Continuous-Time Modeling with Spatial Dependence

(Spatial) panel data are routinely modeled in discrete time (DT). However, compelling arguments exist for continuous time (CT) modeling of (spatial) panel data. Particularly, most social processes evolve in CT, so that statistical analysis in DT is an oversimplification, gives an incomplete representation of reality, and may lead to misinterpretation of estimation results. The most compelling reason for a CT approach is that, in contrast to DT modeling, it allows adequate modeling of dynamic adjustment processes. This article introduces spatial dependence in a CT modeling framework. We propose a nonlinear Structural Equation Model (SEM) with latent variables for estimation of the Exact Discrete Model (EDM), which links CT model parameters to DT observations. The use of a SEM with latent variables enables a specification that accounts for measurement errors in the variables, leading to a reduction of attenuation bias (i.e., disattenuation). The SEM-CT model with spatial dependence developed here is the first dynamic structural equation model with spatial dependence. A simple regional labor market model for Germany, comprising unemployment change and population change as endogenous state variables, and change in regional average wages and in the structure of the manufacturing sector as exogenous input variables, illustrates this spatial econometric SEM-CT framework