Endogenous Growth Paths in Economies with Locally Interacting Agents

The paper presents a dynamic model of endogenous growth with boundedly-rational, locally interacting, firms. Technologies are randomly distributed in a n-dimensional lattice (the productivity space) in such a way that distances between any two practices in the lattice can be taken as a proxy of their technological dissimilarity. At any moment in time, only a finite set of practices can be operated and each firm produces a homogeneous good employing one of them. Production entails dynamically increasing returns to scale in the number of firms operating any given technology. In addition, information about productivities might be locally spread among firms using similar practices. Firms can then learn about known technologies and possibly choose to imitate (i.e. adopt) other known practices. However, if the productivity space is assumed to be open-ended, there is a notionally unbounded set of (higher productivity) technologies waiting to be discovered. Firms are able to locally explore the space around the technology they currently master to find new techniques. If their exploration succeeds, a new (possibly better) technology is introduced in the system. Although imitation and exploration are time-consuming and costly processes for the firm, we assume some degree of path-dependence in learning achievements. Indeed, the likelihood with which a firm will succeed in imitating a higher productivity technology or in introducing a superior innovation is increasing in past firmÌs output. Hence, the activities of exploitation, exploration and imitation take place over a ÎruggedÌ, endogenous, productivity landscape. The properties of the exploitation-exploration trade-off emerging in the economy are thoroughly analyzed by means of both standard analytical tools and extensive Montecarlo exercises. Whenever the productivity space is not open-ended (i.e. the set of known technologies cannot be expanded), it can be analytically shown that: (i) due to the boundedness of the productivity space, the system is not able to generate self-sustaining economic growth; (ii) the economy exhibits multiple steady-states either in GNP levels (e.g. if firms are only able to imitate existing practices) or (statistically) in GNP growth rates (e.g. when firms can explore within a bounded productivity space); (iii) equilibrium selection strongly depends on the rate of information diffusion and returns to scale. However, if the productivity space is open-ended, simulations show that self-sustaining economic growth can emerge, but only for sufficiently high rates of information diffusion, effectiveness of innovation (as measured by the likelihood to find new, better technologies) and cumulativeness of knowledge, together with a certain range of propensities to explore within the population of firms. Whenever these conditions apply, simulated growth-rates time-series display econometric properties (e.g. auto-correlation structure, persistence of fluctuations, etc.) quite similar to those of their empirical counterparts. Despite non-linearities and randomness entailed by local interactions and boundedly- rational behavioral rules, the system can generate a multiplicity of ordered GNP trajectories characterized by small variability both across and within independent runs. In addition, the economy appears to go through subsequent phases of development leading to decreasing long-run volatility in growth-rates over time. Finally, we discuss the conflict potentially arising between individual rationality and collective outcomes. In particular, a simple example is presented in which boundedly-rational firms are replaced by a representative agent with unbounded computational skills and complete information about the structure of the economy. In this case, it can be shown that, for quite general parameter set-ups, the economy reaches average growth rates which are persistently smaller than those reached in the same settings by a boundedly-rational population of firms.