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Post-Keynesian
models of growth
and distribution
Marc Lavoie
Outline
• Old post-Keynesian growth models 1956-1962
– Kaldor
– Pasinetti
– Robinson’s banana diagram
– The inflation barrier
• New Kaleckian growth models 1981- now
• The neo or post Kaleckian model 1990 – now
• Other controversies
– Overhead costs
– The normal rate of utilization in the long run
– Productivity changes
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The old post-Keynesian model
• This model arises from Kalecki’s macroeconomic equation and from
Keynes’s fundamental equations of the Treatise.
• Kalecki: profits = investment + consumption out of profits – saving out
of wages
• P = I + (1 – sp)P – sw(Y – P)
• P(sp – sw) = I – sw.Y
• P = (I – sw.Y)/(sp – sw)
• P/Y = (I/Y – sw)/(sp – sw)
• If sw = 0, then :
• P/Y = (I/Y)/sp and
• P/K = (I/K)/sp that is, r = g/sp
• This is the Cambridge equation
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The Kaldor-Robinson growth model
• The rate of profit is determined by the growth rate and the propensity
to save out of profits (in the simplified case).
• If the growth rate is higher, then for given propensities to save, the
economy requires a higher profit rate (P/K) and a higher profit share
(P/Y).
• If this is the case, there is not a unique Harrodian warranted rate of
growth (I/K = s.Y/K or gw = s.(u/v), with Y/K = (Y/Yfc)(Yfc/K) = u/v
• In the neoclassical view, variations in technology (v) allows for a
multiplicity of warranted rates. This line of thought, however, is
questioned by the Cambridge capital controversies.
• In the old post-Keynesian view, it is variations in income distribution
(the profit rate) that permits a multiplicity of warranted rates (g = sp.r).
• In the new post-Keynesian view (the Kaleckian view), it will be
variations in the rate of utilization (u) that allows many warranted rates
(g = sp.mu/v).
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The Pasinetti correction (1962)
• Pasinetti (1962) claimed that Kaldor (1956) had made a mistake
by omitting that workers also can save. Thus, the saving function:
• S = Sp + Sw = sp.P + sw.W
• had to be rewritten as:
• S = Sc + Sw = sc.Pc + sw.(W + Pw)
• Assuming that the profit rate is the same for both classes,
• Pc/Kc = Pw/Kw = P/K
• And that in the long run, the capital stocks grow at the same rates:
• Sc/Kc = Sw/Kw = S/K = I/K = g
• It follows that: Sw/Pw = Sc/Pc and hence:
• sw.(W + Pw)/Pw = sc.Pc/Pc so that:
• sw.(W + Pw) = sc.Pw and finally
• S = Sc + Sw = sc.Pc + sc.Pw = sc.P
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The Pasinetti paradox
• Thus, we have a revised Cambridge equation, valid however
only in the very long run, where:
• r = g/sc
• The propensity to save of capitalists (who earn only profits,
not wages) determines the profit rate, independently of the
propensity to save of workers.
• This result, along with Kaldor’s equation, has given rise to over
500 articles or book chapters by 200 different scholars, many of
which tried to see what conditions could be changed while
keeping the Pasinetti paradox!
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Joan Robinson’s banana diagram
• In her 1962 book Robinson adds a behavioural equation to the
Cambridge equation (which determines the profit rate, or which is seen
as the saving function).
• gs = spr
• The investment function, in its linear form, would be
• gi = γ + grre
• With a non-linear investment function, we would have two
possible equilibria, one of them being stable.
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Stability analysis: the saving function needs to be steeper
than the investment function
g gs
H gi
gh*
g0
L
gL*
r L* ra r0 rh* r
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The paradox of thrift in PK growth models
Impact of a lower propensity to save
g g s gs(sp2)
H’
g2 H gi
g0
r0 r2 r
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The inflation barrier: a higher growth rate requires
a higher profit rate and a lower real wage rate, which workers
will fight through wage inflation
g g s gs(sp2)
H’
g2 H gi
g0
r0 r2 r
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The inflation barrier: a higher saving rate would allow to evade
the inflation barrier for entrepreneurs with more spirits.
g gs(sp2) gs
H’
g2
gi
g0 H
r0 r2 r
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
First problem with the old PK growth
model
• 1. Sraffians have critized the Cambridge relation, claiming that
there was a confusion between the actual profit rate and the
normal profit rate. For Sraffians, the growth rate may determine
the actual profit rate, but not the normal profit rate. The latter is
strongly influenced by the long-term rate of interest, itself
influenced by the monetary authorities.
• 2. Sraffians reject the compulsory negative relationship between
the growth rate and the real wage rate. They reject the idea that
a higher growth rate needs to be associated with a lower real
wage (even at constant productivity).
• 3. Thus they reject the concept of the inflation barrier.
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Second problem with the old PK
growth model
• This is a problem underlined by Davidson (1972),
Asimakopoulos (1984), and Marglin (1984).
• Kaldor-Robinson-Pasinetti assume that prices, via markups,
adjust the profit share to the higher growth rate.
• There is very little discussion of quantities: the rate of utilization
is assumed to remain or to return at its normal rate.
• When there is a discussion, the discussion is very confused:
• ‘Thus when we descend from the clean air of a golden age,
where normal prices always rule, into the fogs of historical time,
our analysis cannot but be blurred and imprecise’ (Robinson
1956: 190).
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Davidson’s critique
• “The neo-Keynesian models of Robinson, Kaldor and Pasinetti,
which are more directly derived from Kalecki's work and
Keynes's Treatise on Money ... lay emphasis on changes in the
distribution of income and prices as the primary adjustment
mechanism to short-period disequilibrium, and adjustments via
changes in employment and output are considered either to be
of secondary importance or assumed away. In Joan Robinson's
model, if realised aggregate demand is below expected
demand, then it is assumed that competition brings down
market prices (and profit margins) at the normal or standard
value of output.” (Davidson 1972:124-5)
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Marglin’s critique
• `In the short run, fluctuations in investment demand are reflected
in fluctuations in output; the rate of capacity utilization changes
in accordance with aggregate demand.... But in the long run, ...
there is no excess capacity to accommodate investment
demand. Distribution must bear the brunt of adjusting
aggregate demand to supply” (Marglin 1984: 474-5)
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Robinson’s failed traverse with higher
profit margins
• “Now let us suppose that Alaph entrepreneurs begin to form
themselves into rings and raise prices.... As prices rise, with
constant money wages, the volume of sales of consumption
goods gradually falls (or rather fails to rise at its former rate).
Workers become unemployed, and the utilisation of capital
equipment in the consumption sector falls below capacity....
Initially employment in the investment sector is unaffected.... But
with redundant equipment in the consumption sector the
demand for replacements falls off, there is unemployment in the
investment sector and a fall in the rate of profit. We may
suppose that after passing through a period of
disinvestment, accumulation recovers to its former level
(though there is no necessary reason why it should do so).”
(Robinson 1956: 77-8).
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Robinson’s claim
• “Firms may be working plant below designed capacity and still
charging the "full cost" prices at which they were earlier able to
sell their normal capacity output', while assuming however that
`competition (in the short-period sense) is sufficiently keen to
keep prices at the level at which normal capacity output can be
sold” (Robinson, 1962: 46).
• `Although variations in the degree of utilization of capacity are
admitted for the short period, Robinson excludes them as far as
the long period is concerned‘ (Ciccone 1986: 22)
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The new PK model: Kaleckian model
• Del Monte (1975), Rowthorn (1981), Taylor (1983), Dutt (1984)
• Changes in quantities are the main driver.
• It is assumed that income distribution variables, such as the
markup, or the target rate of return, are exogenous. The
feedback effects of growth or employment on income
distribution are omitted in the simple versions.
• The model is made up of three equations: the saving function,
the investment function, and the pricing function.
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
A summary of growth rate implications
Marxists Old PK Kaleckians
Inflation barrier Kaldor Modern Sraffians
Robinson
Eichner Wood
Increase in the Fall in the real Fall in the real Independent real
desired rate of wage rate wage rate wage rate
accumulation
Increase in the Increase in the Decrease in the Decrease in the
propensity to growth rate growth rate growth rate
save
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Equations of a simple Kaleckian model
• The saving equation:
gs = spr
• The investment function is assumed to be the
canonical Kaleckian investment function:
• gi = γ + guu + grr
• The pricing function, which depends on the profit
margin m:
rPC = P/K = (P/Y)(Y/Yfc)(Yfc/K) = mu/v
• The realization curve or effective demand function
(ED), combines gs and gi:
• rED = (guu + γ)/(sp − gr)
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
A change in income distribution
• What happens if there is a reduction in the markup (or in the
profit share) and hence an increase in the real wage (or an
increase in the wage share)?
• Initially, in the short run, as explained by Robinson (1956), there
will be an increase in consumption, and hence an increase in
the rate of utilization.
• Initially, also there will be no change in the rate of profit, as long
as we assume that investment (and propensities to consume) is
not modified. Recall Kalecki’s equation!
• However, the increase in the rate of utilization will eventually
lead to an increase in the rate of accumulation (the accelerator
effect) and hence in the profit rate! This is the paradox of costs!
• Real wages, profit rates and growth rates all rise together.
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
g gs
gi
g1* A decrease
in the profit
g0* margin
u
r
PC
r1 * ED
r0 *
rmic
u
u* u u*
Third International Summer School on Keynesian Macroeconomics and
0 1 1
European Economic Policies, Berlin, 31 July - 7 August 2011
An important variant of the Kaleckian
model: the Bhaduri-Marglin model
• Bhaduri and Marglin (1990) and Kurz (1990) have argued that the
canonical Kaleckian investment function ought to be replaced by
another investment function, that would take into account the normal
profit rate instead of the actual profit rate. Instead of:
• gi = γ + guu + grr
• They propose something like:
• gi = γ + guu + gmm
• Where m is some proxy of the normal profit rate, that is, the profit rate
that would be realized if the economy were at the normal rate of
capacity utilization: rn = mun/v
• Bhaduri and Marglin, and most empirical research, take the profit
share in national income as this proxy.
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Effects of an increase in the wage
share in the Bhaduri-Marglin model
I, S gS0
gS1
gI1
g1
gI2
g0
gI0
u0 u1 u1* q
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Effects of an increase in the wage
share on u and g
Effect on total demand (or the rate of
capacity utilization)
Positive Negative
Effect on Positive Wage-led demand and
investment (or the wage-led growth
rate of
Negative Wage-led demand and Profit-led demand
accumulation)
profit-led growth and profit-led
growth
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Controversy #1: Overhead costs
• There is some tradition in taking overhead costs into
consideration: Kaldor 1964, Harris 1974, Asimakopulos 1975,
Rowthorn 1981, Nichols and Norton 1991, Dutt 1992, Palley
2005 .
• Things are not so simple if we take overhead labour costs into
consideration (Lavoie 1992, 2009). Why?
• Then the profit share is endogenous and does not necessarily
move along with profitability (the normal profit rate or the target
rate of return incorporated into the markup pricing formula).
• The following two graphs show that things can be quite
complicated!
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Impact of an increase in the profit margin (the target rate of return or
the normal profit rate) on the net profit share
when the investment constant is positive
π πS2
B2 πS1
π2
B1
π1
πD
u2 u1 u
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Impact of an increase in the profit margin (the normal profit rate) on the
(net) profit share, when the investment constant is negative
π πS2
πS1
π1 πD
B1
π2 B2
u2 u1 u
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Overheads
• Overhead costs are particularly important now since it has been
shown that the top centiles in income distribution earn most of
their money through salaries and wage bonuses.
• The impact on the economy also depends on how overhead
salaries are included into the pricing formula (here it has been
assumed that firms follow a target-return pricing formula and
hence add overhead costs under the assumption that the firm
operates at its normal rate of capacity utilization).
• Thus changes in the wage share may underestimate the
changes in income distribution which are occurring.
• Also an increase in the proportion of wages going to overhead
labour (supervisory workers) does not always have the same
effect!
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
US top .01% earners
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Inequality within the salary structure
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Macroeconomic impact of an increase in managerial costs,
with target return pricing (positive or negative on u)
r PC2
PC1
EDB
B2
B1
rn
EDA
A1
A2
u
un
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Impact of an increase in managerial costs on the net profit share,
with target return pricing, when the investment constant is positive
π πS2
πS1
B2
πn B1
πDB
A1
A2
πDA
u
un
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Impact of an increase in managerial costs on the net profit share,
with target return pricing, when the investment constant is negative
π πS2
πS1
B2 πDB
B1
πn
πDA
A1 A2
un u
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Controversy #2: Should the rate of utilization
be equal to its normal value in the long run?
• Several authors, mainly Marxist ones (Shaikh, Duménil and
Lévy), but also some post-Keynesians (Skott), argue that the
Kaleckian model is under-determined because it does not
assume a mechanism that will bring back the economy to its
normal rate of capacity utilization in the long run.
• This has been the subject of several articles, both in the mid-
1980s and also more recently.
• It has been argued in particular that economists ought to be
Kaleckians (or Keynesians) in the short run, but that they should
be classical (Marxist) in the long run.
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Mechanisms that bring the economy
back to the normal rate of utilization
• The Cambridge price mechanism (Robinson)
• The central bank (fear of inflation) (Duménil and Lévy)
• The business fear of full employment or full capacity (Skott)
• Some form of rational expectations (Shaikh)
• Changes in the retained earnings ratio of firms (Shaikh)
•
• See Hein, Lavoie, van Treeck (CJE 2011)
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The Kaleckian response
• Firms are content with a large range of rates of utilization (Dutt).
• Firms would like to bring the rate of utilization back to its normal
value, but they face other constraints that stop them from being
able to do so (Dallery and can Treeck).
• The normal rate of utilization will adjust itself to the actual rates
of capacity utilization (path-dependence, Lavoie).
• See Hein, Lavoie, van Treeck (Metroeconomica 2011)
• A mechanism to explore: scrapping unused machines
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The Kaldorian influence
• Kaldor can be said to have a multiple influence on models of
growth:
– In arguing that the natural rate of growth is influenced by
growth in demand;
– In arguing about productivity effects;
– In arguing about cumulative causation;
– In introducing open economy constraints on growth.
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Productivity growth
• Kaldorians have for a long time argued that supply-side growth
is endogenous, thus predating the mainstream theories of
endogenous growth.
• This is the so-called Kaldor-Verdoorn law, for which there is a
substantial amount of empirical evidence (McCombie and
Thirlwall 1994, McCombie 2002) and the formal origins of which
can be traced back to Kaldor’s (1957) technical progress
function.
• The Kaldor-Verdoorn law claims that there is a positive causal
relation going from the growth rates of GDP to the growth rate of
labour productivity.
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
The Kaldor-Verdoorn law
• In other words, demand-led growth will have an impact on the
supply components of growth (Léon-Ledesma and Thirwall
2002, Dray and Thirwall 2011).
• More simply, it is claimed that there is a positive causal
relationship going from the growth rate of the economy to the
growth rate of labour productivity (and even the growth rate of
the labour force).
• McCombie (2002, p. 106) says that the Verdoorn coefficient is in
the 0.3 to 0.6 range, meaning that a one percentage point
addition to the growth rate will generate a 0.3 to 0.6 percentage
point increase in the growth rate of labour productivity.
• This number is also consistent with the one obtained recently by
Storm and Naastepad (2008). Their average estimate is 0.5
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Productivity regimes (revised Storm
and Naastepad)
• λ = β0 + β1.g + β2.w
• g = ε0 + ε1(w – λ) + ε2. λ = ε0 + ε1.w + ε3. λ
• Where ε3 = ε2 – ε1
• λ is the growth rate of labour productivity;
• g is the growth rate of the economy;
• w is the growth rate of real wages .
• If ε1 > 0 then we have a wage-led demand regime (as before)
• The question then is whether productivity growth λ is also wage-led.
• There are two effects: a direct effect through parameter β2; and a
multiple indirect effect, through the Kaldor-Verdoorn effect.
• Also, do increases in real wages lead to employment growth or not?
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Total productivity effect of an
increase in the wage share, when the
partial productivity regime is wage led
Demand Regime Direct (partial) Indirect Overall combined
productivity effect productivity effect productivity and
(Kaldor-Verdoorn demand effect
effect)
Profit led Positive Negative Positive or
negative
Wage led Positive Positive Positive
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
Conclusion
• The Kaleckian growth model is very flexible.
• It has been used by authors coming from several schools of
thought
• It has allowed discussions between different traditions.
• It has an empirical content.
• It can also handle monetary matters (Hein)
• And open-economy matters (Blecker)
Third International Summer School on Keynesian Macroeconomics and
European Economic Policies, Berlin, 31 July - 7 August 2011
