  We present a method for estimating causal effects in time series data when
fine-grained information about the outcome of interest is available.
Specifically, we examine what we call the split-door setting, where the outcome
variable can be split into two parts: one that is potentially affected by the
cause being studied and another that is independent of it, with both parts
sharing the same (unobserved) confounders. We show that under these conditions,
the problem of identification reduces to that of testing for independence among
observed variables, and present a method that uses this approach to
automatically find subsets of the data that are causally identified. We
demonstrate the method by estimating the causal impact of Amazon's recommender
system on traffic to product pages, finding thousands of examples within the
dataset that satisfy the split-door criterion. Unlike past studies based on
natural experiments that were limited to a single product category, our method
applies to a large and representative sample of products viewed on the site. In
line with previous work, we find that the widely-used click-through rate (CTR)
metric overestimates the causal impact of recommender systems; depending on the
product category, we estimate that 50-80\% of the traffic attributed to
recommender systems would have happened even without any recommendations. We
conclude with guidelines for using the split-door criterion as well as a
discussion of other contexts where the method can be applied.
