Some instability puzzles in Kaleckian models of growth and distribution

1
Some instability puzzles in Kaleckian models of
growth and distribution

• Eckhard Hein, Marc Lavoie and Till van Treeck

2
The Kaleckian model

• Three essential equations
• A pricing function (income distribution)
• A saving function
• An investment function
• The actual rate of capacity utilization is
  endogenous, determined by demand, even in the
  long run, and so in general will not be equal to
  the normal rate of capacity utilization
• Consequences the paradox of thrift, and under
  some specifications, the paradox of costs

3
Justification

• The Kaleckian model of growth has become a
  workhorse of heterodox economics since the early
  1980s, proving to be highly flexible.
• Some authors claim however that one may be
  Kaleckian or Keynesian in the short run but
  needs to be Classical in the long run (Duménil
  and Lévy 1999, Shaikh 2007).
• Others argue that the current dominance of the
  Kaleckian model () is unfortunate for
  post-Keynesian and Structuralist macroeconomics
  (Skott 2008).
• The purpose of this paper is to show that
  these opinions are premature.

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Consequences of the critique

• Somehow the actual rate of capacity utilization
  must be brought back to its normal rate
• Somehow Harrods warranted rate of growth must
  constrain the economy, and the classical equation
  must hold
• gw s/v sprn
• The paradoxes of thrift and of costs dont hold
  anymore

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Outline

• We distinguish Keynesian and Harrodian
  instability
• We look at the various mechanisms that have been
  suggested to bring back the actual rate of
  utilization to its normal rate
• We question the need for such a mechanism
• We offer alternative mechanisms that retain
  Kaleckian features

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Instability

• There have been two somewhat related kinds of
  criticisms
• Keynesian stability (the slope of the saving
  function is steeper than that of the investment
  function), as assumed in Kaleckian models, is
  doubtful.
• Harrodian instability (the investment function
  shifts out if u gt un)), as assumed away by
  Kaleckians, is likely.
• Therefore, there must exist some other mechanism
  that brings back the economy towards its normal
  rate of capacity utilization (shifting back in
  the investment function, or shifting the saving
  function)

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Keynesian instability Short period
g
gi
gs
gi(ue)
g
u
u
uK
ue
8
Harrodian instability
g
gs
C
g3
gi
?3
g2
?2
B
?0g0
A
u
u1
un
u2
u3
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Consequences

• Whether there is Keynesian or Harrodian
  instability, the consequences are the same a
  boost in effective demand leads to an ever-rising
  rate of accumulation and rate of utilization.
• In practice, the two kinds of instability may be
  difficult to disentangle.

10
Some classical mechanisms designed to bring
back utilization to its normal rate

• Mechanisms acting on the saving function
• The Cambridge price mechanism, acting on the
  profit margin
• The retention rate solution, acting on the
  overall propensity to save

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The Cambridge price mechanism

• (Robinson 1956, Kaldor 1956 Harcourt/Kenyon
  1977, Eichner 1976, Wood 1975, Marglin 1984,
  Skott 1989)
• The profit margin rises as long as u gt un, thus
  rotating the saving function.
• The paradox of thrift is only retained if
  accumulation depends on the profit rate
• The mechanism has been described either as an
  ultra-short run mechanism, or as a long-run
  mechanism.
• The profit margin, hence real wages fall, when
  employment rates and growth are high. Doubtful?

,
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The retention rate solution

• This is the Shaikh I solution (2007)
• This classical synthesis allows us to preserve
  central Keynesian arguments such as the
  dependence of savings on investment and the
  regulation of investment on expected
  profitability, without having to claim that
  actual capacity utilization will persistently
  differ from the rate desired by firms (Shaikh)
• The retention ratio of firms rises as long as u gt
  un, thus rotating the saving function
• However, the paradoxes of saving and of costs
  disappear, because g ?rrn
• Doubtful?

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Shaikh I solution
g
gs
gi
g1
g2
g0
u
u1
un
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More classical mechanisms designed to bring
back utilization to its normal rate

• Mechanisms acting on the investment function
• Monetary authorities get scared of inflation and
  raise real interest rates
• Capitalists get scared of full employment and
  reduce the rate of growth of output
• Capitalists have perfect foresight and revise
  their sales expectations

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Monetary authorities get scared of inflation, and
raise real interest rates, thus lowering
investment

• The Duménil and Lévy (1999) mechanism
• Similar to the New consensus mechanism
• Also has resemblance with Robinsons inflation
  frontier
• Both the paradoxes of thrift and of costs get
  wiped out

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The Duménil and Lévy mechanism low saving rates
lead to high growth in the short run, but lower
growth in the long run
g
gs
gi
g1
g0
g2
u
u1
us
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Drawbacks of the Duménil and Lévy mechanism

• Higher rates of utilization may not mean higher
  or accelerating inflation rates (horizontal
  segments in the Phillips curve)
• Higher rates of interest may not succeed in
  slowing down demand (it may increase consumer
  demand instead)
• When demand needs to be pumped up, it may be
  impossible to lower real interest rates
  sufficiently (zero lower-bound problem)
• Raising the interest rate is likely to lead to a
  lower normal rate of utilization (a higher
  NAIRU), as firms raise their target profit
  margins, and there is no guarantee that the
  actual rate will converge to this evolving normal
  rate (Hein 2006, 2008).

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Capitalists get scared of full employment and
reduce the rate of growth of output

• This is the Skott mechanism (1989, 2007, 2008).
• In the mature economy, the rate of output
  growth is a positive function of the profit share
  and a negative function of the employment rate.
• If the employment rate rises above its steady
  state value, capitalists reduce output growth,
  sales growth declines, the actual rate of
  utilization falls, and the constant in the
  investment function starts to shrink.
• The cause firms have increasing problems to
  recruit additional workers, workers and labour
  unions are strengthened vis-à-vis management,
  workers militancy increases, monitoring and
  surveillance costs rise, and hence the overall
  business climate deteriorates.

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Drawbacks of the Skott mechanism

• It is not clear why output growth should be a
  positive function of the profit share this
  excludes Kaleckian effects by assumption.
• It is not clear why high employment rates,
  accompanied by more powerful workers and labour
  unions, should induce capitalists to reduce
  output growth in the first place.
• One would rather think that high employment rates
  generate rising nominal wage growth. This should
  cause either rising inflation or a falling profit
  share, or both.
• But the latter would intensify Harrodian
  instability!
• What about labour supply growth being driven by
  labour demand growth?

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Capitalists have perfect foresight and revise
their sales expectations

• The Shaikh II (2007) mechanism
• Based on a special Hicksian stock-flow
  investment adjustment function.
• Investment depends on the rate of utilization and
  the growth rate of sales that will be realized in
  the current period
• If so, it can be shown that the actual rate of
  capacity utilization necessarily converges to its
  normal rate.

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Shaikh II
û

u
0
-
gs
g
gkal
gi gy ?u(u-un)
? gk0 gy0
gk2
gy2
gk3 gy3
u
u1
u2
ukal
un
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Drawbacks of the Shaikh II mechanism

• Firms must know the growth rate of their sales.
• But this rate depends on the investment
  expenditures of all other firms.
• Thus, each firm needs to know what all other
  firms simultaneously decide.
• The informational requirements are huge.
• The behaviour of managers is unlikely following
  a period of rising rates of utilization, firms
  need to believe that sales will grow more slowly.
• If firms act in some adaptive way, Harrodian
  instability reappears.

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Questioning the necessity of any adjustment of u
towards un

• Provisional equilibrium everything moves anyway
  (Chick and Caserta 1997)
• Other stock-flow norms in growth models are not
  realized, even when agents try to achieve them
  wealth/income targets (Godley)
• There is a large range of acceptable desired or
  normal rates of capacity utilization (Dutt
  1990).
• A firm may operate each running plant at optimal
  capacity (cost-minimizing), while being unable to
  to run all plants (idle capacity) (Caserta 1990).

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Acceptable range

• The stock adjustment principle, with its
  particular desired level of stocks, is itself a
  simplification. It would be more realistic to
  suppose that there is a range or interval, within
  which the level of stock is comfortable, so
  that no special measures seem called for to
  change it. Only if the actual level goes outside
  that range will there be a reaction. (Hicks
  1974, p. 19)

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Even Sraffians accept that firms usually have
idle capacity

• It is virtually impossible for the
  investment-saving mechanism to result in an
  optimal degree of capacity utilization. It is,
  rather, expected, that the economy will generally
  exhibit smaller or larger margins of unutilized
  capacity over and above the difference between
  full and optimal capacity. (Kurz 1994)
• One must keep in mind that although each
  entrepreneur might know the optimal degree of
  capacity utilization, this is not enough to
  insure that each of them will be able to realize
  this optimal rate. (Kurz 1993)

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Still, we do not wish to sweep the problem under
the carpet

• There are mechanisms that can bring together the
  actual and the normal rates of capacity
  utilization, by making the normal rate endogenous
  to the values taken by the actual rate (Lavoie
  1992, 1996, 2003 Cassetti 2006, Commendatore
  2006).
• So normal rates adjust to the actual rates.
• With some specifications, these hysteresis models
  safeguard both the paradoxes of thrift and of
  costs.
• A critique of these has been why would firms
  modify the normal rate of utilization just
  because it has not been achieved recently (Skott
  2008)?

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A possible answer because firms have multiple
targets !

• This is the Dallery and van Treeck (2008) model,
  partly based on Lavoie (2003).
• Firms may set themselves target or normal
  rates of utilization.
• But they also may have other targets, such as
  target rates of return (rsf), required for
  financing growth or imposed or suggested by
  shareholders.
• In addition, workers may have a target real wage,
  equivalent to some target rate of return (rw),
  which stops the firms from achieving their target
  rate of return.
• Thus, to follow Skotts analogy, although I may
  always be late arriving at work (u gt un) , I may
  be unable to leave any earlier to arrive on time
  (u un), because of other commitments (rw, rsf).

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The Dallery and van Treeck (2008) mechanisms

• Firms may raise their target rate of return when
  the actual rate is above the target.
• By doing this, running at an over-normal rate of
  utilization, they may succeed in achieving the
  target rate of return.
• Firms may also decide to decrease their retention
  ratio sf (thus distributing more dividends), as
  long as the actual profit rate is below the
  target.
• This is similar to the Shaikh I mechanism. But
  the utilization rate remains endogenous here.

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Conclusion- The Kaleckian model is more flexible
than the critics of the textbook version
supposeFurther developments - Financial
sector instability and real instability- Role
of labour supply (endogeneity channels)-
Integration of economic policies