Back to the Future: Modeling Time Dependence in Binary Data

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Foreign Aid and Regime Change: A Role for Donor Intent (2011, background): “Carter and Signorino (2010) show that non-proportional hazards can be estimated in a logit model by interacting the variable of interest (in this case democratic aid) with the age variables (age, age-squared, age-cubed).”
Climate variability, economic growth, and civil conflict (2012, methodology): “Equation (2) is estimated using logit regression with bootstrapped standard errors.10 To model temporal dependence, time since the last conflict as well as the squared and cubic terms (peaceyears) are included in the model (Carter & Signorino, 2010).”
Why Do Countries Adopt Constitutional Review (2014, positive): “Though intuitive, this time dummy approach performs poorly when N is relatively small and t is relatively large (see Carter & Signorino 2010, reporting, based on Monte Carlo simulations, that time dummies perform poorly if N < 1000 and t> 15).”
Aid Is Not Oil: Donor Utility, Heterogeneous Aid, and the Aid-Democratization Relationship (2015, background): “Carter and Signorino 2010 show that this approximates a hazard model.”
Foreign Aid Shocks as a Cause of Violent Armed Conflict (2011, positive): “Although we used cubic splines as advocated by Beck, Katz, and Tucker (1998), we also considered polynomials of time (time, time2, and time3) to account for time trends as suggested by Carter and Signorino (2010) and obtained similar findings.”