Taking Time (and Space) Seriously: How Scholars Falsely Infer Policy Diffusion from Model Misspecification

Abstract

Scholars have long been interested in how policies and ideas spread from one observation to another. Yet, the spatial and temporal dynamics of policy diffusion present unique challenges that empirical researchers often neglect. Scholars often use temporally lagged spatial lags (TLSL)—such as the number (or percentage) of prior adopters in a neighborhood—to test various mechanisms of delayed policy diffusion but are largely unaware of two under appreciated issues. First, the effects are not limited to one time period but persist over time by changing the future value of neighboring observations. Second, minor, yet common, choices in model specification—such as omitting spatially correlated and/or autoregressive covariates—can increase the risk of falsely inferring that the outcome is a result of spatial diffusion. Indeed, we offer two applications where small changes to the model specification of an otherwise well‐specified model result in drastically different inferences about policy diffusion. We argue that scholars should avoid haphazardly including TLSLs without considerable theoretical justification, and we conclude on an optimistic note by offering straightforward solutions and new software to address these issues.

Policy Innovation Adoption Across the Diffusion Life Course

“…Exploring the distributional assumptions of diffusion research and the effect of censoring on our studies are fruitful future lines of inquiry. Finally, this study relied upon the well‐critiqued measure of neighbor adoptions and does not include spatial analysis (Drolc, Gandrud, & Williams, 2019; Mitchell, 2018). It cannot parse out exactly which mechanisms are represented by that measure (Berry & Baybeck, 2005), nor does it test more complex channels of information (Desmarais et al, 2015; Nicholson‐Crotty & Carley, 2018).…”

Pandemics and Partisanship: Following Old Paths into Uncharted Territory

“…In keeping with previous scholarship that examines the temporal and spatial distribution of state-level policy interventions, we employ event history analysis (EHA). The utility of which is that it allows us to determine the probability of a qualitative policy change occurring during a specific time period (Berry & Berry, 2018; Box-Steffensmeier & Jones, 1997; Drolc et al, 2019). In this case, the qualitative policy change is state declarations of emergency, representing a special case of policy adoptions that occurred within an abbreviated time period in response to the spread of COVID-19.…”

“…In this case, the qualitative policy change is state declarations of emergency, representing a special case of policy adoptions that occurred within an abbreviated time period in response to the spread of COVID-19. The advantage of EHA over more conventional methods of analyzing cross-sectional data is that it takes into consideration the fluctuation of variables over time, and indicates probability of not only policy adoptions occurring but policy adoptions occurring within a specific period of time (Box-Steffensmeier & Jones, 1997; Drolc et al, 2019). The latter is of specific interest here as the timeline of COVID-19 responses has been an important point of debate and criticism (Povich, 2020).…”

No Diffusion at All: Trade, Free Riding, and Government Underspending in Environmental Innovation

“…Actually, Wimpy, Williams, and Whitten illustrates that the TLSL model shall be better viewed as a variant of the spatial-X (SLX) model rather than a variant of the SAR model. The former one is, in general, more theoretically justifiable and empirically flexible than the latter in political science applications (Drolc, Gandrud, and Williams 2019;Wimpy, Williams, and Whitten, forthcoming). For example, when a contiguity weights matrix is supplied, the SLX model does not automatically assume the existence of global effects, but at the same time, researchers who argue higher order effects exist are also able to incorporate them easily.…”