STADL Up! The Spatiotemporal Autoregressive Distributed Lag Model for TSCS Data Analysis

Abstract

Time-series cross-section (TSCS) data are prevalent in political science, yet many distinct challenges presented by TSCS data remain underaddressed. We focus on how dependence in both space and time complicates estimating either spatial or temporal dependence, dynamics, and effects. Little is known about how modeling one of temporal or cross-sectional dependence well while neglecting the other affects results in TSCS analysis. We demonstrate analytically and through simulations how misspecification of either temporal or spatial dependence inflates estimates of the other dimension’s dependence and thereby induces biased estimates and tests of other covariate effects. Therefore, we recommend the spatiotemporal autoregressive distributed lag (STADL) model with distributed lags in both space and time as an effective general starting point for TSCS model specification. We illustrate with two example reanalyses and provide R code to facilitate researchers’ implementation—from automation of common spatial-weights matrices (W) through estimated spatiotemporal effects/response calculations—for their own TSCS analyses.

Capturing the Spatio-Temporal Diffusion Effects of Armed Conflict: A Non-parametric Smoothing Approach

“…For regression analyses and the identification of causal mechanisms, spatio-temporal dependence must similarly be accounted for, otherwise coefficients of interest may be biased (see e.g. Cook et al (2023) for a discussion on this) and incorrect conclusions and ultimately policy implications may be drawn. However, as we demonstrate, simply including individual lags in a regression model will likely lead to overfitting.…”

“…Studies trying to quantify the diffusion effects of conflict are still extremely rare (Zhukov, 2012;Mueller et al, 2022), and regression models more fully accounting for the diffusion patterns do not exist, all while theoretically knowing that past conflict is the best and most important predictor. As a result, forecasting models such as (potentially black-box) early warning system suffer performance losses, while interpretable models studying the determinants of conflict may over-or underestimate the impact of the respective predictors of interest and thus potentially provide incorrect policy implications (Schutte and Weidmann, 2011;Cook et al, 2023).…”

“…Our proposed model is also related to models from both the spatial and temporal econometrics literature, such as the autoregressive (AR) as well as the autoregressive exogenous input (ARX) model (Box et al, 2015), the spatial-autoregressive (SAR) model (LeSage and Pace, 2009) and the recently proposed spatio-temporal autoregressive distributed lag (STADL) model (Cook et al, 2023). Contrary to these models, we do not only include temporal and/or spatial lags, but a large combination of both.…”

Segregated Economies in an Integrated World: The Gendered Consequences of Exchange Rate Movements in Low- and Middle-Income Countries

“…38.See Cook, Hays, and Franzese 2023 regarding the importance of dealing with spatial clustering. The spatial lag model was estimated with the TSCSDEP package for the R environment (Hays et al 2021).…”

Spatial Data Analysis

“…) andCook et al (2023). Meanwhile, those intrigued by non-linear spatial models should delve into LeSage &Pace (2009) andFranzese et al (2016).In framework of this chapter, spatial dependence can be integrated as three distinct processes: a) Spatial interdependence in the outcome, b) Clustering of unobservable factors, and c) Spillovers originating from covariates.…”