Many social events and policy interventions generate treatment effects that persistently spill over into neighboring areas, resulting in a phenomenon statisticians refer to as "interference" both in time and space. In this paper, I put forward a design-based framework to identify and estimate these spillover effects in panel data with a spatial dimension, when temporal and spatial interference intertwine in intricate ways that are unknown to researchers. The framework defines estimands that enable researchers to measure the influence of each type of interference, and I propose estimators that are consistent and asymptotically normal under the assumption of sequential ignorability and mild regularity conditions. I show that fixed effects models in panel data analysis, such as the difference-in-differences (DID) estimator, can lead to significant biases in such scenarios. I test the method's performance on both simulated datasets and the replication of two empirical studies.
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