Inequality and economic theory: has
Piketty’s Capital in the 21st century
changed anything?
Paper for symposium on “Inequality: causes
and consequences”
Geoff Bertram
Institute for Governance and Policy Studies
Victoria University of Wellington
19 June 2014
(in other words what’s new?)
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Piketty’s big empirical findings have
been around for a while now
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Equilibrium level?
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Piketty’s specific policy suggestions have been around
inn the public mind for a while…
• Progressive annual tax on capital (wealth)(p.517):
–
–
–
–
0.1-0.5% on fortunes < €1 million
1% on fortunes €1 million- €5 million
2% on fortunes €5 million- €10 million
Up to 5% or 10% on really big fortunes
• Raise income-tax progressivity with top rate of 80% (p.513)
• Inheritance taxes? Inheritance??….
Even his professional suggestion that Economics should
explicitly study good and evil has been heard before
So has the notion that capitalism exhibits a dis-equalising
dynamic outlook and popular distaste for being ruled by a rich
rentier class.
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None of that is the real point of the book
though
• Looks like a Kuhnian paradigm change
• Not heterodox: tackles the mainstream of economic
theory head-on on its own ground
• Resolves puzzles in mainstream theory and subsumes
them into a unified theoretical framework
• The unified theory subsumes also a lot of what has
been the heterodox fringe of economics
• Has passed the mainstream sniff test: “Piketty is right”
says Solow
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Distribution of the social product
• Wealth of nations lies in the annual flow of
produced goods and services
• Shares in that flow have to be allocated
amongst competing groups
• In a distributional equilibrium some part of
the product is appropriated by each group on
the basis of some objective natural necessity
or some socially-created right
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Three general theories of distribution
• An unchallenged ruling class appropriates for itself the
maximum share consistent with sustainability of the
economy per se [roughly speaking this is the ricardian
and marxian position];
• A contest amongst contending class forces, with shares
reflecting the balance of market power they are able to
wield [the neo-ricardian view];
• A mutually advantageous bargain amongst free and
equal participants in the productive economy in which
each player is paid its just share on the basis of its
productive contribution [the neoclassical view].
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Production versus appropriation
• All individuals/groups/classes stand in some
relation to the product on two dimenions:
– Production: participation or non-participation in
the productive process via direct effort or
contributed resources
– Appropriation: the exercise of a right to receive,
and consume or save, a share of the output
• This distinction is fundamental to Piketty
though he never really spells it out
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Classical distribution theory: Ricardo (1772-1823)
• Production is organised, and all revenue from sale of the
product collected, by capitalists who own the productive
enterprises and the produced means of production.
• Out of this revenue the capitalist-entrepreneurs pay as little
as possible to those who supply them with the two other
essential productive inputs – labour and land – and take
the rest as profit
• Labour must be fed so the wage must be just sufficient to
keep alive the number of workers required: Iron Law of
Wages
• Owners of “land” must be paid rent to make it available to
capitalists. Expanding production drives up rents as land
becomes scarcer
• Profit share therefore is progressively squeezed by rent
claims and eventually growth stops => stationary state
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Marx set land and rent aside and focused on
capital versus labour
• The rate of profit now falls because of diminishing marginal
product of capital as its “organic composition” rises
• Capitalists exercise market power to raise the rate of
exploitation of labour and claim a greater share of the
product
• This is limited ultimately only by workers’ resistance =>
revolution => social control of means of production
• [Piketty argues that Marx would have got an equilibrium
capital/labour ratio had he been aware of the underlying
rate of technical progress (“structural growth rate”) – which
would have solved the puzzle of the open-ended spiral of
accumulation and exploitation]
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Neoclassical distribution theory
•
Each factor of production receives a “just” reward equal to its marginal
product, and competitive market forces impersonally allocate the product
on that basis
•
Labour thus receives its marginal product, which implies that wages
should rise with labour’s productivity.
•
Capital also receives its marginal product, so the profit rate will fall over
time insofar as the marginal product falls – but can rise as technological
progress keeps pushing up the productivity of all factors of production
including capital. [Depends on the elasticity of capital/labour substitution]
•
Rent, as in Ricardo, is determined by the value of scarce natural resources
at the margin
• A key feature is that the great aggregates amongst
which the national product is divided up do not exist
as concrete social formations (e.g. classes of actual
people), but only as macroeconomic abstractions
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Puzzles in neoclassical growth theory
• Predictions of convergence and equalisation encounter empirical
refutation => ad-hoc stories about institutional differences
• Model inhabited not by actual people but by disembodied aggregates
(capital, human capital, labour) or by “representative agents” =>
unstated distributional implication is of equality of owneship, or social
ownership, of factors of production
• Ongoing growth (technical change) not explained by the production
function => complex “endogenous growth models” with epicycles
• Econometric estimation of the Cobb-Douglas production function
produces the “wrong” shares for capital and labour => human capital
theory to plug the gap
• The infinite-horizon intertemporal-optimisation representative-agent
growth model predicts infinite concentration of wealth if other
countries are added (disequalising dynamics keep popping up out of
the sophisticated maths)
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Piketty’s model
• Separate production from appropriation and focus on the latter
• Divide population into two groups: those that have wealth, and the
rest
• Define “capital” to incorporate all wealth, including land
• Extend “labour” to all human effort in production, including CEOs
• Treat all returns on “capital” as rents, accruing at a normal rate of 45%
• Capital is now not a factor of production; it is a property right, a social
artefact, conferring power to appropriate a prespecified chunk of the
product
• The elite’s chunk is the value of capital times the rate of return
• So long as wealth-owners’ property rights and rate of return hold
good their share is secure
• But that assumes no shocks
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Piketty’s distribution model
Stock of
wealth/capital
β
Funds made
available for
production
Productive
effort
Stock of labour
Production
1-(r x β)
rxβ
National income
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• When Piketty speaks of a “market economy with private
property in capital and inheritance allowed” he is referring
to an economy in which claims based on the productive
effort of the mass of the population are the residual, always
subject to the overriding claim of wealth owners to collect
their rents – unless the social order, and hence the value of
wealth claims, is disturbed by untoward events such as
taxes, wars, revolutions, and natural disasters.
• The twentieth century had wars and taxes, which disturbed
the normal placid state of affairs
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Piketty’s big stylised fact: r>g is the norm: but the
twentieth century was briefly different
And his big
assumption: 4-5% is
the long-run norm
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Now the technical bit
• The unit of account for each year is the
current money value of that year’s output.
• The monetary value of capital (wealth), rents,
and output itself can therefore be measured
in output years, avoiding deflators and
exchange rates
• The capital/income ratio β is therefore
expressed as a number of output-years
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The puzzle of the Solow residual is simply set aside:
exogenous givens in Piketty
• Structural growth at 2%± is a stylised fact: that’s g
• A 4-5% rate of return on wealth is a stylised fact
(except in special times): that’s r
• The savings rate is exogenous (standard
assumption) and around 12%: that’s s
• The share α of income claimed by capital is
𝜶=𝒓𝒙𝜷
(this works because everything is measured in
income-years)
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0.05 = 0.05 x 1
𝜶=𝒓x𝜷
0.25 = 0.05 x 5
• Thus if wealth is equal to one year’s annual
= 0.05
10 the share of
0.50 and
income (=output)
r=5%,xthen
each year’s income to which wealth-holders lay
claim is 5% i.e. 0.05 output-years
• If wealth is five years’ income then the rent share
is one quarter (25%).
• If wealth is ten times income then the rent share
is 50%.
• So, why not 100%? The answer is that β is
endogenously determined and has an equilibrium
value
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Determining the capital/income ratio
• Harrod’s growth equation with fixed
𝑠
capital/output ratio: 𝑔 =
𝛽
• Solow’s variable ratio with exogenous s and g:
𝑠
𝛽=
𝑔
• Reinterpreted, this gives Piketty’s long-run
equilibrium value for β defined as the
capital/income ratio.
• If g=2% and s=12% then in steady-state growth
equilibrium β = 6 years of income
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The implication: the twentieth century was
in low-inequality disequilibrium
• Kuznets’ 1955 idea that equality naturally increased as
growth proceeded was only an observation of the
downward path of r and β under the impact of wars,
Depression, and taxes.
• Since 1970 global wars have stopped, Depression has
been avoided and taxes have been dropping
• So the advanced countries are heading back to
equilibrium with rising wealth/income ratios driving
increasingly unequal distribution of income
• Where is this leading?
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(The chart Piketty didn’t draw in the book)
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The growth rate g is expected to fall this century
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The big question: is patrimonial capitalism
sustainable?
• Piketty’s economics say yes, subject to just one noneconomic proviso
• The projected oligarchic order of massive inequality with a
super-rich elite has to be “tolerated”
• Piketty does not offer a theory of democratic tolerance –
this is the big missing piece, and is why he is not following
Marx into revolutionary predictions
• He just wonders politely whether democratic societies can
tolerate the outcomes of the logic of capitalism’s
accumulation of private wealth
• If by chance the answer is no, he has some gentle
suggestions about what might be done (always bearing in
mind the possibility that one day the rentiers might just be
expropriated and their class euthanased…)
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Which brings us back to Piketty’s specific policy
suggestions …
• Progressive annual tax on capital (wealth)(p.517):
–
–
–
–
0.1-0.5% on fortunes < €1 million
1% on fortunes €1 million- €5 million
2% on fortunes €5 million- €10 million
Up to 5% or 10% on really big fortunes
• Raise income-tax progressivity with top rate of 80%
(p.513)
• Inheritance taxes? Inheritance itself??….
• All of these are little wedges put into cracks to
transform the equilibrium solutions in his equations.
• Lots of commentators shrug and say: is that it? They
miss the point of the book.
• Is there a parallel here with the climate change
debate?
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