  Does adding a theorem to a paper affect its chance of acceptance? Does
labeling a post with the author's gender affect the post popularity? This paper
develops a method to estimate such causal effects from observational text data,
adjusting for confounding features of the text such as the subject or writing
quality. We assume that the text suffices for causal adjustment but that, in
practice, it is prohibitively high-dimensional. To address this challenge, we
develop causally sufficient embeddings, low-dimensional document
representations that preserve sufficient information for causal identification
and allow for efficient estimation of causal effects. Causally sufficient
embeddings combine two ideas. The first is supervised dimensionality reduction:
causal adjustment requires only the aspects of text that are predictive of both
the treatment and outcome. The second is efficient language modeling:
representations of text are designed to dispose of linguistically irrelevant
information, and this information is also causally irrelevant. Our method
adapts language models (specifically, word embeddings and topic models) to
learn document embeddings that are able to predict both treatment and outcome.
We study causally sufficient embeddings with semi-synthetic datasets and find
that they improve causal estimation over related embedding methods. We
illustrate the methods by answering the two motivating questions---the effect
of a theorem on paper acceptance and the effect of a gender label on post
popularity. Code and data available at
https://github.com/vveitch/causal-text-embeddings-tf2}{github.com/vveitch/causal-text-embeddings-tf2
