Long-Term Effects in Models with Temporal Dependence

A dominant trend in models with binary outcomes is to control for unmodeled duration dependence by including temporal dependence variables. A second, distinct trend is to interpret both the short- and long-term effects of explanatory variables in autoregressive models. While the first trend is nearly ubiquitous in models with binary outcomes, the second trend has yet to be applied consistently beyond models with continuous outcomes. While scholars use temporal splines and cubic polynomials to model the underlying hazard rate, they have neglected the fact that this causes the explanatory variables to have a long-term effect (LTE) by modifying the future values of the temporal dependence variables. In this article, I propose a simple technique that estimates a wide range of probabilistic LTEs in models with temporal dependence variables. These effects can range from simple LTEs for a one-time change in an explanatory variable to more complex scenarios where effects change in magnitude with time and compound across repeated events. I then replicate Clare's (2010, Ideological fractionalization and the international conflict behavior of parliamentary democracies. International Studies Quarterly 54:965–87) examination of the influence of government fractionalization on conflict behavior to show that failing to interpret the results within the context of temporal dependence underestimates the total impact of fractionalization by neglecting LTEs.