This paper constitutes a first attempt at studying the transition dynamics of the Tsur and Zemel (2007) continuous time endogenous growth framework in which knowledge evolves according to the Weitzman (1998) recombinant process. For a specific choice of the probability function characterizing the Weitzman recombinant process, we find a suitable transformation for the state and control variables in the dynamical system diverging to asymptotic constant growth, so that an equivalent 'detrended' system converging to a steady state in the long run can be tackled. Since the dynamical system obtained so far turns out to be analytically intractable, we rely on numerical simulation in order to fully describe the transition dynamics for a set of values of the parameters.

Summary. We study a one-sector stochastic optimal growth model with a representative agent. Utility is logarithmic and the production function is of the Cobb-Douglas form with capital exponent . Production is a¤ected by a multiplicative shock taking one of two values with positive probabilities p and 1 p. It is well known that for this economy, optimal paths converge to a unique steady state, which is an invariant distribution. We are concerned with properties of this distribution. By using the theory of Iterated Function Systems, we are able to characterize such a distribution in terms of singularity versus absolute continuity as parameters and p change. We establish mutual singularity of the invariant distributions as p varies between 0 and 1 whenever < 1=2. More delicate is the case > 1=2. Singularity with respect to Lebesgue

Knowledge production, Endogenous recombinant growth, Transition dynamics, Projection methods, Least squares, C61, C63, O31, O41,

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This paper concludes the study of transition paths in the continuous-time recombinant endogenous growth model by providing numerical methods to estimate the threshold initial value of capital (a Skiba-type point) above which the economy takes off toward sustained growth in the long run, while it is doomed to stagnation otherwise. The model is based on the setting first introduced by Tsur and Zemel and then further specified by Privileggi, in which knowledge evolves according to the Weitzman recombinant process. We pursue a direct approach based on the comparison of welfare estimations along optimal consumption trajectories either diverging to sustained growth or converging to a steady state. To this purpose, we develop and test three algorithms capable of numerically simulating the initial Skiba-value of capital, each corresponding to initial stock of knowledge values belonging to three different ranges, thus covering all possible scenarios. JEL Classification Numbers: C61, C62, C63, C68, O31, O41.