Bounding Causal Effects in Ecological Inference Problems
Social Science Research Network
T his note illustrates a new method for making causal inferences with ecological data. We show how to combine aggregate outcomes with individual demographics from separate data sources to make causal inferences about individual behavior. In addressing such problems, even under the selection on observables assumption often made in the treatment effects literature, it is not possible to identify causal effects of interest. However, recent results from the partial identification literature provide
... literature provide sharp bounds on these causal effects. We apply these bounds to data from Chilean mayoral elections that straddle a 2012 change in Chilean electoral law from compulsory to voluntary voting. Aggregate voting outcomes are combined with individual demographic information from separate data sources to determine the causal effect of the change in the law on voter turnout. The bounds analysis reveals that voluntary voting decreased expected voter turnout, and that other causal effects are overstated if the bounds analysis is ignored. E cological inference (EI) problems are a class of data combination problems in which aggregate outcome information from one data source is combined with individual demographic information from a separate data source to make inferences about individual outcomes. The objectives of EI include description and prediction of individual behavior, as well as causal inference about individual behavior. King (1997) treats EI problems where the principal objective is description of individual behavior in political science applications. King, Rosen and Tanner (2004) contain articles addressing all three objectives from a number of different fields, including political science, economics, and epidemiology. This note applies new results from the partial identification literature to make causal inferences with ecological data. Specifically, we use new methods in Fan, Sherman and Shum (2014) to infer the causal effect of a change in Chilean voting law on voter turnout in mayoral elections. In the absence of the data combination problem, standard results from the treatment effects literature can be used to investigate causal effects. Specifically, if data on outcomes and covariates are observed in the same data set, then it is straightforward, under standard assumptions using known methods, to identify and consistently estimate the usual causal effects of interest, such as the average treatment effect (ATE) or the average treatment effect on the treated (ATT). For example, one could apply propensity score methods under a standard selection on observables assumption, as in Rosenbaum and Rubin (1983) .