This paper studies aggregate dynamics in a cobweb model where learning takes place through a selection mechanism, by which more successful firms are replicated at a higher rate. The structure of the model allows to characterize analytically the aggregate dynamics, and to compute the effect on welfare of alternative levels of selectivity. A central aspect is that greater selectivity, while bringing the distribution of firm types closer to the optimal one at a given date, tends to make the economy less stable at the aggregate level. As in Nelson and Winter (1982), firms differ in their labor/capital ratio. They do not choose it optimally, rather it is a characteristic of a firm. The distribution of firms evolves over time in a way that favors the most profitable firm types. Selection may be inadequate because firms are being selected on the basis of incorrect market signals. Selection itself may reinforce such mispricing, thus generating instability. I compare economies that differ in the volatility and persistence of their productivity shocks, as well as the elasticity of labor supply. The key findings are as follows. First, a trade-off arises since greater selection allows to better track shocks and limits mutational drift in firm types; on the other hand, selection may strengthen cobweb oscillatory dynamics. Second, there seems to be a value in maintaining a diverse "ecology of firms", in order to cope with future shocks. These observations explain the key results. Optimal selectivity is larger, the less "cobweb unstable" the economy, i.e. the more elastic the labor supply. Second, optimal selectivity is larger, the more persistent the aggregate productivity shocks. Finally, optimal selectivity is larger, the lower the variance of productivity innovations. The model can be extended to allow for firm entry and trend productivity growth, and a selection process with memory. Empirical evidence suggests that, in accordance to the model, countries with less regulated product markets exhibit lower aggregate inertia.
cobweb model adaptive learning selection mutation evolution