Abstract Models testing interactive and quadratic hypotheses are common in Political Science but control strategies for these models have received little attention. Common practice is to simply include additive control variables, without relevant product terms, into models with interaction or quadratic terms. In this paper, we show in Monte Carlos that interaction terms can absorb the effects of other un-modeled interaction and non-linear effects and analogously, that included quadratic terms can reflect omitted interactions and non-linearities. This problem even occurs when included and omitted product terms do not share any constitutive terms. We show with Monte Carlo experiments that regularized estimators, the adaptive Lasso, Kernel Regularized Least Squares (KRLS), and Bayesian Additive Regression Trees (BART) can prevent the misattribution of interactive/quadratic effects, minimize the problems of efficiency loss and overfitting, and have low false-positive rates. We illustrate how inferences drawn can change when relevant product terms are used in the control strategy using a recent paper. Implementing the recommendations of this paper would increase the reliability of conditional and non-linear relationships estimated in many papers in the literature.

Research on government repression often focuses on the comparison between states over time and provides little insight about the targets of repression within a state. This article unpacks government repression against different ethnic groups. It argues that non‐democratic governments use pre‐emptive and targeted repression against ethnic groups that are discriminated, strong, or have a history of protest or rebellion in order to prevent future ethnic rebellions. For democratic governments, on the other hand, the cost of pre‐emptive repression is too high. The article tests this argument in a quantitative analysis of government‐group dyads. It finds at least partial support for some implications of the argument: Autocratic governments use more repression than democracies against discriminated groups, but only when they are also weak, and against groups with a history of protest. There is little evidence that regimes of either type respond to previous violent mobilization or group strength with repression.

Empirical studies show that many governments gear the provision of goods and services towards their ethnic peers. This article investigates governments’ strategies to provide ethnic favors in Africa. Recent studies of ethnic favoritism find that presidents' ethnic peers and home regions enjoy advantages, yet cannot disentangle whether goods are provided to entire regions or co-ethnic individuals. This article argues that local ethnic demography determines whether governments provide non-excludable public goods or more narrowly targeted handouts. Where government co-ethnics are in the majority, public goods benefit all locals regardless of their ethnic identity. Outside of these strongholds, incumbents pursue discriminatory strategies and only their co-ethnics gain from favoritism. Using fine-grained geographic data on ethnic demographics, the study finds support for the argument's implications in the local incidence of infant mortality. These findings have important implications for theories of distributive politics and conflict in multi-ethnic societies.

Recent research has shown that interaction effects may often be nonlinear (Hainmueller, Mummolo, and Xu [2019, Political Analysis 27, 163–192]). As standard interaction effect specifications assume a linear interaction effect, that is, the moderator conditions the effect at a constant rate, this can lead to bias. However, allowing nonlinear interaction effects, without accounting for other nonlinearities and nonlinear interaction effects, can also lead to biased estimates. Specifically, researchers can infer nonlinear interaction effects, even though the true interaction effect is linear, when variables used for covariate adjustment that are correlated with the moderator have a nonlinear effect upon the outcome of interest. We illustrate this bias with simulations and show how diagnostic tools recommended in the literature are unable to uncover the issue. We show how using the adaptive Lasso to identify relevant nonlinearities among variables used for covariate adjustment can avoid this issue. Moreover, the use of regularized estimators, which allow for a fuller set of nonlinearities, both independent and interactive, is more generally shown to avoid this bias and more general forms of omitted interaction bias.