When Time Matters, Use Cox: A Better Approach for Binary Panel Data

Insights from the Field

Cox

Logit

Duration

BTSCS

Transition probabilities

Getting Time Right: Using Cox Models and Probabilities to Interpret Binary Panel Data was authored by Shawna Metzger and Benjamin Jones. It was published by Cambridge in Pol. An. in 2022.

📌 The Problem With Current Binary Panel Models

Logit and probit (L/P) models are the standard tools for binary time-series cross-sectional (BTSCS) data, and researchers typically add cubic splines or time polynomials to capture temporal dynamics. However, L/P models struggle with three other temporal features that commonly arise in BTSCS data:

whether covariate effects vary depending on time,
whether the underlying process is causally complex, and
whether the assumed functional form for time is correct.

Failing to account for any of these features produces misspecification bias and threatens the validity of inferences.

📊 How the Models Were Compared (Monte Carlo Evidence)

Monte Carlo simulations compare Cox duration models to standard logit models across a range of BTSCS settings.
Simulations include both a basic BTSCS scenario and more complex situations that introduce time-conditional effects and causal complexity.
Assessment focuses on the ability to test the same hypotheses, estimator performance, and susceptibility to misspecification bias.

🔍 Key Findings

Cox duration models create fewer opportunities for the kinds of misspecification bias that afflict L/P models with temporal complexity.
In basic BTSCS settings, Cox models perform about as well as logit models and sometimes better.
In more complex BTSCS situations, Cox models perform considerably better than logit models.

📈 A New Way to Read Cox Results

Transition probabilities are introduced as an interpretation technique for Cox models to make coefficients and effects more readily interpretable for practitioners.

🧭 Applied Example

An application to interstate conflict illustrates the practical differences in inference and interpretation between Cox and L/P approaches.

⚠️ Why It Matters

For BTSCS research, Cox duration models offer a viable alternative that reduces misspecification risk while allowing researchers to address the same substantive hypotheses as logit/probit models.
Using transition probabilities improves the accessibility of Cox-model results for applied audiences.