Bounding Causal Effects in Ecological Inference Problems

Abstract

This paper is concerned with making causal inferences with ecological data. Aggregate outcome information is combined with individual demographic information 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 the tightest upper and lower 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.