Innovation and Rent Protection in the Theory of Schumpeterian Growth

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Innovation and Rent Protection in the Theory of
Schumpeterian Growth
Schumpeterian Growth Theory

• By
• Elias Dinopoulos

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Organization

• This topic presents a state-of-the art growth
  model based on quality improvements.
• The model generates endogenous long-run
  Schumpeterian growth without scale effects.
• Readings
• Dinopoulos and Syropoulos (2007)
• Jones, Chapters 4 and 5.
• Dinopoulos and Thompson (1999)

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Motivation

• RD investment occurs in an uncertain and
  insecure environment.
• The rents from past innovations might be captured
  through imitation or further innovation.
• Incumbents may engage in activities that retard
  the pace of innovation by potential competitors.
• These activities include
• Trade secrecy
• distribution systems that exploit lead time
• increased product complexity
• various litigation mechanisms.

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Rent-protection mechanisms

• The technological mechanism
• Higher product complexity trade secrecy
• The legal mechanism
• Effective monitoring and litigation concerning
  possible patent infringement by challengers.
• The political mechanism
• Lobbying politicians
• Bribing government officials in order to
  restrict access to government services to
  potential competitors.

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Definitions

• This paper introduces formally the concept of
  Rent Protection Activities (RPAs) in the theory
  of Schumpeterian Growth.
• Rent-protection activities are costly (resource
  using) attempts by incumbents to delay the
  innovation success of challengers.
• Schumpeterian Growth is based on the introduction
  of new goods or processes (as opposed to physical
  or human capital accumulation).

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RPAs and removal of scale effects

• This paper proposes a new mechanism that removes
  the scale-effects property.
• The mechanism is based on the notion of RPAs.
• We model the RD difficulty, D(t), as an
  increasing function of RPAs.
• RD may become more difficult over time because
  incumbent firms may allocate more resources to
  RPAs.

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RPAs and removal of scale effects

• The discovery process is modeled as an RD
  contest (instead of an RD race)
• Challengers spend resources on RD investments
• Incumbents allocate resources to RPAs.
• Both the levels of RD and RPAs are chosen
  endogenously, and increase exponentially in the
  steady-state equilibrium.

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Preview of results

• The model generates endogenous long-run
  Schumpeterian growth without scale effects.
• Scale effects are removed from real income per
  capita as well.
• Long-run growth is positively related to
  proportional RD subsidies and the rate of growth
  of population.
• Long run growth is closely related to income
  distribution.
• Several steady-state properties and comparative
  statics results are consistent with time series
  and international cross-sectional evidence.

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The model An overview

• A continuum of identical households with
  infinitely lived members.
• Each household is a dynastic family whose size
  grows at the rate of population growth.
• Population is partitioned into specialized and
  non specialized labor.
• There is a continuum of structurally identical
  industries producing final consumption goods.
• Innovation takes the form of higher quality
  products discovered through stochastic sequential
  RD contests.

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The model An overview

• Each industry has three activities that exhibit
  constant returns to scale.
• Manufacturing of final goods
• This activity uses non-specialized labor.
• Innovative RD services
• This activity uses non-specialized labor.
• Rent-protection activities
• This activity uses only specialized labor.

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The knowledge-creation process

• There is a continuum of industries indexed by ?
  ? 0.1
• A challenger j that engages in innovative RD
  discovers the next higher quality product with
  instantaneous probability

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The knowledge-creation process

• The industry-wide probability of innovating is

• We will refer to I(?,t) as the effective RD.
• Variable I(?,t) is the intensity of the Poisson
  process that governs the arrival of innovations
  in industry ?.

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The knowledge-creation process

• The present paper assumes that the level of RD
  difficulty is given by

• We also assume that population N(t) grows at a
  constant and exogenous rate gN gt 0.

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Production

• A firm that produces Z(?,t) units of
  manufacturing output incurs the cost

• RPA services are produced with specialized
  labor according to the following cost function

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Production and household behavior

• Firm j produces innovative RD services using
  only non-specialized labor according to the cost
  function

• Each household maximizes its discounted utility

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Household behavior

• Per capita utility u(t) is defined by the
  following equation

• This a standard sub utility function used in
  quality-ladders growth models.

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Household behavior

• The solution to the consumers maximization
  problem yields

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RD contests

• The flow of profits for the incumbent monopolist
  in a typical industry is given by

• Each challenger engages in RD investment, R, and
  each incumbent engages only in RPAs, X(t).
• The strategic interactions between incumbents and
  challengers are modeled as a stochastic
  differential game for Poisson jump processes.

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Factor markets

• The full-employment condition for
  non-specialized labor is

• The full-employment condition for specialized
  labor is

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Steady-state (balanced-growth) equilibrium

• The following variables are constant over time
• Effective RD, I
• per capita consumption expenditure, c
• wages of specialized and non-specialized labor,
  wH and wL
• long-run growth, gU.
• Long-run real per capita income, u(t), and its
  growth rate, gU, are given by

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Innovation and resource allocation.

• The solution to the stochastic differential game
  yields the following expression for the long-run
  rate of innovation

• Combining several equations yields the resource
  condition

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RD Condition

• Solving for the interest rate from the
  zero-profit condition and using equation (10)
  yields the RD condition (26)

• The resource condition defines a negatively
  sloped line and the RD condition defines a
  positively sloped line in the c, I space.

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Figure 1 Steady-state equilibrium
E
c
I
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Basic results of the analysis

• Proposition 1 There exists a unique steady-state
  equilibrium such that
• Effective RD, the relative wage of specialized
  labor, per capita IBA output, and per capita
  consumption expenditure are all bounded and
  constant over time.
• Long-run Schumpeterian growth is bounded and
  does not exhibit scale effects.
• The removal of scale effects is consistent with
  time-series evidence.

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Comparative steady-state results

• Proposition 2 The long-run Schumpeterian growth
  rate depends
• Positively on the proportional RD subsidy rate,
  the population growth rate, and the size of
  innovations
• Negatively on the fraction of specialized labor,
  the market interest rate, the unit labor
  requirement in the production of RD services,
  and the productivity of RPAs.
• Proposition 3 compares the social and market
  rates of innovation.

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Commercial versus University Patenting
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Commercial versus University Patenting
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Concluding remarks

• The removal of scale effects from Schumpeterian
  growth models is an important step in growth
  theory
• It improves the empirical relevance of the new
  growth theory.
• It increases the likelihood of integrating the
  neoclassical and the new growth approach.
• It will increase our understanding of the
  interactions between growth, income distribution
  and international market linkages.
• The present paper contributes to these
  developments by highlighting the implications of
  RPAs.

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Avenues for further research

• The analysis suggests several avenues for further
  research
• The transitional dynamics and welfare properties
  of the model can be analyzed.
• A multi-country model might shed light on the
  connection between comparative advantage,
  international technology transfer, growth and
  income differences across countries.
• Introduction of endogenous patents and
  imitation-blocking activities is feasible and
  interesting.