Continuous-Time Modelling with Spatial Dependence

This discussion paper led to an article in Geographical Analysis (2012). Volume 44, issue 1, pages 29-46. (Spatial) panel data are routinely modelled in discrete time (DT). However, there are compelling arguments for continuous time (CT) modelling 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 modelling, it allows adequate modelling of dynamic adjustment processes. The paper introduces spatial dependence in a CT modelling framework. We propose a nonlinear Structural Equation Model (SEM) with latent variables for estimation of the Exact Discrete Model (EDM), which links the CT model parameters to the DT observations. The use of a SEM with latent variables makes it possible to take measurement errors in the variables into account, leading to a reduction of attenuation bias (i.e., disattenuation). The SE M-CT model with spatial dependence developed here is the first dynamic structural equation model with spatial dependence. The spatial econometric SEM-CT framework is illustrated on the basis of a simple regional labour market model for Germany made up of the endogenous state variables unemployment change and population change and of the exogenous input variables change in regional average wage and change in the structure of the manufacturing sector.