Prof. Reinhold Kosfeld (p)

In reduction of CO2 emissions, the transition to environmentally friendly transport modes has a high significance. In Germany the Climate Action Programme 2030 includes various measures for promoting electric mobility. Although electric cars hold a market share of just 3.3% by the end of 2025, its stock is more than doubled in the past three years. Their share of new cars reaches almost 20%. Special measures like tax incentives, charging benefits and purchase subsidies have been put in place to promote the shift towards electric cars and boost their diffusion.
Knowledge on the future expansion of electric cars is required for planning purposes and adaptation measures. With view of the spatial dimension of electric mobility, regions are expected to differently contribute to national goal achievements. In as much as neighboring regions interact with one another, spatial spillovers come into the fore. To cover the national and regional dimension in the diffusion of electric mobility, both time series and panel data models are designed for forecasting the development of electric vehicles. In particular, we make use of spatial panel data models that is grounded on the partial adjustment mechanism and peculiarly adapted for forecasting purposes in presence of regional spillovers.
Regional data on the stocks of electric cars and motor vehicles at the national, state and district level is available from the Federal Motor Transport Authority . While the national time series is provided since 2009, district and state data are only available for the period 2016 - 2025. Using additional information of Statistical offices of the Federal States panel data at the state level can be constructed for the period 2013 – 2025. Data on regional characteristics is from the Federal Employment Agency and the Federal Statistical Office.
To account for spatial and temporal effects in market diffusion of electric mobility, we utilize dynamic spatial panel data models. Regional characteristics are involved as control variables. Additionally, the effect of the environmental bonus on newly registered electric cars is tested. Econometric estimation reveals the importance of autoregressive processes in the dissemination of electric vehicles. The inclusion of spatial spillovers can improve the forecasting performance more at the district level than at the state level. The environmental bonus exerts a relevant but limited influence on the electric car sales. By aggregating regional predictions, regional forecasting errors are partially balanced out in the prediction of the electric vehicle fleet at the national scale.

Dr. Umut Türk (p), Prof. John Östh, Dr. Marina Toger (p)

This study develops and evaluates a matrix-free spatial econometric framework built upon the EquiPop neighborhood structure introduced by John Östh (2016). The objective is to examine whether spatial autoregressive models can be estimated without constructing explicit sparse spatial weight matrices, while preserving the theoretical foundations of spatial dependence modeling.
We begin by validating the framework using Anselin’s Columbus dataset, a benchmark dataset in spatial econometrics, and subsequently extend the analysis to large-scale Airbnb listing data. Neighborhood relationships are derived directly from the EquiPop structure, and spatial lags of both the dependent variable and explanatory variables are computed without forming a full spatial weights matrix. For SAR and SDM specifications, the spatial autoregressive parameter is estimated via grid search, and the log-determinant term is approximated using the Pace–Barry (1999) stochastic trace method. This allows likelihood evaluation in a fully matrix-free manner.
Comparisons with traditional implementations using sparse-matrix routines show that coefficient estimates and spatial parameters are broadly consistent across approaches. At the same time, the matrix-free EquiPop implementation substantially reduces computational burden when spatial lags are precomputed. Residual spatial autocorrelation diagnostics highlight the importance of properly capturing global feedback effects in autoregressive specifications.
The results demonstrate that matrix-free spatial econometric estimation is feasible, computationally efficient, and scalable. Future research will focus on improving Neumann-series approximations within the EquiPop framework, exploring Bayesian estimation strategies, and extending the approach to origin–destination flow models where high-dimensional spatial structures present significant computational challenges.

Dr. Caterina Morelli (p), Dr. Paolo Maranzano, Dr. Raffaele Mattera, Prof. Philipp Otto

This paper proposes a heterogeneous spatiotemporal panel data model designed to capture three pervasive features of regional and socio-economic data: spatial spillovers, dynamic persistence, and structural heterogeneity. The starting point is that spatial units are rarely homogeneous, and that interdependence is often shaped not only by geographic proximity but also by the characteristics of the interacting units. To reflect these mechanisms, we introduce a dynamic Spatial Durbin-type specification in which both the marginal effects of covariates and the strength of spatial feedback can vary across latent clusters of units. In particular, the model allows for group-specific temporal dependence and heterogeneous spatial interactions that may differ within clusters and across clusters, accommodating symmetric or asymmetric cross-group spillovers. This structure yields a flexible representation of diffusion patterns that standard homogeneous spatial panel models cannot reproduce.
Within this framework, we derive the full matrix of partial derivatives that maps changes in covariates into changes in outcomes, and we decompose it into direct and indirect (spillover) effects. Unlike conventional spatial models, these effects naturally exhibit a block structure, enabling separate summaries for within-cluster direct effects, within-cluster spillovers, and cross-cluster spillovers, thus providing an interpretable characterization of heterogeneous propagation mechanisms.
For estimation, we develop a two-step quasi maximum likelihood (QML) procedure that jointly recovers the heterogeneous parameters and the latent group memberships without requiring the researcher to pre-specify a clustering partition. The algorithm alternates between parameter estimation conditional on group assignments and group reassignment that explicitly accounts for spatial dependence, thereby avoiding procedures that treat units as conditionally independent when updating clusters. We evaluate the finite-sample performance of the proposed estimator through an extensive Monte Carlo study across alternative model restrictions and heterogeneity patterns, assessing both parameter recovery and the accuracy of the implied direct and indirect effects. The proposed framework is particularly suited to environmental applications, such as regional greenhouse gas emissions, where socio-economic drivers and spillover intensities may differ systematically across groups of regions with different development levels and institutional capacity.