Emergent Pareto-Levy Distributed Returns to Research in a Multi-Agent Model of Endogenous Technical Change

We build a multi-agent model of endogenous technical change in which heterogeneous investments in patented knowledge generate Pareto-Levy and lognormal distributed returns to investment in research from very weak distributional assumptions. Firms produce a homogenous good and a public stock of knowledge accumulates from the expired patents of privately produced knowledge. Increasing returns to scale are derivative of endogenously produced technology, but the market remains competitive due to imperfect information and costly household search. The interaction of heterogeneous knowledge, research investment, revenues, and search outcomes across agents endogenously generates the empirically observed but seemingly idiosyncratic Pareto- Levy and lognormal mixture distribution of market returns. These distributional characteristics have ramifications for endogenous growth models given the importance of extreme values and market leaders in technological advancement. Average growth rates in the model have a global maximum at a finite, non-zero patent length. The distribution of growth rates is characterized by “fat tails.” The variance of growth rates increases with patent length.