  Using observed language to understand interpersonal interactions is important
in high-stakes decision making. We propose a causal research design for
observational (non-experimental) data to estimate the natural direct and
indirect effects of social group signals (e.g. race or gender) on speakers'
responses with separate aspects of language as causal mediators. We illustrate
the promises and challenges of this framework via a theoretical case study of
the effect of an advocate's gender on interruptions from justices during U.S.
Supreme Court oral arguments. We also discuss challenges conceptualizing and
operationalizing causal variables such as gender and language that comprise of
many components, and we articulate technical open challenges such as temporal
dependence between language mediators in conversational settings.
