The effect of technical progress upon distribution along Kaldor-Kennedy line

The effect of technical progress upon
distribution along Kaldor-Kennedy line

 Up Sira Nukulkit
 Email: sira.nukulkit@economics.utah.edu
 Ph.D. student, University of Utah
 M.A. in economics, University of Denver
 B.S. in civil engineering,
Chulalongkorn University, Bangkok
 I am Thai, a Bangkokian.
 "Up" is my "given" name.

 The classic question of "the effect of progress upon distribution"
 Hicks, Harrod, Robinson, Kaldor, Samuelson and Kennedy.
 A post-Keynesian history of thought behind the analysis
 Focuses on Kennedy's writings and his suggestion along Kaldor-
Kennedy line.
 inquiries on
 elasticity of substitution between capital and labor
 the equivalency of Hicks and Harrod neutral technical change
 concerns over value and stylized facts.
 A synthesis model constructed from intuitions behind the
debate.
 JEL Classification: B22, O31, E12

Introduction: effect of progress upon
distribution
 Charles Kennedy's paper "Induced Biased in
Innovation and the Theory of Distribution" (1964)
 Paul Samuelson (1965) adopted the theory to comply
with economic stylized facts
 Neoclassical method
 Kennedy disapproved Samuelson's approach.
 He had "hoped that the innovation-possibility frontier might be
able, so to speak, to swallow up the traditional production
function and replace it altogether" (1966, p.442)
 There were histories behind this concept more
profound than Samuelson's adaptation.

distribution
 J. R. Hicks introduced "the effect of progress upon
distribution" to modern economics.
 The Theory of Wage (1932, p.112)
 New terminologies on invention and distribution
 labor-saving, capital-saving, neutral inventions
 Elasticity of substitution!!! Most importantly
 Price substitution between capital and labor
 The price of capital is its value or interest rate?
 Hicks seemed to suggest it is interest rate.
 Tendency of elasticity of substitution less than unity!!
 Falling profit (interest) rate

distribution
 Joan Robinson followed through
 Essays on the Theory of Employment (1937)
 Harrod did not like her analysis on long run equilibrium
 Robinson used Hicks' neoclassical terminologies
 Harrod proposed an alternative definition
 To categorize invention
 Bypass difficulties on theory of value
 Development of the concept of "neutral technical
progress"

distribution
 After twenty years
 Kaldor introduced stylized facts (1957)
 constancy on capital/output ratio, rate of profit, and
distributive share.
 Neoclassical production function failed to produce these
results.
 Kennedy's "innovation possibility frontier" (1964) follow
by Samuelson's adaptation (1965)
 We have two concerns!!
 Value…...Harrod neutral == Hicks neutral
 Stylized facts……constant interest rate?

Technical progress and the value of
factors of production
 Hicks coined the term "elasticity of substitution"
 An increase one factor of production (i.e capital
accumulation, surplus labor )
 increase the overall output
 increase the absolute share of the factor and all other factors.
 However, there was no criterion to look at relative share
 "Elasticity of substitution" addressed the change in relative
share.
 Neutral distribution
 Elasticity of substitution is unity (equal to 1)
 "the increase in one factor will raise the marginal product of all
other factors taken together in the same proportion as the total
product is raised" (p. 117).
 But, marginal product is capital value or interest rate.

 Invention changes relative distribution share too.
 More confusing because a labor, capital, or neutral
saving invention
 saves the amount of input factor used in production.
 increases in unequal amount of factors marginal product
 Saving factor input≠ increase in marginal product
 In contrast to each other
 Furthermore, Hicks mentioned labor-saving invention
as dominance in the system.
 Robinson and Harrod would argue on the same issue.

 Joan Robinson debate dwith Harrod on the definition of
neutral invention.
 Hicks' neutral technical change
 "thus if a neutral invention occurs in conjunction with an
elasticity of substitution equal to unity, the relative share of
labour is unchanged" (1937, p.133)
 Harrod criticized her on the measurement of capital.
 He suggested instead an alternative definition to characterize
invention that was more general.
 "divide inventions into those at a given interest rate, and an
infinitely elastic supply of capital at that rate, increase, leave
unchanged or diminish the length of productive process"
(p.329).
 Bypassed difficulties on value, and used length of productive
process as measurement for capital.

 Joan Robinson defended her position in a famous paper
"Classification of Invention"(1938).
 She insisted on using Hicks' conceptual framework
 indicated the compatibility of Hicks and Harrod's
frameworks
 Kennedy came into the same conclusion as Robinson's 13
years later
 Harrod neutral technical change was equivalent to Hicks
neutral technical change.

 Kennedy (1961) asked a question whether an investment was
needed for technical progress.
 His first paper on technical progress
 If investment was not needed, the volume of capital can be
exactly determined a priori before the effect of invention.
 Adopted Robinson's classification and her concept of "real
capital"
 A neutral invention implied a constant capital/output ratio.
 Wage will increase, if relative share of distribution was
unchanged.
 Furthermore, higher wage will increase the value of real capital
when multiply to wage unit.
 We have a rise in the value of capital with a rise in wage that
leave interest rate constant, which was a definition of neutral
technical change

 Kennedy's multi sectors model(1962).
 clarified the dichotomy on Hicks' characteristic of specific kind of
invention
 the contrast between saving efficiency and an increase in marginal
product
 specified invention to the investment sector.
 An invention in capital producing sector will lower the cost of machine
leading to an increase on the number of machine per man.
 more volume of capital will be used in the production, but aggregate real
capital was unchanged.
 This will affect production in the economy as a whole triggering technical
progress that raised wage from labor productivity.
 It went back to an increase in value of aggregate real capital when
multiply to wage.
 Neutral technical progress
 An increase in value applied to the whole economic system, while it was
specific in investment sector that had capital saving invention bias

 Kennedy proposed in his rejoinder (1962) to Harrod's
extended paper on neutral technical progress (1962)
 Hicks neutral technical change and Harrod neutral
technical change were actually equivalent.
 The issue is really complex on value and the characters
of invention.
 Harrod denied to use labor as measure for capital
 "to have labour measure. It implies that the average of
money rewards paid to workers never rises…Is it not a
little sadistic to seek to deprive men of this increment of
pleasure, for the sake of –what?—a mere academic
preference. (Harrod 1948, p.29)"

Technical progress and stylized facts
 Harrod did not consider
 that neutral technical progress explained a rise of labor
productivity and wage.
 the empirical outcomes of this mechanism were implicit
in the analysis of Hicks, Harrod, and Robinson.
 Kaldor (1957, 1961 Corfu) was explicit
 attracted a bigger audience
 constancies in distributive share, capital/output ratio, and
the rate of profit.
 "technical progress function"

 Kaldor (1957, 1961 Corfu)'s "technical progress function"
 neoclassical production function "assumed to be a unique
relationship between capital and output, which conforms to the
general hypothesis of diminishing productivity, but this
relationship is constantly shifting with the passage of time"
(1961, p. 204).
 the tangent of the production function to be maintained on the
same slope for every upward shift on production function by
technical progress
 a circular determination of profit rate from the shift and the
move along production function.
 "any sharp or clear-cut distinction between the movement
along a "production function" with a given state of knowledge,
and a shift in the "production function" caused by a change in
the state of knowledge is arbitrary and artificial" (1957, p. 959).

 Kaldor (1957, 1961 Corfu)'s "technical progress function"
 'technical progress function' which postulates a relationship
between the rate of increase of capital and the rate of increase
in output and which embodies the effect of constantly
improving knowledge and know-how, as well as the effect of
increasing capital per man, without any attempt to isolate the
one from the other." (1961, p. 207)
 cut through the 45 degree line pinpointed the stable long run
equilibrium of the system, where the rate of accumulation
equal to rate of increase in output.
 Integrated both a shift in the production function and a
movement along the production function into one postulate.
 Kennedy criticized Kaldor's formulation

 Kennedy criticized Kaldor's formulation
 the capital/output ratio was assumed constant a prior.
 Kaldor relied on adjustment assumptions of entrepreneur
investment behavior
 Capital/output ratio adjusts through prospective on profit
rate
 Kennedy pointed out to many weaknesses
 should not use profit rate which supposed to be a long run
solution of the model.
 an expectation behavior scheme was insufficient
 behavior did not guarantee that invention will be labor-saving.
 "Mr. Kaldor had already assumed what he was trying to
prove" (1962, p.910) constant capital/output ratio

 Kennedy was hoping to retain some of Hicks' neoclassical
assumptions.
 Kennedy chose not to use neoclassical factor price.
 "changes in relative factor price are not essential for a theory of
induced biased in innovation" (1964, p. 542).
 consider both factor price and volume of input factor as one
component of share on cost of production.
 Economic system will choose bias in innovation that affected the
share specific to capital cost and labor cost separately.
 However, "innovation possibility" frontier between labor-saving
innovation and capital-saving innovation was concave. Tradeoff
 Adjustment to equilibrium depended on the choice between labor
and capital saving inventions that sustained the optimization on unit
cost.
 "in the long run the equilibrium values of the distributive shares will
be determined by the characteristics of the purely technological
innovation possibility function" (1964, p.545).
 With Hicks neutral technical change

 Kennedy expanded his model to a multi-sectors model of
invention.
 implicitly addressed complications on accumulation of capital
and factor price of capital.
 If invention occurred in capital sector, there was an exogenous
shock that disturbed innovation possibility frontier of the
consumption sector on the increased volume of capital.
 The system will adjust to optimize the reduction in unit cost on
labor and capital by focusing on endogenous labor-saving
invention
 adjusted to Harrod neutral technical change with labor-saving
invention bias.
 Kennedy made use of the equivalency of Hicks and Harrod
neutral technical change.

 Samuelson (1965, 1966) adopted Kennedy's innovation
possibility frontier.
 Samuelson insisted on using factor price derived from
production function.
 neglected the complex structure of value from capital to
labor and did not consider the equivalency of Hicks and
Harrod neutral
 Samuelson's factor share was determined in competitive
market outside of the model.
 sharp contrast to Kennedy's endogenous determination of
factor share on innovation possibility frontier.
 Factor price VS factor share

 Samuelson still reached similar results to Kennedy.
 If innovation possibility frontier was symmetric and factor
input ratio did not change (no accumulation)
 Hicks neutral technical change and a strange equal
dividend of factor share (Kindleberger).
 Samuelson would dropped this assumption on fixed
factor ratio and "replacing it by the more realistic
recognition that capital is 'deepening relative to labor'"
(1965, p. 348).

 Capital deepening
 If elasticity of substitution was less than unity, there was a
tendency for labor relative share to rise more than capital.
 There had to be a bias on invention that offset diminishing
marginal productivity from accumulated capital.
 only under Harrod neutral technical change with labor-saving
invention.
 impossible to retain Hicks neutral technical change.
 Interest rate had to rise to counter balance a fall in price of
capital to attain constant relative factor share.
 interest rate became an endogenous variable.
 "fail to account for one of the stylized facts of modern
development, namely that the interest or profit rates show no
clear trend upward or downward" (Samuelson 1965, p. 348)

 Kennedy (1966) objected to Samuelson's used of production
function.
 inter-correlations that would alter innovation possibility
frontier
 Samuelson's capital accumulation was not superior to his
contingent to constant interest rate.
 reconcile Samuelson's capital accumulation Kenndy previous
results
 same mechanism of his two sectors one product model
 the equality of capital deepening and labor augmentation
 Capital deepening was already an endogenous result of
Kennedy multi sectors one product model.
 Harrod neutral technical change was an endogenous result of
his model.
 "in Kennedy's case, the Harrod-neutral result is not "supposed
to come about," it does come about" (1966, p.442).

A synthesis model along Kaldor-Kennedy
 Concerns over value and stylized facts
 This paper describes a theoretical puzzle of value and
stylized facts engaged by our Keynesian predecessor.
 There were clues in those writings.
 There are gaps in growth and distribution theory on
technical progress and stylized facts??
 I would like to build a model based on this puzzle and
theoretical debates
 How to get a 45 degree constant capital/output ratio?
 What a synthesis model should be like?
 Kennedy's optimization of concave invention possibility
frontier
 Kaldor's prospective profit behavior on technical progress
function

 Kennedy's optimization of concave invention possibility frontier
 Kaldor's prospective profit behavior on technical progress function
 What a synthesis model should be like?
 My very loose idea is on
 Adjustment through value
 Maintain full employment in parody of Jean Baptist Kaldor
 Elasticity of substitution between capital and labor
 Price of capital is interest(profit) rate
 Invention this time did not save factor input. Invention can be
assumed implicit as increasing returns function?
 Increasing returns
 Sum up the movement and the shift of production function in one
postulate

 Elasticity of substitution between capital and labor
 Invention can be assumed implicit as increasing returns
function?

 I still have to come up with a story…

The effect of technical progress upon distribution along Kaldor-Kennedy line

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The effect of technical progress upon distribution along Kaldor-Kennedy line