Jason Weitze

When faced with multiple causes, researchers often ask, ``How much did each cause contribute to their combined effect?'' For instance, advertisers want to attribute the effect of an ad campaign to each ad, while economists want to decompose the effect of a policy bundle. This seemingly simple question hides a fundamental problem: there is no single, agreed-upon estimand, so competing methods naturally yield contradictory results. This paper confronts this challenge by developing a novel framework for causal attribution. I characterize a causal decomposition, establishing that it attributes to each cause its individual effect plus some convex share of its jointly-produced effects (e.g., interaction or indirect effects). The result is not a single causal decomposition, but rather a set, formally capturing the fundamental ambiguity of attribution. While standard practice masks this ambiguity by reporting a single point estimate, I propose embracing it by reporting a new estimand: attribution bounds. These bounds transparently communicate the minimum and maximum attributable to a cause across all causal decompositions, collapsing to a single point when there are no joint effects. To make the bounds practical, I provide design-based and observational methods for identification and estimation. Finally, I demonstrate the bounds utility in two applications: one where wide bounds underscore the limitations of reporting a single point estimate, and another where tight bounds indicate minimal ambiguity.

We estimate the effect of receiving Supplemental Security Income (SSI) in childhood on adult outcomes using multiple sources of variation. Across quasi-experiments, we find that the program has heterogeneous effects that vary with the parental earnings response to SSI benefits: SSI has positive effects on children when parents do not adjust their labor supply in response to SSI income (meaning household income increases), but zero or negative effects on children when parents reduce their earnings (meaning household income remains constant or falls). These results suggest that, relative to parent non-work time, consumption is crucial in the human capital production of low-income children with disabilities. We estimate a model of maternal labor supply and child human capital formation to quantify the relative importance of these channels. Our findings indicate that 1) the income effects of SSI on children's human capital are substantial, with a limited role for perverse incentive effects from conditioning benefits on disability status, and 2) parental work on net improves children's outcomes by increasing household resources, despite the potential decrease in parental time.

Determining which data identifies a structural model can be cumbersome if not infeasible, leading researchers to rely on heuristic arguments regularly. This paper proposes an intuitive, computational alternative in two steps. First, I embed identification questions within a more general decision problem: What data (e.g., moments) should be collected to inform an economic quantity of interest (e.g., a policy counterfactual)? Second, I translate the decision problem into an algorithmic prediction exercise by showing that the value of a particular type of data corresponds to how well it predicts the quantity of interest. I provide a simulation-based algorithm that uses machine learning to assess the predictive ability of the data and, thus, its value. When using population data, the resulting metric reflects a decision-relevant notion of the size of the identified set; when using sample data, the metric also addresses finite-sample concerns. By conditioning on existing data, our framework also yields a natural analog to local identification measures, and I provide a simple algorithm for efficiently computing it. Leveraging these core algorithms, I show how one can systematically choose which (additional) moments to collect. I illustrate the practical utility of our approach through simulation experiments and an application to the life-cycle savings model in Gourinchas and Parker (2002).

Recent work has demonstrated the value of flexibly incorporating covariates when analyzing experiments with many experimental units. It is less clear how, or even if, we should incorporate covariate information in settings with few experimental units, like clustered experiments. For this case, we propose a Leave One (or Two) Cluster Out (LOCO) estimator that leverages the cluster-level randomization to guarantee an unbiased estimate, while simultaneously incorporating individual-level information in a flexible way to reduce variance. While clustered experiments tend to have few experimental units (e.g., villages), we often observe outcome data and covariates for a much larger number of individuals (e.g., people living in those villages). In practice, researchers often choose between leveraging this more granular data in individual-level linear regressions that control for covariates and a simple difference in means that ignores the covariates. While the former reduces variance, it comes at the expense of the latter's unbiasedness guarantee. Our proposed estimator aims to combine the best of both strategies.