Rent Protection, Innovation and Growth Slide 1 Innovation and Rent Protection in the Theory of Schumpeterian Growth By Elias Dinopoulos Schumpeterian Growth Theory

Rent Protection, Innovation and Growth Slide 2 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)

Rent Protection, Innovation and Growth Slide 3 Motivation R&D 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.

Rent Protection, Innovation and Growth Slide 4 Rent-protection mechanisms The technological mechanism 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.

Rent Protection, Innovation and Growth Slide 5 Definitions This paper introduces formally the concept of Rent Protection Activities (RPAs) in the theory of Schumpeterian Growth. Rent-protection activities Rent-protection activities are costly (resource using) attempts by incumbents to delay the innovation success of challengers. Schumpeterian Growth Schumpeterian Growth is based on the introduction of new goods or processes (as opposed to physical or human capital accumulation).

Rent Protection, Innovation and Growth Slide 6 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 R&D difficulty, D(t), as an increasing function of RPAs. may may R&D may become more difficult over time because incumbent firms may allocate more resources to RPAs.

Rent Protection, Innovation and Growth Slide 7 RPAs and removal of scale effects R&D contest The discovery process is modeled as an R&D contest (instead of an R&D race):  Challengers spend resources on R&D investments  Incumbents allocate resources to RPAs.  Both the levels of R&D and RPAs are chosen endogenously, and increase exponentially in the steady-state equilibrium.

Rent Protection, Innovation and Growth Slide 8 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 R&D 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.

Rent Protection, Innovation and Growth Slide 9 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 R&D contests.

Rent Protection, Innovation and Growth Slide 10 The model: An overview Each industry has three activities that exhibit constant returns to scale. Manufacturing of final goods  Manufacturing of final goods This activity uses non-specialized labor.  Innovative R&D services This activity uses non-specialized labor.  Rent-protection activities This activity uses only specialized labor.

Rent Protection, Innovation and Growth Slide 11 The knowledge-creation process There is a continuum of industries indexed by   [0.1] A challenger j that engages in innovative R&D discovers the next higher quality product with instantaneous probability:

Rent Protection, Innovation and Growth Slide 12 The knowledge-creation process  We will refer to I( ,t) as the effective R&D.  Variable I( ,t) is the intensity of the Poisson process that governs the arrival of innovations in industry .  The industry-wide probability of innovating is

Rent Protection, Innovation and Growth Slide 13 The knowledge-creation process  The present paper assumes that the level of R&D difficulty is given by  We also assume that population N(t) grows at a constant and exogenous rate g N > 0.

Rent Protection, Innovation and Growth Slide 14 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

Rent Protection, Innovation and Growth Slide 15 Production and household behavior  Firm j produces innovative R&D services using only non-specialized labor according to the cost function  Each household maximizes its discounted utility

Rent Protection, Innovation and Growth Slide 16 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.

Rent Protection, Innovation and Growth Slide 17 Household behavior The solution to the consumer’s maximization problem yields: and

Rent Protection, Innovation and Growth Slide 18 R&D contests The flow of profits for the incumbent monopolist in a typical industry is given by  Each challenger engages in R&D investment, R, and each incumbent engages only in RPAs, X(t). stochastic differential game  The strategic interactions between incumbents and challengers are modeled as a stochastic differential game for Poisson jump processes.

Rent Protection, Innovation and Growth Slide 19 Factor markets The full-employment condition for non- specialized labor is The full-employment condition for specialized labor is

Rent Protection, Innovation and Growth Slide 20 Steady-state (balanced-growth) equilibrium The following variables are constant over time Effective R&D, I; per capita consumption expenditure, c; wages of specialized and non-specialized labor, w H and w L ; long-run growth, g U. Long-run real per capita income, u(t), and its growth rate, g U, are given by

Rent Protection, Innovation and Growth Slide 21 Innovation and resource allocation. rate of innovation : The solution to the stochastic differential game yields the following expression for the long-run rate of innovation : resource condition Combining several equations yields the resource condition

Rent Protection, Innovation and Growth Slide 22 R&D Condition Solving for the interest rate from the zero-profit condition and using equation (10) yields the R&D condition (26) The resource condition defines a negatively sloped line and the R&D condition defines a positively sloped line in the c, I space.

Rent Protection, Innovation and Growth Slide 23 Figure 1: Steady-state equilibrium c 0 I E I* c* R&D Condition Resource Condition

Rent Protection, Innovation and Growth Slide 24 Basic results of the analysis Proposition 1: There exists a unique steady- state equilibrium such that: Proposition 1: There exists a unique steady- state equilibrium such that: Effective R&D, the relative wage of specialized labor, per capita IBA output, and per capita consumption expenditure are all bounded and constant over time. Effective R&D, 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. Long-run Schumpeterian growth is bounded and does not exhibit scale effects. The removal of scale effects is consistent with time-series evidence.

Rent Protection, Innovation and Growth Slide 25 Comparative steady-state results Proposition 2: The long-run Schumpeterian growth rate depends Proposition 2: The long-run Schumpeterian growth rate depends Positively on the proportional R&D subsidy rate, the population growth rate, and the size of innovations; Positively on the proportional R&D 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 R&D services, and the productivity of RPAs. Negatively on the fraction of specialized labor, the market interest rate, the unit labor requirement in the production of R&D services, and the productivity of RPAs. Proposition 3 Proposition 3 compares the social and market rates of innovation.

Rent Protection, Innovation and Growth Slide 26 Commercial versus University Patenting

Rent Protection, Innovation and Growth Slide 27 Commercial versus University Patenting

Rent Protection, Innovation and Growth Slide 28 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.

Rent Protection, Innovation and Growth Slide 29 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.