Non-stationary Mean Birth Rate

In all previous chapters, we have studied the steady-state mean density g(s) given by (3.18) of firm’s asset values and its properties, for a stationary intensity ν of firm’s births. In real life, ν is not constant, with periods of strong growth, such as during “new economy bubbles” (Galbraith, 1997; Kindleberger, 2000; Shefrin, 2000; Shiller, 2000; Shleifer, 2000; Sornette, 2003; White, 1996) or during and after political transitions, and periods of stagnation, for instance during depressions. Over large times, there are even secular variations of firms creations, such as for instance during the transition associated with the political “big bang” of the Soviet Bloc in the 1990s (Nowak et al., 2005). In some countries, (e.g., Poland), not long after the transition, the economy started to grow at a fast rate soon surpassing the level of its economy under socialism, with a large growth of the number of privately owned enterprises during the transition from centrally governed to the market economy (Nowak et al., 2000, 2005; Gur et al., 2008). In this chapter, we first derive some properties resulting from a non-stationary birth intensity ν(t) of the mean density g(s, t) of firm’s asset values given by (3.15). Then, we introduce and study a model in which the intensity of firm’s birth is coupled with the overall firm’s asset value: as the later grows, the former is also assumed to grow correspondingly. This simple model accounts more realistically for the fact that firm’s creation is indeed related to the innovation dynamics and capital availability, both being stronger in periods of firm’s growth.