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.

Multiplicative interaction models are widely used in social science to examine whether the relationship between an outcome and an independent variable changes with a moderating variable. Current empirical practice tends to overlook two important problems. First, these models assume a linear interaction effect that changes at a constant rate with the moderator. Second, estimates of the conditional effects of the independent variable can be misleading if there is a lack of common support of the moderator. Replicating 46 interaction effects from 22 recent publications in five top political science journals, we find that these core assumptions often fail in practice, suggesting that a large portion of findings across all political science subfields based on interaction models are fragile and model dependent. We propose a checklist of simple diagnostics to assess the validity of these assumptions and offer flexible estimation strategies that allow for nonlinear interaction effects and safeguard against excessive extrapolation. These statistical routines are available in both R and STATA.

The fixed-effects estimator is biased in the presence of dynamic misspecification and omitted within variation correlated with one of the regressors. We argue and demonstrate that fixed-effects estimates can amplify the bias from dynamic misspecification and that with omitted time-invariant variables and dynamic misspecifications, the fixed-effects estimator can be more biased than the ‘naïve’ OLS model. We also demonstrate that the Hausman test does not reliably identify the least biased estimator when time-invariant and time-varying omitted variables or dynamic misspecifications exist. Accordingly, empirical researchers are ill-advised to rely on the Hausman test for model selection or use the fixed-effects model as default unless they can convincingly justify the assumption of correctly specified dynamics. Our findings caution applied researchers to not overlook the potential drawbacks of relying on the fixed-effects estimator as a default. The results presented here also call upon methodologists to study the properties of estimators in the presence of multiple model misspecifications. Our results suggest that scholars ought to devote much more attention to modeling dynamics appropriately instead of relying on a default solution before they control for potentially omitted variables with constant effects using a fixed-effects specification.

The item count technique (ICT-MLE) regression model for survey list experiments depends on assumptions about responses at the extremes (choosing no or all items on the list). Existing list experiment best practices aim to minimize strategic misrepresentation in ways that virtually guarantee that a tiny number of respondents appear in the extrema. Under such conditions both the “no liars” identification assumption and the computational strategy used to estimate the ICT-MLE become difficult to sustain. I report the results of Monte Carlo experiments examining the sensitivity of the ICT-MLE and simple difference-in-means estimators to survey design choices and small amounts of non-strategic respondent error. I show that, compared to the difference in means, the performance of the ICT-MLE depends on list design. Both estimators are sensitive to measurement error, but the problems are more severe for the ICT-MLE as a direct consequence of the no liars assumption. These problems become extreme as the number of treatment-group respondents choosing all the items on the list decreases. I document that such problems can arise in real-world applications, provide guidance for applied work, and suggest directions for further research.

Recent developments in the U.S. pecan industry appear to limit the utility of past research. The importance of pecan variety has emerged as an issue which could alter past results. The linear and double-log models previously fitted to all-pecans (averaged) data may be too restrictive and hence, are less useful for variety-specific analysis. Past research also analyzed price turning points using nominal data. This study investigated functional form and data-averaging problems by fitting separate flexible Box-Cox price-dependent models for all-pecans and each variety of pecans (1970/71-1988/89 deflated data). Results indicate: other nuts substitute for different pecan varieties, estimated all-pecans price flexibility is biased and clouds variety-specific flexibilities, and restrictive functional forms are inappropriate.