Week Ten

1
Week Ten

• Economic Dynamics

2
Recap

• Methodology
• Linear progression from myth to science (Popper)
  vs
• Competing paradigms (Kuhn/Lakatos)
• This week
• Dynamics vs Statics

3
The Problem

• Economy is dynamic
• Exists in time
• Changes over time
• But 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
• Dont! Develop dynamic, nonequilibrium economics
  instead
• Both approaches compete in literature

4
An Analogy

• Riding a bicycle
• 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 art of riding bike exploits centripetal
  forces which dont exist when bike is stationary
• Static art of balancing irrelevant to dynamic art
  of riding!
• So why do economists do Statics?

5
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)

6
20th Century as the Century of Dynamics?

• 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 sonn 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
  father of marginal productivity theory of
  distribution 1898 1)
• 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. (Clark 1898 9)

7
20th Century as the Century of Dynamics?

• 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 10-11)
• Great expectations but little done until Great
  Depression
• Frisch and exogenous explanation for economic
  cycles
• Harrods endogenous explanation

8
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

9
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 Keyness GT into
  dynamics
• His dynamic equilibrium unstable nonequilibrium
  model
• Derivation starts from static Keynesian equality
  of S and I

10
Harrods knife edge
11
Harrods knife edge
12
Harrods knife edge
13
Harrods knife edge
14
Harrods knife edge
Savings ratio
Rate of growth
Incremental stock to output ratio (ICOR)
15
Harrods knife edge

• Types of growth
• Actual growth
• g.cps
• cp actual ICOR actual accumulation of stocks in
  given period
• Warranted growth what fulfilled capitalist
  expectations
• gw.cs
• c desired ICOR ratio of change in stocks to rate
  of growth that capitalists want
• Natural maximum sustainable rate of growth
• gn

16
Harrods knife edge

• Reciprocal relation between g gw
• If actual growth exceeds warranted, then actual
  ICOR (accumulation of stocks) less than desired
  ICOR
• If g gt gw, then cp lt c since both g.cpgw.cs
• 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 lt gw, then cp gt c
• Capitalists decrease orders to restore desired
  ICOR
• Growth declines
• Dynamic equilibrium unstable

17
Harrods knife edge

• Explains growth and cycles
• If ggtgw
• economy booms
• eventually hits overfull employment constraints
• economy turns down
• If gltgw
• economy slumps
• hits rock bottom
• need to replace equipment (depreciation) forces
  ive investment
• restarts upward pattern

18
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 Harrods model
• Define growth as

• Desired investment a function of change in output

• Define actual consumption as

• Therefore actual saving is

• Equate the two (Keynesian SI)

• 2nd order difference equation

19
Hicks interprets Harrod
Cycles alright, but whatever happened
to Growth? Knife-edge instability?
20
Hicks interprets Harrod
clt1, cycles peter out
cgt1, cycles explode
21
Hicks interprets Harrod

• Problems
• Equation generates cycles, but not growth Ye
  zero!
• Cycles unstable for c gt 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 lt 1
• Assume exogenous shocks to explain persistence of
  cycle

22
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 Hickss model based on an error
• Equation results from equating desired investment
  to actual savings
• Keynesian SI applies to ex-post, actual figures
  only
• Correcting this

23
Correcting Hicks on Harrod

• Desired investment becomes actual investment

• Investment added to capital stock

• Capital stock determines output

• A 3rd order difference equation

• Generates growth cycles, as Harrod believed

24
Correcting Hicks
25
The importance of being nonlinear

• Previous model a quirk
• Linear model (just constants and variables, no
  powers, etc.)
• Generates sustained cycles (for cgtv)
• Most linear models
• Cycle to equilibrium (clt1 in Hicks)
• Rigid cycles (c1 in Hicks)
• Unstable (cgt1 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

26
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
• Nonlinearity necessary for proper dynamics

27
The importance of being nonlinear
Linear models can be
Cycles in linear system require
Frisch/Hicks/Econometrics approach
Harrods 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 Lorenzs weather model
29
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
• Many non-mainstream nonlinear models developed
• Key example Goodwins predator-prey model
  (1967)
• Based on Marxs model, Capital I Ch. 25 (Week 4)

30
Sample nonlinear model

• Marxs model
• High wages--gtlow investment--gtlow growth--gtrising
  unemployment--gtfalling wage demands--gtincreased
  profit share--gtrising investment--gthigh
  growth--gthigh employment--gtHigh wages cycle
  continues
• Goodwin draws analogy with biology
  predator-prey models
• Rate of growth of prey (fish--gtcapitalists!)
  depends ively on food supply and -ively
  interactions with predator (shark--gtworkers)
• 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 growth of Sharks
Rate of death in absence of Fish to eat

• Generates a cycle
• Lots of fish--gtlots of interactions with
  Sharks--gtrapid growth
• of Sharks--gtFall in Fish numbers--gtless
  interactions with Sharks
• --gtFall in Shark numbers--gtLots of fish again...

32
Predator-Prey cycles
Equilibrium here, but system will never reach it
33
Goodwins model

• Goodwin saw in Marxs 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
Goodwins model
35
Goodwins model
36
Goodwins model
37
Goodwins model
Labor productivity (a) and population (N) both
assumed to grow at constant rates
38
Goodwins model
Worked out using chain rule
Model reduces to system of 2 equations
and results in predator-prey system
39
Goodwins model
Generates growth with cycles
40
Goodwins model

• Successfully renders Marxs model
• Explains trade cycle via class conflict over
  income shares
• Nonequilibrium model
• Both growth and cycles
• Cycles have long term impact

Lost output (and employment) due to cycles
41
Current state of dynamics

• Undergoing revival since mid-80s
• 3 streams
• Neoclassical
• real business cycle
• Increasing returns to scale explanation
• Still using linear models
• Non-neoclassical
• Kaldor/Goodwin based nonlinear models
• Complexity analysis
• Inspired by chaos theory in physics, evolution
  in biology

42
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

43
Complexity Theory
For low values of a, tapers to stable equilibrium
For a2, a 2-valued cycle population overshoots
equilibrium, then undershoots, etc.
For a gt 2.7, apparently random behaviour
44
Conclusion

• Dynamics now hot area of economics
• Much interaction with other sciences
• Biology
• Computing
• Physics
• Non-neoclassical models now match neoclassicals
  in mathematical sophistication
• Economics may finally grow up
• but most economists today still woefully ignorant
  of dynamics

45
Conclusion

• Jevons/Marshall attitude still dominates most
  schools of economic thought, from textbook to
  journal
• Taslim Chowdhury, Macroeconomic Analysis for
  Australian Students the examination of the
  process of moving from one equilibrium to another
  is important and is known as dynamic analysis.
  Throughout this book we will assume that the
  economic system is stable and most of the
  analysis will be conducted in the comparative
  static mode. (1995 28)
• Steedman, Questions for Kaleckians The general
  point which is illustrated by the above examples
  is, of course, that our previous 'static'
  analysis does not 'ignore' time. To the contrary,
  that analysis allows enough time for changes in
  prime costs, markups, etc., to have their full
  effects. (Steedman 1992 146)

46
Conclusion A mathematician on economics

• A baby is expected to first crawl, then walk,
  before running. But what if a grown-up man is
  still crawling? At present, the state of our
  dynamic economics is more akin to a crawl than a
  walk, to say nothing of a run. Indeed, some may
  think that capitalism as a social system may
  disappear before its dynamics are understood by
  economists. (Blatt 1983 5)