Transition Dynamics in Endogenous Recombinant Growth Models by Means of Projection Methods

This study provides a step further in the computation of the transition path of a continuous time endogenous growth model discussed by Privileggi (Nonlinear dynamics in economics, finance and social sciences: essays in honour of John Barkley Rosser Jr., Springer, Berlin, Heidelberg, pp. 251-278, 2010)-based on the setting first introduced by Tsur and Zemel (J Econ Dyn Control 31:3459-3477, 2007)-in which knowledge evolves according to the Weitzman (Q J Econ 113:331-360, 1998) recombinant process. A projection method, based on the least squares of the residual function corresponding to the ODE defining the optimal policy of the 'detrended' model, allows for the numeric approximation of such policy for a positive Lebesgue measure range of values of the efficiency parameter characterizing the probability function of the recombinant process. Although the projection method's performance rapidly degenerates as one departs from a benchmark value for the efficiency parameter, we are able to numerically compute time-path trajectories which are sufficiently regular to allow for sensitivity analysis under changes in parameters' values.