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Abstract:
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There is increasing demand for causal inference from observational data, but randomization is the reasoned basis for causal inference. Randomization inference was developed within the context of experiments, long before the era of ubiquitous observational data. To support causal inference from natural experiments we generalize the notion of randomization inference and introduce the randomness of the data generating process as a novel and practical sensitivity parameter. The randomness of the data generating process is formally defined within a general framework of stochastic counterfactuals. With minimal assumptions we compute a threshold of sufficient randomness from observed data by solving a constrained optimization problem over a space of joint propensity distributions. If the actual randomness is greater than the threshold then causal inference is warranted. The actual randomness of the data generating process is easier to specify than the structure of a causal graph, and it is intuitively connected with classic coefficients of determination rather than odds ratios or relative risks.
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