Lecture Ten

1. Lecture Ten Economic Dynamics

2. The Problem • Economy is dynamic • Exists in time • Changes over time • But most economists analyse it “as if” static—ignore time • Some mathematicians (e.g., Blatt) see this as “immaturity” • How to reconcile dynamic reality & static methods? Two ways • Argue static determines long term • Short-term cycles explained by external shocks to stable economic system • Don’t! Develop dynamic, nonequilibrium economics instead • Both approaches compete in literature

3. Classical Economics and Dynamics • Classical economists sometimes worked with “verbal differential equations” • Expressed ideas as relations between variable • E.g., level of division of labour • And economic growth. E.g., Smith: growth in capitalism driven by increasing specialisation of labor: • “a workman not educated to this business … could scarce, perhaps, with his utmost industry, make one pin in a day… • But in the way in which this business is now carried on, … ten persons … could make among them upwards of forty-eight thousand pins in a day…” • Rate of growth of capitalism thus a function of rate of increase in specialisation of labor…

4. Classical Economics and Dynamics • Ricardo: eventual stagnation of capitalism propelled by dynamics of food production and population growth: • “The most fertile, and most favourably situated, land will be first cultivated… • When land of an inferior quality is taken into cultivation, the exchangeable value of raw produce will rise, because more labour is required to produce it… • the advantages of fertile over inferior lands are … transferred from the cultivator, or consumer, to the landlord… • if, as is absolutely certain, wages should rise with the rise of corn, then their profits would necessarily fall… • The natural tendency of profits then is to fall; for, in the progress of society and wealth, the additional quantity of food required is obtained by the sacrifice of more and more labour.”

5. Classical Economics and Dynamics • Marx: stagnation and overthrow of capitalism driven by tendency of capitalists to increase machinery/labour ratio: • “the gradual growth of constant capital in relation to variable capital must necessarily lead to a gradual fall in the general rate of profit, so long as the rate of surplus-value, … remains the same.” • Classical economists therefore “dynamic friendly” (whether notions erroneous or not!) • But in 1870, Classical school supplanted by neoclassical • emphasis upon dynamics replaced by emphasis upon equilibrium • dynamics dispensed with completely… • First, why does “dynamics” matter?

6. An Analogy • Riding a bicycle: do you need to do “statics” before “dynamics” • do you need to know how to balance a stationary bicycle before you can ride it? • Economist: “Yes!: must learn statics before you can do dynamics” • (1) Learn how to balance bike while stationary • (2) Ride in straight line, using skills acquired in (1) • (3) Turn bike…? How? Try handlebars… • (4) Fall flat on face! • Real world: “No!” • Dynamic act of riding bike exploits centripetal forces, which don’t exist when bike is stationary • Static balancing act irrelevant to dynamics of riding! • So why do economists “do” Statics?

7. The early days: Statics “because it was easy” • Historically, the “KISS” principle: • “If we wished to have a complete solution … we should have to treat it as a problem of dynamics. But it would surely be absurd to attempt the more difficult question when the more easy one is yet so imperfectly within our power.” (Jevons 1871 [1911]: 93) • “...dynamics includes statics… But the statical solution… is simpler…; it may afford useful preparation and training for the more difficult dynamical solution; and it may be the first step towards a provisional and partial solution in problems so complex that a complete dynamical solution is beyond our attainment.” (Marshall, 1907 in Groenewegen 1996: 432) • Neoclassical “Founding Fathers” expected successors would make the move from statics to dynamics:

8. 20th Century as the Century of Dynamics? • J.B. Clarke, originator of marginal product theory of income distribution, in 1898: • “A point on which opinions differ is the capacity of the pure theory of Political Economy for progress. • There seems to be a growing impression that, as a mere statement of principles, this science will soon be fairly complete… • It is with this view that I take issue. • The great coming development of economic theory is to take place, as I venture to assert, through the statement and the solution of dynamic problems.” (J.B. Clark 1898: 1)

9. 20th Century as the Century of Dynamics? • Why does dynamics matter (according to Clark)?: • “A static state is imaginary. All actual societies are dynamic… Heroically theoretical is the study that creates, in the imagination, a static society.” • “It will bring the society that figures in our theory into a condition that is like that of the real world. It will supply what a static theory openly and intentionally puts out of sight; namely, changes that alter the mode of production, and act on the very structure of society itself.” (Clark 1898: 9-11) • Great expectations… but little development of dynamics until Great Depression • Then two competing approaches put forward: • Frisch’s exogenousexplanation for economic cycles • Harrod’s endogenous explanation

10. Frisch’s dynamics • Had preference for causal model: Deterministic dynamic macro-model “to explain the movements, cyclical or otherwise, of the system” (Frisch 1933) • But too difficult; instead modelled cycles as damped propagation mechanism + exogenous shocks: “rocking horse and hammer” analogy • Standard became: • Stable linear system (propagation) • Subject to random exogenous shocks (impulse)

11. The beginnings of dynamics • Frisch 1933: trade cycle explained “by the fact that certain exterior impulses hit the economic mechanism and thereby initiate more or less regular oscillations” • Underlying highly stable “propagation mechanism” (like rocking horse) • Random shocks from outside (“impulses”) • Each shock sets up single regular harmonic pattern (like stone in pool of water) • Overlay of many shocks gives irregular cycles (lots of stones) • Gave rise to econometrics • Dominant method: fit “linear stochastic” model to economic data

12. Harrod: Growth & cycle theory • Harrod (1939) • Criticised Frisch paradigm • Divorces growth from cycles when “the trend of growth may itself generate forces making for oscillation” (OREF II 38) • Has no explanation for growth or shocks • Developed combined theory of growth/cycle • Basic method: extension of Keynes’s GT into dynamics • His dynamic equilibrium unstable: nonequilibrium model • Derivation starts from static Keynesian equality of S and I:

13. Harrod’s “knife edge” Savings ratio Rate of growth Incremental stock to output ratio (“ICOR”)

14. Harrod’s “knife edge” • Types of growth • Actual growth: • g.cp=s • cp actual ICOR: actual accumulation of stocks in given period • “Warranted growth”: what fulfilled capitalist expectations • gw.c=s • c desired ICOR: ratio of change in stocks to rate of growth that capitalists want • “Natural”: maximum sustainable rate of growth • gn • Should have called it “gm” for “maximum” rather than “gn” for “natural”!

15. Harrod’s “knife edge” • Reciprocal relation between g & gw: • If actual growth exceeds warranted, then actual ICOR (accumulation of stocks) less than desired ICOR: • If g > gw, then cp < c since both g.cp=gw.c=s • Capitalists will increase orders to restore desired ICOR • Growth accelerates • If actual growth below warranted, then actual ICOR (accumulation of stocks) more than desired ICOR: • If g < gw, then cp > c • Capitalists decrease orders to restore desired ICOR • Growth declines • Dynamic equilibrium unstable

16. Harrod’s “knife edge” • Explains growth and cycles • If g>gw • economy booms • eventually hits overfull employment constraints • economy turns down • If g<gw • economy slumps • hits rock bottom • need to replace equipment (depreciation) forces +ive investment • restarts upward pattern

17. Hicks “interprets” Harrod • Hicks could not accept that equilibrium unstable: • “A mathematically unstable system does not fluctuate; it just breaks down” (OREF II 56) • Reworked Harrod’s model: • Define growth as • Desired investment function of change in output: • Define actual consumption as • Therefore actual saving is • Equate the two (“Keynesian S=I”): • 2nd order difference equation:

18. Hicks “interprets” Harrod • With sample parameter values, one simulation yields: • Cycles alright, but whatever happened to • Growth? • “”Knife-edge” instability?

19. Hicks “interprets” Harrod • Depending only on value of c, model has just 4 possible states: c<1, cycles peter out: c>1, cycles explode: • c=1, cycles continue forever • c>>1, explosive collapse—infinitely negative Y!

20. Hicks “interprets” Harrod • Problems • Equation generates cycles, but not growth: Ye = zero! • Cycles unstable for c > 1 • But c similar to v, the accelerator: ratio of capital stock to output • v between 2 & 3 for most countries • “Solutions” • Assume exogenous growth at “natural” rate • Assume c < 1 • Assume exogenous shocks to explain persistence of cycle

21. Hicks “interprets” Harrod • Hicks interpretation dominates trade cycle theory • Growth becomes separate topic, dominated by neoclassical models • Hicks approach extended/modified by Samuelson, Domar • Led nowhere; interest in trade cycle declined over 60-70s • Revival in 80s with neoclassical “real business cycle” models • But Hicks’s model based on an error • Equation results from equating desired investment to actual savings • Keynesian S=I applies to ex-post, actual figures only • Correcting this:

22. Correcting Hicks on Harrod • Desired investment function of change in output: • Actual investment is increase in capital: • Capital stock determines output • Desired investment is undertaken and added to capital: • Substituting for K with vYt: • A 3rd order difference equation: • Generates growth & cycles, as Harrod believed:

23. Correcting Hicks • Cycles & exponential growth if c>v: • Linear growth if c=v: • Taper to equilibrium if c<v: • Far more robust & “interesting” behaviour than accepted Hicks model…

24. The importance of being nonlinear • Previous model a “quirk”: • Linear model—just constants & variables • Yet generates sustained cycles (for c>=v) • Most linear models: • Cycle to equilibrium (c<1 in Hicks) • Rigid cycles (c=1 in Hicks) • Unstable (c>1 in Hicks) • Frisch/Hicks argument that “unstable system … just breaks down” only true for linear systems • Nonlinear systems can have unstable equilibria and not break down • Truly useful dynamic models are nonlinear:

25. The importance of being nonlinear • Economist attitudes garnered from understanding of linear dynamic systems • Stable linear systems do move from one equilibrium to another • Unstable linear dynamic systems do break down • Statics is the end point of dynamics in linear systems • So economics correct to ignore dynamics if economic system is • linear, or • nonlinearities are minor; • one equilibrium is an attractor; and • system always within orbit of stable equilibrium • All the above false: • Nonlinearity therefore essential for proper dynamics:

26. The importance of being nonlinear • Kaldor (1940) first economist to realise this • Began with linear model • Realised that this had only 2 states • “dangerous instabilities” or • “more stability than the real world appears, in fact, to possess” • Deduced that therefore, economic relations “cannot be linear” • Nonlinearities can arise: • Naturally: one variable (wage) times another (employment) • Behaviourally: Phillips curve, investment as function of rate of profit… • Result in very different, more realistic dynamics…

27. The importance of being nonlinear Linear models can be: Cycles in linear system require Frisch/Hicks/Econometrics approach Harrod’s initial model

28. The importance of being nonlinear • Nonlinear systems can be: • Cycles can occur because system is: Not so different from linear model Completely unlike linear model An example: Lorenz’s weather model Click here to download Vissim viewer • Many non-mainstream nonlinear economic models now • Key example: Goodwin’s “predator-prey” model (1967)

29. Marx’s “cyclical growth model” • Based on Marx’s model, in Capital I Chapter 25: • “a rise in the price of labor resulting from accumulation of capital implies … • accumulation slackens in consequence of the rise in the price of labour, because the stimulus of gain is blunted. • The rate of accumulation lessens; • but with its lessening, the primary cause of that lessening vanishes, i.e. the disproportion between capital and exploitable labour power. • The mechanism of the process of capitalist production removes the very obstacles that it temporarily creates. • The price of labor falls again to a level corresponding with the needs of the self-expansion of capital, whether the level be below, the same as, or above the one which was normal before the rise of wages took place…

30. Sample nonlinear model • Marx’s model • High wages low investment  low growth  rising unemployment  falling wage demands  increased profit share  rising investment  high growth  high employment  High wages: cycle continues • Goodwin draws analogy with biology “predator-prey” models • Rate of growth of prey (fish=capitalists!) depends +ively on food supply and -ively interactions with predator (shark=workers) • Rate of growth of predator depends -ively on number of predators and +ively on interactions with prey:

31. Predator-Prey cycles Food supply Rate of growth of Fish Interactions with Sharks Interactions with Fish Rate of death in absence of Fish to eat Rate of growth of Sharks • Generates a cycle: • Lots of fish lots of interactions with Sharks rapid growth of Sharks Fall in Fish numbers less interactions with Sharks Fall in Shark numbers Lots of fish again...

32. Predator-Prey cycles Equilibrium here, but system will never reach it

33. Goodwin’s model • Goodwin saw in Marx’s model • Rate of change of workers’ wage demands a nonlinear function of rate of employment/output • Rate of change of employment/output a function of wages share Basic mechanisms of model Wage change depends on employment Capitalists invest all their profit and a “Phillips curve” Profit Wages Rate of change of wages depends upon Output Rate of employment

34. Goodwin’s model Labor productivity (a) and population (N) both assumed to grow at constant rates

35. Goodwin’s model Worked out using “chain rule” Model reduces to system of 2 equations and results in predator-prey system:

36. Goodwin’s model • Successfully renders Marx’s model • Explains trade cycle via class conflict over income shares • Nonequilibrium model • Both growth and cycles • Cycles have long term impact: • System spends short time above equilibrium, long time below it • Goodwin one of many strands of modern economic dynamics • Many dynamic researchers today influenced by Schumpeter’s “evolutionary economics”:

37. Evolutionary Economics • Model of evolutionary change and “creative destruction” • “Micro” level: firms search for advantages over other firms • Advantages come from innovation (rather than price competition) • Process leads to macro-level business cycles: • “I explain the phenomenon of business fluctuations … solely by an objective chain of causation which runs its course automatically, that is by the effect of the appearance of new enterprises upon the conditions of the existing ones.” (Schumpeter, Theory of Economic Development, p. 213)

38. Schumpeter & Evolutionary Economics • Growth process necessarily non-equilibrium and discontinuous: • “does this … proceed in unbroken continuity, is it similar to the gradual organic growth of a tree? • Experience answers in the negative. It is a fact that the economic system does not move along continually and smoothly. • Counter-movements, setbacks, incidents of the most various kinds, occur which obstruct the path of development; there are breakdowns in the economic value system which interrupt it.” (216)

39. Schumpeter & Evolutionary Economics • Breakdowns could be randomly distributed through time • There would then be no “trade cycle”, only “deviations from trend” • But “new combinations are not, as one would expect according to general principles of probability, evenly distributed through time … but appear, if at all, discontinuously in groups or swarms.” (223) • “If the new enterprises … were to appear independently of one another, there would be no boom and no depression as special, distinguishable, striking, regularly recurring phenomena. For their appearance would then be, in general, continuous…” (224) • Three reasons for the “clumped” nature of new innovations & associated booms:

40. Schumpeter & Evolutionary Economics • “new combinations will not grow out of the old firms or immediately take their place, but appear side by side, and compete, with them.” (226) • Credit extended to new entrepreneurs causes “a very substantial increase in purchasing power all over the business sphere. This starts a secondary boom, which spreads over the whole economic system and is the vehicle of the phenomenon of general prosperity…” • General prosperity allows all to profit: • “new purchasing power goes in bulk from the hands of entrepreneurs to the owners of material means of production, to all producers of goods for "reproductive consumption", and to the workers, and then oozes into every economic channel, … • all existing consumption goods finally sold at ever-rising prices…” (226)

41. Schumpeter & Booms • “Every normal boom starts in one or a few branches of industry (railway building, electrical, and chemical industries, and so forth), and … derives its character from the innovations in the industry where it begins. • But the pioneers remove the obstacles for the others not only in the branch of production in which they first appear, but, owing to the nature of these obstacles, ipso facto in other branches too… • Hence the first leaders are effective beyond their immediate sphere of action and so the group of entrepreneurs increases still further and • the economic system is drawn more rapidly and more completely than would otherwise be the case into the process of technological and commercial reorganisation which constitutes the meaning of periods of boom.” (229)

42. Schumpeter & Booms • So a boom is a positive feedback process: • Financing of one invention makes it easier for other inventions to be financed • One success in one industry sector makes it easier for others in the same sector to succeed • Spillover of finance into rest of economy makes new businesses and old ones profitable • Conventional economics dominated by presumption of negative feedback: • Increase in price reduces demand • Rise of profits encourages new entrants who reduce profits…, etc…

43. Schumpeter & Turning points… • Boom forces up costs of existing businesses: • “the new entrepreneur's demand for means of production, which is based upon new purchasing power … drives up the prices of these.” (232) • “the new products come on the market after a few years or sooner and compete with the old… • “At the beginning of the boom costs rise in the old businesses; • later their receipts are reduced, first in those businesses with which the innovation competes, but then in all old businesses, • in so far as consumers' demand changes in favor of the innovation…”

44. Schumpeter & Slumps… • “The average time which must elapse before the new products appear—though of course actually dependent upon many other elements—fundamentally explains the length of the boom. • This appearance of the new products causes the fall in prices, • which on its part terminates the boom, • may lead to a crisis, • must lead to a depression, • and starts all the rest…” (233) • New technology often only has general impact upon economy after it causes a slump:

45. Schumpeter & Slumps… • “the appearance of the results of the new enterprises leads to a credit deflation, • because entrepreneurs are now in the position—and have every incentive—to pay off their debts; • and since no other borrowers step into their place this leads to a disappearance of the recently created purchasing power just when its complement in goods emerges…” (233) • Cycle seen as necessary aspect of capitalism, rather than something to be eradicated; • Has negative aspects as well as positive…

46. Schumpeter & Cycles… • “the boom … creates out of itself an objective situation, which … makes an end of the boom, leads easily to a crisis, necessarily to a depression, and hence to a temporary position of relative steadiness and absence of development. • The depression as such we may call the "normal" process of resorption and liquidation; • the course of events characterised by the outbreak of a crisis—panic, breakdown of the credit system, epidemics of bankruptcies, and its further consequences—we may call the "abnormal process of liquidation."” (236) • But even depressions are “worthwhile”:

47. Schumpeter & Cycles… • “the period of depression does something else, which indeed comes less to the fore than those phenomena to which it owes its name: • it fulfils what the boom promised. • And this effect is lasting, while the phenomena felt to be unpleasant are temporary. • The stream of goods is enriched, production is partly reorganised, costs of production are diminished, • and what at first appears as entrepreneurial profit finally increases the permanent real incomes of other classes.” (245)

48. Current state of dynamics • Undergoing revival since mid-80s • 3 streams • Neoclassical • “real business cycle” • Increasing returns to scale explanation • Still using linear models • Unstable model with hyper-rational agents • Non-neoclassical • Kaldor/Goodwin based nonlinear models • “Complexity” & Evolutionary analysis • Inspired by “chaos theory” in physics, evolution in biology

49. Complexity Theory • Nonlinear dynamic systems can develop complicated behaviour from interaction of simple rules • Systems live on border between “chaos” and “order” • Tiny changes can push system from order into chaos • Undermines “rational expectations” (Week 7): • Impossible to predict course of complex system • Example: lemmings • Rate of growth of lemmings • +ive fn of current population • -ive fn of overcrowding • Combining:

50. Complexity Theory Low values of a: taper to equilibrium: • For a=2, a 2-valued cycle: • Population overshoots equilibrium, then undershoots, etc. • For a > 2.7, apparently random behaviour • System “chaotic” • Generates aperiodic cycles • “Logistic map” a common type of dynamic model today