Integrating Real Sector Growth and Inflation Into An Agent-Based Stock Market Dynamics

Concentrating on speculative flow rather than stock demand, the paper puts forward a deterministic continuous-time model of the equity market that is compatible with a growing and inflationary economy. Instead of the systematically rising equity price, the central state variable in now Tobin's q, which makes it necessary to consider explicitly the financing of fixed investment in the real sector. Integrating a number of suitable re-specifications and fixing the variables in the real sector, the model succeeds in the re-establishing (almost) the same mathematical structure as the elegant two-dimensional Lux (1995) model, which implicitly was set up in the usual stationary and non-inflationary environment. Thus a speculative dynamics is obtained that can generate persistent oscillations as well as bubble equilibria and a rich sequence of local and global bifurcations. The model is ready to be combined with the growth cycles in a real sector, where the short-term fluctuations of Tobin's q may then also affect aggregate demand.