Download Lecture notes on accumulation theories and policy applications

Lecture notes on accumulation theories
The mather (or father) of all growth models: Harrod’s
model and the instability problem
• Dual nature of investment: it generates capacity, it generates
aggregate demand
The model:
• S1 = sY1
(1) (multiplier)
• I1 = vn (Y1E - Y0)
(2) (accelerator)
• S1 = I1
(3) (equilibrium in the commodity
market: there is dynamic equilibrium if I1 generates a growth of AD
and capacity such as to generate an identical S1)
• vn = K/Y = DK/DY is the desired (or required) capital coefficient, s
marginal propensity to save
• "The axiomatic basis of the theory which I propose to develop
consists of three propositions, namely: (a) that the level of a
community income is the most important determinant of its supply of
saving; (b) that the rate of increase of its income is an important
determinant of its demand for saving; and (c) that demand is equal
to supply. It thus consists in a marriage of the 'acceleration principle'
and the 'multiplier' theory" (Harrod, 1939, p.43).
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The warranted rate
• By simple substitution we get:
• vn (Y1E - Y0) = sY1
• or gw = (Y1E - Y0) /Y1 = s/vn
• gw is the rate of growth at which capacity savings (savings
forthcoming from existing capacity utilised at its normal or ‘expected
level) is equal to investment.
• Note that gw = gE, that is the economy will grow in equilibrium (I =
capacity saving) if the entrepreneurs expect a rate of growth (gE)
equal to gw.
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The warranted rate and the instability question
• gw = s/vn, is the so-called warranted growth rate . "The warranted rate
of growth is taken to be that rate of growth which, if it occurs, will
leave all parties satisfied that they have produced neither more nor
less than the right amount" (1939, p.45).
• gE = s/vn , that is if the entrepreneurs expect a growth rate gE = gw =
s/vn, then the economy grows with a goods market equilibrium (gA =
gE)
• If the entrepreneurs knew gw, they would decide an investment level
that would precisely generate gw. But they do not know it.
• Instability:
• If gE > gW  gA > gE and next time they will expect an even larger GE
• If gE < gW  gA < gE and next time they will expect an even lower GE
•
(a simple proof due to A.Sen in Jones)
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A simple example
• Suppose v = 2, s = 0.2 so that gw = 0.1 (or 10%).
• Suppose current output is 90, if ge = gw = 0.1, firms would invest 20
(= 2 x 10) and output at t+1 will indeed be 100 (we take the growth
rate as a proportion of final output).
• If ge > gw, and they expect, say, 101, firms will invest 22 and output
will be 110, so investors will feel that they anticipated too little (ga >
ge > gw  0.2 > 0.11 > 0.1).
• So they will revise ge upward and ga will diverge even more from
gw.
• Similarly if they anticipate 99, they will invest 18 and output at t+1
will be only 90
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Problems with Harrod
• Harrod’s model raised two questions:
• gw is not a full employment path: this is a problem only for
neoclassical economists
• gw is unstable, that is the economy does not gravitate around it (not
surprisingly, unless you believe in Say’s Law, there is no reason why
in Harrod S = I).
• Instability seen through the lenses of the degree of capacity
utilisation
• Normal degree of capacity utilisation : the average degree of
capacity utilisation desired by the entrepreneurs
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Degree of capacity utilisation and the capital
coefficient
un= Yn/Yf where Yf is the maximum physical output from a given
capacity K. In general Yn < Yf and un < umax = 1. The main reason
(Steindl) is that firms want to keep a margin of non utilised capacity
to meet sudden peaks of demand; if peaks persist, they will increase
capacity.
When gA > gw, it means that s/va> s/vn,, that is
va = K/Ya < vn = K/Yn  Ya > Yn
or, in terms of degree of capacity utilisation u,
ua = Ya/Yf > un = Yn/Yf  Ya > Yn
Read in the opposite direction: whenever gA > gw, Ya > Yn  ua > un,
the actual degree of capacity utilisation ua is higher than normal (so
entrepreneurs invest even more to restore un , but in this way they
aggravate the disequilibrium).
The opposite would of course happen when gA < gw (ua < un and
investment would keep falling to absorb the less-than-normal u).
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Anticipation
• To anticipate what will follow when we shall consider the heterodox
growth models, one way to accommodate Harrod’s instability is to
say: if gA > gw and both va < vn and ua > un , then we take va and ua
as the “new normal” capital coefficient and degree of capacity
utilisation. But this sounds a post hoc ergo propter hoc kind of
reasoning however adopted by the influential ‘neo-Kaleckian’ growth
models.
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Two roads to get out from Harrod’s troubles
• Harrod influential in the 1950s (the market economy is unstable,
then the State must plan the economy: France’s planning, in Italy
Piano Vanoni, India’s planning). This is normative, but Harrod is
unsatisfactory as a positive explanation, markets are unstable, but
not explosive.
• Note a “traditional” feature of Harrod’s model: s positively influences
gw and growth is endogenous (in the sense that it depends on
preferences about present an future consumption). Perfect for a
neoclassical economist, were not for the absence of full
employment. Solow’s neoclassical growth model (1956) recovers full
employment, but losses, somewhat paradoxically, the influence of s
on g. Endogenous growth theory (that actually begun in the early
1960s) is just on having both.
• Two early ways out form Harrod’s problems: Solow’s neoclassical
growth model and the Cambridge Equation (later followed by other
heterodox schools)
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Two roads to get out from Harrod’s troubles II
• Main characteristic of the neoclassical approach is the dependence
of investment from savings, more specifically from full-capacity
savings, savings that spring from a productive capacity that both is
fully (or normally) employed, and also fully employs all the labour
supply.
• Main characteristic of (most of ) the alternative approaches is what
Garegnani named (after Kaldor) the “Keynesian Hypothesis” (KH)
that investment are independent from savings both in the short and
in the long run.*
• This is the striking difference between neoclassical economists of all
persuasions (including neo-Keynesians a là Blanchard, Stiglitz,
Krugman, De Long etc): aggregate demand determines output both
in the short and in the long period, or more precisely, it is capacity
that adjusts to aggregate demand both in the short and in the long
period. We shall begin from neoclassical growth story.
• * However, there are a number of “heterodox models” that are
“keynesian” in the short-run and “Classical” (in the sense of Say’s
Law) in the long-run (e.g. Shaikh, Foley and Michl; Dumenille and
Levy; Kurz and Salvadori?). We shall not study them.
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After Harrod
Harrod
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Solow
Cambridge equation
EGT
Neo-kaleckian
and/versus Sraffians
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Before we consider some heterodox models, let us remind
some critical aspects of neoclassical growth theory
• Solow’s fundamental equation:
Dk  sy  (  n)k
•
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The Solowian warranted growth rate
• At k*, sy = ( + n)k, and Dk=0.
• Note that in equilibrium gw = sy/k= ( + n)k that is s/v* = ( + n),
where v* is the long-run value of v.
• Neglecting , gw = n, a stable, full employment path
• In Solow the actual growth rate gravitates towards the warranted
rate
• This depends of factors’ substutability
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Gravitation towards the equilibrium
On the left of k*: sy > ( + n)k, i falls, k rises.
On the right of k*: sy < ( + n)k, i rises, k falls.
• “In its basic form the neo-classical model depends on the
assumption that it is always possible and consistent with equilibrium
that investment should be undertaken of an amount equal to fullemployment savings. The mechanism that ensures this is as a rule
not specified. Most neo-classical writers have, however, had in mind
some financial mechanism. In the ideal neo-classical world one may
think of there being a certain level of the rate of interest (r) that will
lead entrepreneurs, weighing interest cost against expected profits,
to carry out investment equal to full-employment savings.” Hahn &
Metthews EJ dec. 1964
• On the left of k*, since sy > ( + n)k, then sy/k > ( + n), and given
that k/y = va, GA = s/va > ( + n), where va is the actual value of v.
• va has to rise to realise the neoclassical warranted equilibrium path
s/ v* = ( + n).
• And indeed (from the left) the increase of k implies a fall of v =
y/k=f(k)/k  next slide
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Solowian stability
• Why (on the left of the stationary state k*) when k rises,then v also
rises (so that ga = s/v falls)?
• va = k/y: when k rises,also y rises,but given the falling marginal
productivity of capital, it rises less than proportionally than k. So v
rises and va  v* (A visual inspection is enough, for a given Dk, Dy
is smaller).
• we see that the neocl. subst. mech.s entail the gravitation towards
a full employment path: the fall in the interest rate induce the
entrepreneurs to adopt more capital intensive techniques
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Solowian stability
• Note that this result depends upon what Hahn & Metthews pointed
out, a decreasing demand function for investment (capital)
negatively elastic to the interest rate. The capital theory controversy
has shown that this function can have any shape. So Solow’s model
is not robust, it’s deadly wrong.
• Seen from a different perspective: there is no rigorous foundation to
the proposition that a falling interst rate induce firms to adopt more
capital intensive techniques. So no increase of k when we are on the
left of k*. Rigorously, k can rise, then fall, then rise again. No
convergence, no stability, no full employment growth.
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Comparative statics: a change in s entails higher y and k but not a
higher gw: a disappointing result (it came as a surprise)
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Just a word about Endogenous Growth Theory
• Many empirical studies show that there is a positive correlation
between I/Y (the investment share) and g (the growth rate).
• Through neoclassical lenses (according to which I = S) this is a
correlation between s = S/Y and g.
• But in Solow a rise of s only affect y not g!.
• From the very early sixties this is the start of EGT: a desperate
attempt to establish a connection between s and G.
• Not surprisingly, most of EGT is a return to Harrod (g is
“endogenous” in Harrod, endogenous in the specific marginalist
sense that it depends on s, on preferences between present and
future consumption)
• If curious, please see my papers on EGT (see my web page)
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