Conditional relationships in dynamic models

Abstract Many political science theories posit empirical relationships that are conditioned by some moderating variable, which scholars model using a multiplicative interaction term in a regression. In recent years, scholars have begun using such terms in dynamic regression models with time series data. However, the lack of guidance on adding multiplicative interactions to these workhorse models exposes problems with the consistency of the estimator, model restrictions, and interpretation. This paper provides theoretical and practical guidance to address these problems. First, we define the conditions under which scholars can ensure consistent estimates when estimating relationships conditioned by a moderating variable in dynamic models. Second, we introduce a general model that makes no theoretical assumptions about precisely how conditional relationships unfold over time. Third, we develop a flexible approach for interpreting such models. We demonstrate the advantages of this framework with simulation evidence and an empirical application.