The concepts of principal strata direct and indirect effects are compared with and contrasted to definitions of direct and indirect effects which make reference to interventions on intermediate variables. Certain simple relations hold for direct effects but not indirect effects.

We give a definition of a bounded edge within the causal directed acyclic graph framework. A bounded edge generalizes the notion of a signed edge and is defined in terms of bounds on a ratio of survivor probabilities. We derive rules concerning the propagation of bounds. Bounds on causal effects...

Analyses of social network data have suggested that obesity, smoking, happiness, and loneliness all travel through social networks. Individuals exert “contagion effects” on one another through social ties and association. These analyses have come under critique because of the possibility...

The effect of periods of nontrading on volatility is examined. The empirical evidence suggests that volatility is higher on days which follow a period of nontrading. A nonparametric kernel regression is used to estimate a diffusion model with a volatility term dependent on the number of days of...