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Vladimir Matveenko
Economic Growth and International
Trade:
Role of Intermediate Goods
XIII Annual International Conference “Leontief Readings”,
St. Petersburg, 15 February 2014
Interdependence
Interpedendence
Leontief. Input-output production structure:
intermediate goods are used to produce other
intermediate goods.
Von Neumann – Gale model
Makarov and Rubinov (1973)
Rubinov, Borisov, Desnitskaya and Matveenko
(1990)
Makarov, Levin and Rubinov (1995)
Interpedendence (continuation)
• Countries with relatively cheap labor (China,
India, Eastern Europe) integrate into the
World economy
• global production sharing
• offshoring
• fragmentation of production
• global supply chains
• comparative advantage at the component
level
• intrafirm trade
Interpedendence (continuation)
• Input-output ideology
Jones. Misallocation, economic growth, and inputoutput economics. NBER WP, 2011.
• Network economics
Acemoglu et al. The network origins of aggregate
fluctuations. Econometrica, 2012.
“This paper argues that in the presence of intersector
input-output linkages…”
• Network games with
substitutability/submodularity or
complementarity/supermodularuty
Interpedendence (continuation)
• Models of misallocation
Jones. American Economic Journal: Macroeconomics, 2011.
Banerjee and Moll, 2010
Fernald and Neiman, 2011
Epifani and Gancia, 2011
Restuccia and Rogerson 2012
• Intermediate goods in international trade
Yi. Can vertical specialization explain the growth of world trade? J. of
Political Economy, 2003.
Eaton and Kortum. Technology, geography, and trade. Econometrica, 2002.
Alvarez and Lucas. General equilibrium analysis of the Eaton-Kortum model
of international trade. J. of Monetary Economics, 2007.
Waugh. International trade and income differences. American Economic
Review, 2007.
Ventura. Growth and interdependence.
Quarterly Journal of Economics, 1997
• Countries: j = 1,…,J
• Endowments: Labor, Initial capital
• Production of intermediate goods i=1,2
1 unit of labor produces A j units of product 1
1 unit of capital produces 1 unit of product 2
• Production of final good (GDP)
1
b
(x  x ) ,
b
1j
b
2j
b 1
• Utility and budget constraint:

e
0
( n  )t
ln c j (t )dt
c j  k j  nk j  r j k j  w j
Ventura. Growth and interdependence.
Quarterly Journal of Economics, 1997
(continuation)
• “Conditional” factor price equalization
corresponding to Trefler. International factor prices:
Leontief was right! Journal of Political Economy, 1993
w j  A j p1
rj  p2
• If the average for the world per capita outputs of
the intermediate products are A (product 1) and k
(product 2) then
p1 / p2  (k / A)
1b
Ventura. Growth and interdependence.
Quarterly Journal of Economics, 1997
(continuation)
• World economy equilibrium dynamics
1 b
b b
с
 ( Ab  k )
с
k b 1  
b
b 1/ b

k  ( A  k )  nk  c
• Natural question: What is the dependence
between degree of complementarity and the
growth rate?
Ventura: Sustainable development for high b  1
Recent interest to important economic measures
• Total factor productivity.
• Elasticity of factor substitution – labor and capital.
Pitchford, J.D., “Growth and the Elasticity of Substitution,”
Economic Record 36 (1960), 491-503.
• Direction of technological progress and relation to
institutions.
• Role of intermediate goods in formation of aggregate
economic measures
• Dependence of the aggregate TFP on the TFPs of sectors
• Misallocation
• Relation of the aggregate elasticity of substitution and the
elasticities of substitution in sectors
• Dependence of the growth rate of the economy on the
TFPs and elasticiries of substitution in sectors and the
structure of production in sectors
In complex economic systems
• High interrelation of agents and complex interactions
across them
• Special role of externalities
• Complementarity of activities
• Intermediate products (among them ideas)
Complementarity of intermediate goods in production
(possible model: Leontief function or a system of
Leontief functions).
Complementarity of ideas (different types of
knowledge)
• Complementarity  Weak links  Misallocation
3-sector model of general equilibrium
with intermediate goods
Miyagiwa K. and Papageorgiou C. 2007. Endogenous
aggregate elasticity of substitution.
Journal of Economic Dynamics and Control
Xue J. and Yip C.K. 2013. Aggregate elasticity of
substitution and economic growth: A synthesis. Journal of
Macroeconomics.
• Intermediate goods i=1,2 are produced by use of
capital and human capital
сi  Ai F ( Ki , Li ), i  1, 2
The intermediate goods are used too produce the
final good:
Y  R(c1 , c2 )
3-sector model of general equilibrium
with intermediate goods
(continuation)
• Distribution of capital and labor between sectors
K1  K 2  K , L1  L2  L
• Consider the case when the aggregation function
has the form


Y  B  1 X 1t   2 X 2t
B  0,   (, 0)  (0, 1)

 1/ 
1  0
2  0
3-sector model of general equilibrium
with intermediate goods
(continuation)



 1/ 
Y  B  1 X 1t   2 X 2t
• Two known specifications of the CES function
1   2  1
1)
 1  0,  2  0,  1   2  1
2)
• Question: How does the final product depend on
the elasticity of factor substitution?
• Unexpected result: the absence of robustness on
functional form
Dependence of the total factor productivity
(TFP) on the elasticity of factor substitution
4-sector model of general equilibrium with
intermediate goods
We develop the approach of Jones, 2011. Intermediate
goods and weak links in the theory of economic
development. American Economic Journal:
Macroeconomics
• Basic goods i=1,2 are produced by use of capital,
human capital and intermediate goods
Qi  Ai F ( Ki , Hi , X i ), i  1, 2
The basic goods are used in production of the final
good and the aggregate of intermediate goods:
Qi  ci  zi
Y  R(c1 , c2 )
X  S ( z1 , z 2 )
Y.Martemyanov, V.Matveenko. 2014:
1
p
 n

p
xi (t  1)     ij [ Aij x j (t )]  , p  0,  ij  0, Aij  0
 j 1

• Natural question: What is the dependence
between degree of complementarity and the
growth rate?
• In all three models we come to the absence of
robustness to functional form.
Model of development with positive
externalities
Matveenko. Journal of Policy Modeling 1995
• N economic agents
xt(i 1)  aii xt( i ) , t  0,1,...; i  1,..., n;
xt(i 1)  aij xt( j ) , t  01
, ,...,
xt(i )1  min aij xt( j )
j
xt 1  Axt
  min,   
For martix
1.01 1  any trajectory leads to a

A  
cyclic growth
 1 1.01
Для матрицы
1 1.01

A  
1 1.01
any trajectory leads to a stationary
state
Conclusion
• In the interdependent world a special role is
played by the elasticity of substitution of
intermediate goods and other parameters of the
production function
• They depend on policies and institutions
• A change in parameters easily leads to a change
in measures of development – in such way the last
crisis can be explained
• Under big complementarities, a complex dynamics
dominates
• A challenge for such models is accounting for
differences in institutions, technologies and tastes
Thank you for your attention
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