scale effects in schumpeterian growth theory by elias dinopoulos
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Scale Effects in Schumpeterian Growth TheoryScale Effects in Schumpeterian Growth Theory
By By Elias DinopoulosElias Dinopoulos
Schumpeterian Growth Theory Slide - 2 Elias Dinopoulos
Lecture Organization
Introduction Anatomy of Scale Effects Endogenous Schumpeterian Growth Models with Scale
Effects (Earlier endogenous growth models) Exogenous Schumpeterian Growth Models without Scale
Effects (Semi-endogenous growth models) Endogenous Scale-Invariant Schumpeterian Growth Models
(Fully-endogenous growth models). An Assessment Summary, conclusions and extensions
Schumpeterian Growth Theory Slide - 3 Elias Dinopoulos
Introduction
Schumpeterian growth is a particular type of growth which is generated by the endogenous introduction of product and/or process innovations.
The development of Schumpeterian growth theory started in the early 1990s.
Until the mid 1990s the theory expanded rapidly under the label of “endogenous” growth.
By mid 1990s the theory reached a blind intersection.
Schumpeterian Growth Theory Slide - 4 Elias Dinopoulos
Introduction
Jones (1995) criticized the scale-effects property: The rate of technological progress is assumed to be proportional to the level of R&D investment services.
– In the presence of positive population growth, the presence of scale effects implies that per-capita growth rate becomes infinite in the steady-state equilibrium.
– Time-series evidence from developed countries is inconsistent with the scale-effects property.
The Jones critique raises several fundamental questions:
Schumpeterian Growth Theory Slide - 5 Elias Dinopoulos
Introduction
Is the scale-effects property empirically relevant? Can one develop Schumpeterian growth models with
positive population growth and bounded long-run growth?
Can one develop scale-invariant Schumpeterian growth models that maintain the policy endogeneity of long-run growth?
Affirmative answers to the above questions are crucial to the evolution of the theory for the following reasons:
Schumpeterian Growth Theory Slide - 6 Elias Dinopoulos
Introduction
Removal of scale effects enhances the empirical relevance of the theory.
Scale-invariant Schumpeterian growth models can serve as templates for a unified growth theory.
Scale-invariant endogenous Schumpeterian growth theory improves its policy relevance and is closer to the spirit of Schumpeter (1937):
– “There must be a purely economic theory of economic change which does not merely rely on external factors propelling the economic system from one equilibrium to another. It is such theory that I have tried to build…[that] explains a number of phenomena, in particular the business cycle, more satisfactorily than it is possible to explain them by means of either the Walrasian or Marshalian apparatus”
Schumpeterian Growth Theory Slide - 7 Elias Dinopoulos
An Anatomy of Scale Effects
The scale-effects property arises from assumptions on an economy’s knowledge production function and its resource constraint.
Consider an economy producing final output by the following production function:
The knowledge production function is
)()()( tLtAtY Y
)(
)(
)(
)(
tX
tL
tA
tAg AA
Schumpeterian Growth Theory Slide - 8 Elias Dinopoulos
An Anatomy of Scale Effects
Assumptions that govern the evolution of X(t) are crucial. If the production of X(t) does not require any resources, the
model closes with the resource constraint
Where
Denote with s(t) the share of labor devoted to manufacturing and notice that the economy’s income per capita is y(t) = Y(t)/L(t) = A(t)s(t). Therefore, we have
)()()( tLtLtL AY LtgeLtL 0)(
Schumpeterian Growth Theory Slide - 9 Elias Dinopoulos
An Anatomy of Scale Effects
The economy’s long-run growth rate of output per capita is
The per-capita resource condition can be written as
)1()(
)()1(
)(
)(
)(
)(
tX
tLs
tA
tA
ty
tyg y
)2(1)(
)()1(
tL
tXgss A
Schumpeterian Growth Theory Slide - 10 Elias Dinopoulos
Endogenous Schumpeterian Growth Models with Scale Effects
They assumed that and that the R&D difficulty was also constant .
0)( LtL
0)( XtX
)1()1()(
)(
)(
)(
0
0
X
Ls
tA
tA
ty
tyg y
)2(1)1(0
0 L
Xgss A
Any policy that changes share of labor devoted to R&D (1 – s), has long-run growth effects.
If L(t) increases exponentially, the long-run growth goes to infinity.
Schumpeterian Growth Theory Slide - 11 Elias Dinopoulos
Endogenous Schumpeterian Growth Models with Scale Effects
Jones (1995) tested directly the knowledge production function
He argued that the rate of TFP growth is roughly constant over time, whereas the resources devoted to R&D increased exponentially.
Models of this class include Romer (1990), Segerstrom, Anant, Dinopoulos (1990), Grossman and Helpman (1991) and Aghion and Howitt (1992).
0
)(
)(
)(
X
tL
tA
tAg AA
Schumpeterian Growth Theory Slide - 12 Elias Dinopoulos
United States per capita GDP
Schumpeterian Growth Theory Slide - 13 Elias Dinopoulos
The evolution of number of scientists and engineers
Schumpeterian Growth Theory Slide - 14 Elias Dinopoulos
Exogenous Scale-Invariant Schumpeterian Growth Models
The first approach to the removal of scale effects property employs the notion of diminishing technological opportunities.
The level of R&D difficulty is related to the level of technology:
Substituting this expression into the two fundamental equations yields:
/1)()( tAtX
Schumpeterian Growth Theory Slide - 15 Elias Dinopoulos
Exogenous Scale-Invariant Schumpeterian Growth Models
)1()(
)()1(
)(
)(
)(
)(/1 tA
tLs
tA
tA
ty
tyg y
)2(1)(
)()1(
/1
tL
tAgss A
These equations imply that the constant steady-state of growth is proportional to the exogenous population growth rate:
LA ggtL
tL
tA
tA
)(
)(
)(
)(1
Schumpeterian Growth Theory Slide - 16 Elias Dinopoulos
Exogenous Scale-Invariant Schumpeterian Growth Models
Since the rate of population growth is not affected by policies, this class of models generates exogenous scale-invariant growth.
It should be emphasized that these models generate transitional growth of technological progress that can be analyzed by ranking the steady state values of per-capita R&D difficulty x = X(t)/L(t).
These models are also very tractable and useful tools for analyzing other dynamic dimensions (such as globalization, wages, trade patterns etc).
Jones (1995), Segerstrom (1998), Kortum (1997), Li (2003), Dinopoulos and Segerstrom (1999, 2006).
Schumpeterian Growth Theory Slide - 17 Elias Dinopoulos
Endogenous Scale-Invariant Schumpeterian Growth Models
The second approach to removing the scale-effects property uses a two dimensional framework with vertical and horizontal product differentiation.
Variety accumulation removes the scale-effects property in the same way as the exogenous growth approach.
• The level of R&D difficulty is a linear function of the level of varieties.
• The level of varieties is a linear function of the level of population.
Quality improvements generate endogenous long-run Schumpeterian growth.
Schumpeterian Growth Theory Slide - 18 Elias Dinopoulos
Endogenous Scale-Invariant Schumpeterian Growth Models
Consider an economy consisting of n(t) industries producing horizontally differentiated products, with each industry’s output given by
The knowledge production function is a function of the economy’s aggregate R&D and the R&D difficulty.
The R&D level of difficulty is given by
ZtAtz )()(
)(
)(
)(
)(
tX
tn
tA
tAg AA
)()()( tLtntX
Schumpeterian Growth Theory Slide - 19 Elias Dinopoulos
Endogenous Scale-Invariant Schumpeterian-Growth Models
Substituting X(t) into the knowledge production function yields
The resource constraint is
AA tA
tAg
)(
)(
1)(
)()()( AZAZ
tntLtntn
Schumpeterian Growth Theory Slide - 20 Elias Dinopoulos
Endogenous Scale-Invariant Schumpeterian-Growth Models
Aggregate output is given by
Long-run growth of per-capita output is therefore
Models of this class include Peretto (1998), Young (1998), Aghion and Howitt (1998), Dinopoulos and Thompson (1998), and Howitt (1999).
)()()()()()()( tLtAtntAtntztY ZZ
AY tA
tA
ty
tyg
)(
)(
)(
)(
Schumpeterian Growth Theory Slide - 21 Elias Dinopoulos
Endogenous Scale-Invariant Schumpeterian-Growth Models
Dinopoulos and Syropoulos (2007) have proposed a different approach to remove the scale-effects property based on innovation contests.
We introduced explicitly the actions of incumbents to protect their monopoly rents.
We call these actions rent-protecting activities (RPAs). The level of R&D difficulty is assumed to be proportional to
the level of RPAs. This approach has been used by Sener (2006) and Dinopoulos
and Syropoulos (2004) to address questions of globalization and wage income inequality.
Schumpeterian Growth Theory Slide - 22 Elias Dinopoulos
An Assessment Endogenous Schumpeterian growth models employ a
linear relationship between the level of R&D difficulty and the level of population.
• Is this “knife-edge” property unsatisfactory?– There are many knife edge properties in economics.
Constant returns to scale Saddle-point stability path Labor-augmenting technological progress
– The linear property is the result of market-based mechanisms.
Under monopolistic competition the number of varieties is proportional to the economy’s size measured by the number of consumers.
Schumpeterian Growth Theory Slide - 23 Elias Dinopoulos
An Assessment
In the case of RPAs, the level of R&D difficulty is chosen optimally to maximize expected discounted profits.
Conjecture: For any scale invariant endogenous growth mechanism, there exists a market based mechanism that determines endogenously the evolution of R&D difficulty.
The following remark on the issue of “functional robustness” is borrowed from Temple (2003).
Schumpeterian Growth Theory Slide - 24 Elias Dinopoulos
An Assessment
Five obvious rules for thinking about long-run growth:– The long-run is a theoretical abstraction that is
sometimes of limited practical value.– Do not assume that a good growth model needs to have a
balanced growth, or that long-run growth have to be endogenous.
– Do not dismiss a model of growth because the long-run outcomes depend on knife-edge properties.
– Long-run predictions might be impossible to test.– Do not undervalue level effects.
Schumpeterian Growth Theory Slide - 25 Elias Dinopoulos
An Assessment
I believe that all approaches to the removal of scale effects are extremely useful.
• Exogenous Schumpeterian growth models are analytically more tractable and have been used analyze a variety of current issues.
• Focus on steady-state analysis is very useful because of its simplicity.
• We should be analyzing the robustness of policy effects by using a variety of scale-invariant growth models.
Schumpeterian Growth Theory Slide - 26 Elias Dinopoulos
An Assessment
The development of exogenous scale-invariant growth models necessitates the use of “Schumpeterian” as opposed to “endogenous” growth.
The term “Schumpeterian growth” is policy neutral and offers the well deserved recognition and credit to Joseph Schumpeter.
Schumpeterian Growth Theory Slide - 27 Elias Dinopoulos
Conclusions
This paper offered an overview of recent development and directions in Schumpeterian growth theory.
Scale invariant growth models can be exogenous or endogenous.
These models can serve as templates for a unified growth theory that combines the insights of the neoclassical model with endogenous thennological progress and positive rate of population growth.