What would have happened? : Four essays investigating causality

Abstract: This dissertation consists of four self-contained essays.Essay 1. A common method to reduce the uncertainty of causal inferences from experiments is to assign treatments in fixed proportions within groups of similar units: blocking. Previous results indicate that one can expect substantial reductions in variance if these groups are formed so to contain exactly as many units as treatment conditions. This approach can be contrasted to threshold blocking which, instead of specifying a fixed size, requires that the groups contain a minimum number of units. In this essay, I investigate the advantages of respective method. In particular, I show that threshold blocking is superior to fixed-sized blocking in the sense that it always finds a weakly better grouping for any objective and sample. However, this does not necessarily hold when the objective function of the blocking problem is unknown, and a fixed-sized design can perform better in that case. I specifically examine the factors that govern how the methods perform in the common situation where the objective is to reduce the estimator's variance, but where groups are constructed based on covariates. This reveals that the relative performance of threshold blocking improves when the covariates become more predictive of the outcome.Essay 2. Inferences from randomized experiments can be improved by blocking: assigning treatment in fixed proportions within groups of similar units. The use of the method, however, is limited by the difficulty in deriving these groups. Current blocking methods are restricted to special cases or run in exponential time; are not sensitive to clustering of data points; and are often heuristic, providing an unsatisfactory solution in many common instances. This essay introduces an algorithm that implements a new, widely applicable class of blocking—threshold blocking—that solves these problems. Given a minimum required group size and a distance metric, we study the blocking problem of minimizing the maximum distance between any two units within the same group. We prove this is a NP-hard problem and derive an approximation algorithm that yields a blocking where the maximum distance is guaranteed to be at most four times the optimal value. This algorithm runs in O(n log n) time with O(n) space complexity. This makes it the first blocking method with an ensured level of performance that works in massive experiments. While many commonly used algorithms form pairs of units, our algorithm constructs the groups flexibly for any chosen minimum size. This facilitates complex experiments with several treatment arms and clustered data. A simulation study demonstrates the efficiency and efficacy of our blocking algorithm; tens of millions of units can be blocked using a desktop computer in a few minutes.Essay 3. Scholars study political incumbency effects to disentangle how office holding affects subsequent election results. Several types of effects have been discussed and investigated in this time-honored literature, but few have been formally defined. The recent popularity of the regression discontinuity design to investigate the topic has, however, converged the focus to one particular effect: the party incumbency effect. That is, the effect on parties from being an incumbent party. In this essay, I introduce a causal model with which most of the previously discussed effect can be defined. In particular, I can give formal definitions of the incumbent legislator effect—the effect on parties of having an incumbent office holder as candidate—and the personal incumbency effect—the effect on candidates of being the incumbent office holder. Using the model, I decompose the party incumbency effect into these newly defined effects, thereby providing a link between the different effects. The model also allows me to revisit previous estimator and derive which effect they estimate. This investigation reveals that the legislator effect has been in focus in much of the past literature. Motivated by the lack of identification strategies for the personal effect, I introduce several strategies which, under suitable assumptions, can identify the effect. Last, to illustrate these strategies, I investigate the personal incumbency effect in recent Brazilian mayoral elections.Essay 4. Recent research has reported positive effects on schooling, particularly for girls, due to in utero protection from iodine deficiency resulting from iodized oil capsule distribution in Tanzania. These results suggest that similar health interventions might have contributed to the reduction of the educational gender gap and, more generally, unveiled a mechanism through which the natural health environment affects social and economic development. In this essay, we revisit the Tanzanian experience by investigating how these effects differ over time and across surveys; across different treatment specifications; and across additional educational outcome measures. Contrary to previous studies, we find that the estimated effects tend to be small and not robust across specifications or samples. Using all available data and a medically motivated iodine depletion function, we find no evidence of a positive long-run effect of iodine deficiency protection on educational attainment.