A Simple Characterization of Dynamic Completeness in Continuous Time

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.)

Demographic Transitions: analyzing the effects of mortality on fertility

The effect of mortality reductions on fertility is one of the main mechanisms stressed by the recent growth literature in order to explain demographic transitions. We analyze the empirical relevance of this mechanism based on the experience of all countries since 1960. We distinguish between the effects on gross and net fertility, take into account the dynamic nature of the relationship and control for alternative explanatory factors and for endogeneity. Our results show that mortality plays a large role in fertility reductions, that the change in fertility behavior comes with a lag of about 10 years and that both net and gross fertility are affected. We find comparatively little support for explanations of the demographic transition based on economic development or technological change.