbolism is apt inasmuch as its immanent patterns as well as the dynamic patterns of its manipulation run parallel to the rules and operations that have been grasped by insight and formulated in concepts. [CWL 3, 18-19/]

By now the reader is familiar with Lonergan’s explanatory schematic and the formulae preceding it [CWL 15, 52-55], but we ask the reader to read once more the three paragraphs at the bottom of that framework and to pay special attention to the meanings and implications of the utterances “function”,  “per”, “interval”, “per interval”, “surplus”, “basic”, and “dividends” for imminent application to the Romer-Lonergan diagram.  Here are those three paragraphs:

Per interval, surplus demand [function], I”, pays E” for current surplus products, and receives dividends i”O” from surplus production [i.e. surplus supply function] and i’O’ from basic production [i.e. basic supply function].

Per interval, basic demand [function], I’, pays E’ for current basic products and for its services receives c”O” from surplus supply [function] and c’O’ from basic supply [function].

Vertical arrows represent transactions between the redistributional area and surplus and basic supply [functions]; horizontal arrows the dealings of demand [functions] with the redistributional area. [CWL 15, 55]

Also, please consider the significance of the key words of several possible alternative titles of Lonergan’s framework other than Diagram of Rates of Flow.  Depending on one’s momentary interest and point of view, this schematic may alternatively be called:

  • The Diagram of Two Operative Circuits Connected by Operative Crossovers
  • The Diagram of Functional Monetary Interdependencies
  • The Configuration of Monetary Conditions
  • The Diagram of Operative Functional Flows of Products, Payments, and Financings
  • The Diagram of Monetary Channels
  • The Diagram of Monetary Transfers
  • The Diagram of the Monetary Correlatesof the Productive Process
  • The Diagram of Interdependent, Implicitly-Defining, Mutually-Conditioning, Velocitous Monetary Functionings
  • The Double-Circuited, Credit-Centered Diagram which Sublates, Supervenes, and Replaces the Single-Circuit, Credit-Centered Diagram of Macroeconomics Textbooks
  • The Functional Framework
  • (Colloquially, because of its shape) Lonergan’s Baseball Diamond

Lonergan replaced the single circuit of the textbooks with the credit-centered, double circuit of Functional Macroeconomic Dynamics.

The entire tradition slipped past Lonergan’s simple move.  I describe the move as paralleling Newton’s move. Newton started within an old culture of two flows: an earthly flow and, to recall ancient searchings, a quintessential flow.  Newton went from two to one.  Lonergan started with a dominant one-flow economic analysis  –  think in terms of the household-firm diagram  –  and separated it into two flows “to form a more basic concept and develop a more general theory.” 21  [McShane 2017, viii]; also see [CWL 21, 11]

Lonergan’s Table of Contents might be labeled:

  • Part I              The Productive Process                                            Sections 1-11
  • Part II             The Exchange Process and Monetary Velocities   Sections 12-17
  • Part III            Phases in Expansion of the Process                         Sections 18-22
  • Part IV             Healing and Creating in History
  • Part V             Cycles, Circuits, and Monetary Circulation             Sections 23-28
  • Part VI             Superposed Circuits – Gov’t and Foreign Trade    Sections 29-31
  • Appendix: History of the Diagram, 1944-1998

Relevant to Parts I, II, III, and V (above) are diagrams (below) which show how the always current process plays out in intrinsically cyclical fashion many times over Romer’s very long term. These are easily located by their Figure numbers corresponding to section numbers in CWL 15.

In these first two diagrams, suppose that k = 1.05 and that r = .9524.

Now, when the surplus stage of the process is effecting a long-term acceleration of surplus activity but as yet not affecting basic activity, one may expect successive values of Q”to increase in geometrical progression.  This gives an initial period, in which the graph of dQ”/Q”is approximately a level straight line. Next, as the surplus expansion develops and devotes more and more of its activity to the long-term acceleration of the basic stage, one may expect no more than a uniform acceleration of the surplus stage.  This gives a second period in which dQ”/Q”is curving downwards with successive values in  decreasing geometrical progression.  Thirdly, as the expansion approaches its maximum in the surplus stage, dQ”reverts to zero and Q”becomes constant.  In this third period dQ”/Q”is again a level straight line but now coincidental with the x-axis; h” is zero, but h’Q”may be great for a notable period to effect a long-term acceleration of the basic stage which, however, gradually declines as replacement requirements begin to mount. [CWL 15, 122-24]

Now, when the acceleration of Q” is uniform, the long-term potential of the surplus stage is increasing, and so the surplus stage is devoting more and more of its efforts to the long-term acceleration of the basic stage; then Q’ will be increasing at an increasing rate, and time series of its values may stand in a geometrical progression to make dQ’/Q’ a level straight line.  When, however, Q” becomes constant, the acceleration of Q’ becomes uniform, and then dQ’/Q’ will curve downwards; and as replacement requirements begin to mount, this downward curve is accentuated until dQ’ reverts to zero.  Thus, both dQ”/Q’ and dQ’/dQ’ are described as initially straight level lines that eventually curve downwards till the acceleration ratios become zero.  One may well ask for an account of the movement of the acceleration ratios  from their initial zeros to the level straight lines.  ¶There are two factors in such a movement: short-term acceleration and the period of generalization of a long-term acceleration. … [CWL 15, 126]

The editors of CWL 15 are careful to point out in a footnote that

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, and is not central to his argument.  In later sections of this essay, where other graphs have been supplied to illustrate Lonergan’s points (for example, in §27, ‘The Cycle of Pure Surplus Income’), an effort has been made to stay as close as possible to the assumptions Lonergan introduced here. [CWL 15, 126, ftnt 165]

However, the instance of a pure cycle which Lonergan uses is based solidly on the valid notions of a surplus period of gestation and a generalization of long-term acceleration.  He remarks:

Without urging the necessity of such a (particular) cycle, one may say that it is solidly grounded in a dynamic structure of the productive process; and one has only to think of the practical impossibility of calculating the acceleration ratios dQ’/Q’and dQ”/Q” to smile at the suggestion that one should try to ‘smooth out the pure cycle.’ [CWL 15, 128]

So, for further background for readers, we insert a graph of Solutions of the  Logistic Equation, AKA the familiar S-Curve, suggesting a pattern of expansion from one level of output to a higher level in a finite world whose economic process is characterized by series of logistic surges and tapering to an asymptote.  Treatment of the Logistic Equation may be found in many calculus texts under the headings: Integration Techniques, or Applications of Integration, or Separable Equations.  The accumulations accelerate increasingly up to the inflection point at the halfway mark where the second derivative (acceleration) is zero; then they decelerate and the  curve begins to bend down.  The S-curve continues asymptotically to the maximum, but, as quoted above, in his model of the pure cycle, Lonergan transfers at the inflection point to a path of uniform increase – “solidly grounded in a dynamic structure of the productive process” – up to the maximum.

Next, we insert a Table of Possibilities from [CWL 15, 114] as a basis for considering a succession of economic phases requiring shifts in incomes in accord with the shifts in the ratio of consumption to investment in cyclical expansion.

Finally, we show the Romer-Lonergan Schematic.  The reader should not leapfrog this detailed Romer-Lonergan schematic; it contains together at once Romer’s long-term formulation – but with permanent current significance – and Lonergan’s current formulation, universally applicable throughout the long run.  Understanding this schematic is vital to the understanding of all we say hence.  It is critical that the reader master the diagram’s a) titles, b) introductory notes, c) the scheme itself, and d) Romer’s equations pertinent to the different levels or circuits of the diagram and comprising his proof of endogeneity and constant exponential growth. Here is the Romer-Lonergan schematic representing Romer’s explanatory conjugates and relations and locating his co-herent equations (some by reference to Romer’s essay) arranged within  Lonergan’s general and universal explanatory framework.  Underneath this minimized image is a download capability to view it in normal magnitude.

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There is no royal road to Romer.  One must wrestle with a) relations among terms within each equation, and b) the interrelations of equations to one another.  Like the scientist Lonergan, the scientist Romer employed implicit definition to reach explanatory conjugates defining mutual relations and mutual relations defining explanatory conjugates.  Also, one must – here and in a subsequent section entitled  Romer’s Assumptions and Their Implications- evaluate Romer’s assumptions and premises: are they acceptable, advantageous and advisable simplifications to teach valid economic principles and relations; or are they unacceptable departures from essential macroeconomic principles and relations rigged to make the mathematics bring us to a foregone conclusion; is the form of  terms and relations isomorphic with real economic relations, or does it fail to be?

Romer’s explanation regarded the very long run.  Lonergan’s essay in CWL 15 explained a) in pages 3-55) the instantaneous conditions of continuity and equilibrium among flows at all times, therefore in the very short run, long run, and very long run, and b) in pages 56-176 the intelligibility of the wavelike expansions and the conditions of the normative equilibrium of interdependent flows in the short run, long run, and very long run.  In the Romer-Lonergan schematic above, justified by formal similarities of the two essays, we have rendered Romer’s long-run form in Lonergan’s general, universal, all-times framework.  And elsewhere we will be noting frequently but uncritically that, because of his narrow purpose and limited scope, Romer deliberately did not treat the lagged temporality and intrinsic cyclicality of the frequently occurring transitions in the growth of the very-long-run process.  And, consequently, while Romer formally demonstrated the possibility of the endogeneity of the expansion of economically useful knowledge and innovation, his form is not a fully satisfactory theoretical model of equilibria and disequilibria with respect to the transitional dynamics of the economic process.