Development Economics
Structural Change
Andreas Schäfer
University of Leipzig
– Institute of Theoretical Economics –
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Contents
5.1 Introduction
5.2 Early Contributions to the Literature
5.3 Structural Change and Balanced Growth
5.4 Other Theories of Structural Change
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5.1 Introduction
Interest in poor nations of the world began to materialize following
WWII.
Economists had no apparatus available with which to analyze the
process of economic growth in largely agrarian societies.
Development theory and policy was characterized by two
observations:
1
2
The Marhall Plan enabled Europe to rebuild and modernize their
economies.
All modern industrialized countries were once underdeveloped agrarian
countries.
→ emphasis on role of accelerated capital accumulation: ”capital
fundamentalism”
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5.1 Introduction
Rostow’s Stages of Growth
The transition from underdevelopment to development can be
described by series of steps/stages through which all countries must
proceed
1
2
3
4
Traditional society
Pre-conditions for take-off into self-sustaining growth
Take-off
Age of high mass consumption
The underdeveloped countries had only to follow a set of rules of
development.
One of the principal strategies: mobilization of domestic and foreign
saving.
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5.1 Introduction
Rostow’s Stages of Growth - Criticism
Empirical evidence is not really supporting the theory of stages.
Savings and investment are not a necessary condition but a sufficient
condition for economic development.
Rostow’s theory assumes the existence of the same attitudes,
arrangements and institutions for developed as well as for
underdeveloped countries.
The Marshall Plan was a success for Europe because the receiving
countries possessed the necessary structural and institutional settings
to convert new capital efficiently into higher levels of output.
Nevertheless it is reasonable to ask how the developed economies of today
did develop! → Theory of structural change.
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5.1 Introduction - Kaldor facts
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5.1 Introduction - Kaldor facts
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5.1 Introduction - Kaldor facts
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5.1 Introduction - Kaldor facts
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5.1 Introduction - Kuznets facts
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5.1 Introduction - Kuznets facts
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5.1 Introduction - Kuznets facts
Agriculture
Manufacturing
Services
Share of
total employment
declines
stable
increases
Share of
total consumption expenditure
declines
stable
increases
Remark: this reflects the last hundred years. Prior to this period there has
been a rise in manufacturing (see Laitner (2000)).
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5.2 Early Contributions to the Literature
Lit.: Todaro and Smith (2006), Economic Development, Pearson (9th
edition).
One of the best-known early theoretical models of development that
focused on structural change was formulated by Nobel laureate W.A.
Lewis (Economic development with unlimited supplies of labour,
Manchester School 22 (1954): 139-191).
Lewis-two-sector model became the work horse during the 1960s and
early 1970s.
In the Lewis-model, a underdeveloped economy consists out of a
traditional, overpopulated rural subsistence sector and a
high-productivity modern urban industrial sector.
Primary focus of the model: process of labor transfer and the growth
of output and employment in the modern sector.
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5.2 Early Contributions to the Literature
The traditional agricultural sector
Total output T PA is determined by changes in the quantity of labor
employed in agriculture, LA , whereas the level of technology t̄A as well
as the amount of capital K̄A is fixed.
The marginal product of labor M PA is zero for finite levels of labor.
That is additional amounts of labor do not affect the level of output
after a certain threshold - surplus labor.
The wage rate in agriculture equals the average product of labor, that
is WA = T PA /LA .
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5.2 Early Contributions to the Literature
The agricultural sector
T PA
T PA
f L A , K A , t A
WA
T PA
LA
QA LA
WA
A PL A
M PL A
Surpluslabor
LA
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5.2 Early Contributions to the Literature
The modern sector
Total output in the modern sector denoted by T PMi is produced again
with labor LMi , capital KMi at a given level of technology, t̄M .
Lewis allows capital to grow, as a result of the reinvestment of profits
= capital incomes.
The labor market in the modern sector is perfectly competitive.
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5.2 Early Contributions to the Literature
The modern sector with increasing levels of capital
TPM i
K Mi
TPM 3 f LM i , K M i , tM ^K M 3 ! K M 2 ! K M 1 `
TPM 2 TPM 1 L1 WM
M PLM 2
M PLM 1
L1 Andreas Schäfer (University of Leipzig)
L3 L2 L2 M PLM 3 L3 Structural Change
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5.2 Early Contributions to the Literature
The Lewis model of modern-sector growth
TPM 3 TPA TPM2 TPM1 Surpluslabor
WM WA LM1 LM2 Andreas Schäfer (University of Leipzig)
LM 3 Structural Change
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5.2 Early Contributions to the Literature
As labor markets in the industrial sector are perfectly competitive, the
downward sloped marginal product of labor curves are the profit
maximizing demand curves for labor.
WA is the subsistence income in the traditional sector.
WM is the real wage in the modern/industrial sector. At this wage,
supply of rural labor is perfectly inelastic.
WM > WA implies that firms can employ as many workers as they
wish without increasing in wages.
Assuming a neoclassical production function in the modern sector, the
reinvestment of capital incomes induces increasing levels of output at
constant wages. The increase in physical capital moves the
M P -schedule to the right raising the demand for labor.
Employment expansion continues until all surplus rural labor is
absorbed in the modern sector. Now, additional workers can be
withdrawn from agriculture only at the cost of higher wages
(M PLA = 0).
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5.2 Early Contributions to the Literature
Criticisms of the Lewis model
Capital incomes are reinvested. There is no capital flight.
Labor saving technical progress would increase capital income while
labor income and employment levels remain constant.
Assumption of rural surplus labor is generally not valid.
Prior to the 1980s in almost all developing countries wages rose
substantially, in absolute terms and relative to rural incomes.
Diminishing returns in the the modern industrial sector are at least
debateable. There is increasing evidence for increasing returns, posing
special problems for policymaking.
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5.3 Structural Change and Balanced Growth
Growth literature which make heavily use of BGP-models, generally
disregards sectoral reallocation of labor.
Literature on structural change ignores Kaldor facts (in part because
it focuses on longer periods of time.
Research question: is there a model that is consistent with both the
Kaldor facts and massive sectoral labor reallocations?
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5.3 Structural Change and Balanced Growth
Lit.: Kongsamut, P., S. Rebelo, and D. Xie (2001). Beyond Balanced
Growth, Review of Economic Studies, Vol. 68, pp. 869-882.
Production
Output in agriculture:
A(t) = BA F (φ(t)A K(t), N (t)A X(t))
(1)
Output in services:
S(t) = BS F (φ(t)S K(t), N (t)S X(t))
(2)
A(t) and S(t) can only be used for consumption.
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5.3 Structural Change and Balanced Growth
Production
Output in manufacturing can be consumed (M (t)) or invested
(K̇(t) + δK(t)):
M (t) + K̇(t) + δK(t) = BM F (φ(t)M K(t), N (t)M X(t))
(3)
The functions F (., .) satisfy the neoclassical properties.
Exogenous technological progress (labor augmenting): Ẋ(t) = X(t)g.
The shares of labor N i and capital φi sum up to one
φ(t)A + φ(t)M + φ(t)S
A
M
N (t) + N (t)
Andreas Schäfer (University of Leipzig)
S
+ N (t)
Structural Change
= 1
(4)
= 1.
(5)
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5.3 Structural Change and Balanced Growth
Resource constraint
The Production functions of different sectors are proportional, such
that relative prices of agriculture and services are given by
pA =
pS =
BM
BA
BM
.
BS
(6)
(7)
The economy’s resource constraint reads as
M (t) + K̇(t) + δK(t) + PA A(t) + PS S(t) = BM F (K(t), X(t)). (8)
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5.3 Structural Change and Balanced Growth
Preferences
In this setting, sectoral movements must originate from differences in
the income elasticities of demand for the different goods.
Income elasticity of demand
agricultural good: < 1
manufacturing goods: = 1
services: > 1
Moreover preferences are time-separable, such that
∞
[(A(t) − Ā)β M (t)γ (S(t) + S̄)θ ]1−σ − 1
dt,
e−ρt
U (t) =
σ
0
(9)
where β + γ + θ = 1, and σ, β, γ, θ, ρ, Ā, S̄.
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5.3 Structural Change and Balanced Growth
Equilibrium
In equilibrium profit maximizing behavior induces
r = BM F1 (k, 1) − δ,
(10)
K
X.
where k ≡
Equality of marginal utilities induces
M (t)
PA (A(t) − Ā)
=
(11)
β
γ
M (t)
PS (S(t) + S̄)
=
.
(12)
θ
γ
Optimal path for consumption of manufacturing goods is given by the
Keynes-Ramsey rule
r−ρ
Ṁ (t)
=
.
M (t)
σ
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(13)
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5.3 Structural Change and Balanced Growth
Equilibrium
Marginal rate of technical subsitution is equal across sectors, hence
φM
φS
φA
=
=
= 1.
NA
NM
NS
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(14)
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5.3 Structural Change and Balanced Growth
Balanced Growth Path
Suppose that Ā = S̄ = 0. From the aggregate resource constraint it
becomes clear that A(t), M (t), S(t), K(t) must grow at rate g along
the BGP.
Factor market equilibrium and Keynes-Ramsey rule imply
BM F1 (k, 1) − δ = σg + ρ.
(15)
→ the economy will follow a BGP whenever k is consistent with a
real interest rate that leads households to choose to expand their
consumption of A, S, M at rate g.
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5.3 Structural Change and Balanced Growth
Generalized Balanced Growth Path
Suppose that Ā, S̄ > 0. From (11) and (12) imply that A and S do
not grow at constant rates even if the real interest rate is constant.
For Ā, S̄ > 0 balanced growth does not exist.
Definition:
A generalized balanced growth path is a trajectory along which the real
interest rate is constant.
Rewriting the resource constraint gives:
M (t)K̇(t) + δK(t) + PA A(t) + PS S(t) = BM F (k, 1)X(t).
(16)
RHS expands at rate g.
LHS M, K̇ and δK grow at rate g, but A and S do not!
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5.3 Structural Change and Balanced Growth
Generalized Balanced Growth Path
Suppose: ĀBS = S̄BA (knife-edge condition, but convergence to
GBG is it is violated!), this implies
Ps S̄ − PA Ā = 0.
(17)
This allows us to write the resource constraint as
M (t) + K̇(t) + δK(t) + PA (A(t) − Ā) + PS (S(t) + S̄)
= BM F (k, 1)X(t).
Since A(t) − Ā and S(t) + S̄ grow at rate g, all terms grow at rate g.
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5.3 Structural Change and Balanced Growth
Results
A generalized BGP exists whenever ĀBS = S̄BA .
The GBG exhibits constant relative prices, constant aggregate labor
income share, constant growth rate for aggregate output and capital,
constant capital-output ratio and time-varying sectoral growth rates
and employment shares.
Growth rates of output in agriculture and services:
Andreas Schäfer (University of Leipzig)
Ȧ(t)
A(t)
= g
A(t) − Ā
,
A(t)
(18)
Ṡ(t)
S(t)
= g
S(t) + S̄
S(t)
(19)
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5.4 Structural Change and Balanced Growth
Results
Evolution of labor shares:
Ṅ A (t) = −g
Ā
,
BA X(t)F (k, 1)
(20)
Ṅ M (t) = 0,
Ṅ S (t) = g
(21)
S̄
,
BS X(t)F (k, 1)
(22)
The share of labor in agriculture declines, while the share in services
increases.
As the economy grows, the importance of Ā and S̄ declines and the
economy converges to a standard BGP (USA: sectoral reallocation of
labor out of agriculture has been limited since the 1970’s; slowdown
in the expansion of employment in in services.)
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5.4 Structural Change
Results
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5.4 Other Theories of Structural Change
The theory presented in the former section was demand based. That
is, different demand elasticities with respect to income induced
structural change.
Structural change can also be generated through (either) factor
accumulation and (or) technological progress which affects sectors to
a different extend.
Hence, structural change can also be induced through the technology
side of an economy.
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5.4 Other Theories of Structural Change
In the literature two (competing) explanations have been put forward
for structural change
1
2
Technology based explanation: structural change is attributed to
different growth rates of total factor productivity (TFP) over different
sectors
Utility based explanation: requires different income elasticities for
different goods. Hence, structural change may result even with equal
TFP growth in all sectors.
A very recent example for the first channel is the paper by Ngai and
Pissarides (2006), Structural Change in a Multi-Sector Model of
Growth, American Economic Review. They confirm William
Baumol’s (1967) claims about structural change who divided the
economy in two sectors, a progressive one that uses new technology
and a stagnant that uses labor as the only input.
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5.4 Other Theories of Structural Change
Another candidate of the second channel is the paper by Foellmi and
Zweimller (2006), Income Distribution and Demand-Induced
Innovations, RES, 73, 941-960. Endogenous growth is driven by
introduction of new goods into a hierarchic utility function.
General concern: the theory of structural change explains the development
patterns of developed countries, but doesn’t shed much light on the causes
which trap underdeveloped countries in poverty.
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