Technical Progress
Growth Economics
Roberto Pasca di Magliano
2015/2016
Introduction
• The technical progress in the Solow model, the exogenous
cause of the growth of per capita income steady state.
• Before explaining the causes of technical progress (growth
theories endogena), this raises the problem of its
measurement.
• The 'approach' growth accounting 'is proposed to decompose
the growth rate of the economy in the contributions of the
accumulation of factors of production on the one hand and
technical progress on the other.
The Production Function
• The product of an 'economy is represented by:
Y = f ( K , L, t )
• The increase of production may 'be due to:
• Increase in the factors of production, capital (K) and labor (L).
• Technological change. The shape of the production function changes
over time (t).
The representation of the output through isoquants
• The isoquants of the production function provide a geometric
representation of the production function are the pairs of K and L
that produce a given output Y.
The representation of
the output through isoquants
• The production increases for the following reasons:
• Increase of only one of the factors. But given the diminishing
returns of the single factor, that increase will stop.
• Increase of both factors:
• Constant returns, increasing or decreasing.
• The Solow model assumes constant returns to use the theory
of marginal distribution
• Technological improvement.
Taxonomy
Initial date technology with an infinite number of
production techniques (possible combinations of K
and L), technical progress is said:
- 'Labor augmenting', or Harrod neutral, if it increases
the productivity 'of the work of all production
techniques leaving the productivity' of capital
unchanged. (Hypothesis of the Solow model).
Yt = f ( K t , (1 + γ )t Lt )
where γ and 'the growth rate of productivity' of
work
- 'Factor augmenting' or Hicks neutral, if increases in
equal measure productivity 'of labor and capital of all
production techniques,
leaving
the ratio
K /tL
t
t
t
Yt = f ((1 + χ ) K t , (1 + γ ) Lt ) = f ((1 + γ ) K t , (1 + γ ) Lt ) =
unchanged.
(1 + γ )t f ( K t , Lt )
Growth accounting
• Separates the effect of the accumulation of factors from that of
technical progress on the rate of growth of the economy
ΔY = f ΔK + f ΔL + f , f = df / dx
K
L
t
x
ft
ΔY
f K K ΔK
f L L ΔLK
=
+
+
Y
Y
K
Y
L
Y
• The growth rate of the economy and 'equal to the sum of the
growth rates of factors, each multiplied by the relative elasticity
of production, and a measure of technological change.
• Note that the elasticity of production are not directly
observable, but under the assumptions of the Solow model,
same as the percentage of national income of the factors.
• where χ and 'the growth rate of productivity' of capital
Growth accounting
•TFP, or measure of technical progress, is measured as a residual:
ft
= g Y − πg K − (1 − π ) g L
Y
• where π and 'the share of profits in national income, eg expressing
growth rates.
•This method, first suggested by Solow (1957), is typically applied using
the Cobb-Douglas production and Hicks neutral technical process:
Y = AK α L1−α
•Where α turns out to be both the elasticity 'of production to capital, and
the share of profits in income.
Growth accounting –results• The first estimates for the United States for the first half 'of
the century ('56 Abramovitz, Solow '57) show that TFP is
responsible for almost 90% of the growth of output per
capita.
• However, this result is' vitiated by errors of measurement in
the quality of the factors that tend to underestimate their
impact.
Growth accounting – insights –
1) Technical progress embodied in capital goods.
The new technologies, at least in part, are incorporated in the
new capital goods. Need 'to measure the stock of capital in
units' efficiency (τ):
t
τ t = ∑ K i (1 + λk ) i
i =0
where λk and 'the rate of improvement of the quality' of capital
goods. The growth rate (τ) depends on: the growth of the stock
of physical capital, the rate of improvement of the quality 'of
goods, changes in the age' average stock of capital.
Growth accounting – insights –
2) Improvements in the quality 'of the work.
Each one unit 'of physical work can' increase its efficiency
by:
- Accumulation of human capital (eg education)
- job experience (learning by doing)
These two channels have become the starting point of
the analysis of endogenous growth
Growth accounting – insights –
3) structural change in the use of factors in favor of the
activities 'more' productive.
The aggregation of the factors K and L hides the different
productivity of the various capital goods quality and
heterogeneous work.
The contribution of a factor shifting resources from one
sector with low productivity to high productivity increases
(ex from 'agriculture industry).
Growth accounting – developing countries –
Main trends (1960-94):
The key role of accumulation of factors
Important but limited compared to developed countries TFP
Important role in the reallocation of resources between
sectors.
interpretation:
The industrialized countries are more 'close steady state
and have to resort to technical progress in order to grow, on
the contrary the developing countries can use the initial
benefits from capital accumulation