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We propose a new method to estimate causal effects from nonexperimental data.Each pair of sample units is first associated with a stochastic 'treatment' -differences in factors between units - and an effect - a resultant outcomedifference. It is then proposed that all such pairs can be combined to providemore accurate estimates of causal effects in observational data, provided astatistical model connecting combinatorial properties of treatments to theaccuracy and unbiasedness of their effects. The article introduces one suchmodel and a Bayesian approach to combine the $O(n^2)$ pairwise observationstypically available in nonexperimnetal data. This also leads to aninterpretation of nonexperimental datasets as incomplete, or noisy, versions ofideal factorial experimental designs.  This approach to causal effect estimation has several advantages: (1) itexpands the number of observations, converting thousands of individuals intomillions of observational treatments; (2) starting with treatments closest tothe experimental ideal, it identifies noncausal variables that can be ignoredin the future, making estimation easier in each subsequent iteration whiledeparting minimally from experiment-like conditions; (3) it recovers individualcausal effects in heterogeneous populations. We evaluate the method insimulations and the National Supported Work (NSW) program, an intensivelystudied program whose effects are known from randomized field experiments. Wedemonstrate that the proposed approach recovers causal effects in common NSWsamples, as well as in arbitrary subpopulations and an order-of-magnitudelarger supersample with the entire national program data, outperformingStatistical, Econometrics and Machine Learning estimators in all cases...

What can the millions of random treatments in nonexperimental data reveal about causes?