Martin Reismann

Knowledge Spillovers and Total Factor Productivity: Evidence Using a Spatial Panel Data Model

This paper investigates the impact of knowledge capital stocks on total factor productivity through the lens of the knowledge capital model proposed by Griliches (1979), augmented with a spatially discounted cross-region knowledge spillover pool variable. The objective is to shift attention from firms and industries to regions and to estimate the impact of cross-region knowledge spillovers on total factor productivity (TFP) in Europe. The dependent variable is the region-level TFP, measured in terms of the superlative TFP index suggested by Caves, Christensen and Diewert (1982). This index describes how efficiently each region transforms physical capital and labour into output. The explanatory variables are internal and out-of-region stocks of knowledge, the latter capturing the contribution of cross-region knowledge spillovers. We construct patent stocks to proxy regional knowledge capital stocks for N=203 regions over the 1997- 2002 time period. In estimating the effects we implement a spatial panel data model that controls for the spatial autocorrelation due to neighbouring regions and the individual heterogeneity across regions. The findings provide a fairly remarkable confirmation of the role of knowledge capital contributing to productivity differences among regions, and add an important spatial dimension to the discussion, by showing that productivity

Neural Network Modeling of Constrained Spatial Interaction Flows: Design, Estimation, and Performance Issues

In this paper a novel modular product unit neural network architecture is presented to model singly constrained spatial interaction flows. The efficacy of the model approach is demonstrated for the origin constrained case of spatial interaction using Austrian interregional telecommunication traffic data. The model requires a global search procedure for parameter estimation, such as the Alopex procedure. A benchmark comparison against the standard origin constrained gravity model and the two-stage neural network approach, suggested by Openshaw (1998), illustrates the superiority of the proposed model in terms of the generalization performance measured by ARV and SRMSE. Copyright Blackwell Publishing, Inc. 2003

Spatial Interaction and Spatial Autocorrelation

The objective is to combine insights from two research traditions, spatial interaction modelling and spatial autocorrelation modelling, to deal with the issue of spatial autocorrelation in spatial interaction data analysis. First, the problem is addressed from an exploratory perspective for which a generalisation of the Getis–Ord G statistic is presented. This statistic may yield interesting insights into the processes that give rise to spatial association between residual flows. Second, the log-additive spatial interaction model is extended to spatial econometric origin-destination flow models consistent with an error structure that reflects origin, destination or origin-destination autoregressive spatial dependence. The models are formally equivalent to conventional spatial regression models. But they differ in terms of the data analysed and the way in which the spatial weights matrix is defined.

Neural Network Modelling of Constrained Spatial Interaction Flows

Fundamental to regional science is the subject of spatial interaction. GeoComputation - a new research paradigm that represents the convergence of the disciplines of computer science, geographic information science, mathematics and statistics - has brought many scholars back to spatial interaction modeling. Neural spatial interaction modeling represents a clear break with traditional methods used for explicating spatial interaction. Neural spatial interaction models are termed neural in the sense that they are based on neurocomputing. They are clearly related to conventional unconstrained spatial interaction models of the gravity type, and under commonly met conditions they can be understood as a special class of general feedforward neural network models with a single hidden layer and sigmoidal transfer functions (Fischer 1998). These models have been used to model journey-to-work flows and telecommunications traffic (Fischer and Gopal 1994, Openshaw 1993). They appear to provide superior levels of performance when compared with unconstrained conventional models. In many practical situations, however, we have - in addition to the spatial interaction data itself - some information about various accounting constraints on the predicted flows. In principle, there are two ways to incorporate accounting constraints in neural spatial interaction modeling. The required constraint properties can be built into the post-processing stage, or they can be built directly into the model structure. While the first way is relatively straightforward, it suffers from the disadvantage of being inefficient. It will also result in a model which does not inherently respect the constraints. Thus we follow the second way. In this paper we present a novel class of neural spatial interaction models that incorporate origin-specific constraints into the model structure using product units rather than summation units at the hidden layer and softmax output units at the output layer. Product unit neural networks are powerful because of their ability to handle higher order combinations of inputs. But parameter estimation by standard techniques such as the gradient descent technique may be difficult. The performance of this novel class of spatial interaction models will be demonstrated by using the Austrian interregional traffic data and the conventional singly constrained spatial interaction model of the gravity type as benchmark. References Fischer M M (1998) Computational neural networks: A new paradigm for spatial analysis Environment and Planning A 30 (10): 1873-1891 Fischer M M, Gopal S (1994) Artificial neural networks: A new approach to modelling interregional telecommunciation flows, Journal of Regional Science 34(4): 503-527 Openshaw S (1993) Modelling spatial interaction using a neural net. In Fischer MM, Nijkamp P (eds) Geographical information systems, spatial modelling, and policy evaluation, pp. 147-164. Springer, Berlin

Evaluating Neural Spatial Interaction Modelling by Bootstrapping

This paper exposes problems of the commonly used technique of splitting the available data in neural spatial interaction modelling into training, validation, and test sets that are held fixed and warns about drawing too strong conclusions from such static splits. Using a bootstrapping procedure, we compare the uncertainty in the solution stemming from the data splitting with model specific uncertainties such as parameter initialization. Utilizing the Austrian interregional telecommunication traffic data and the differential evolution method for solving the parameter estimation task for a fixed topology of the network model [i.e. J = 8] this paper illustrates that the variation due to different resamplings is significantly larger than the variation due to different parameter initializations. This result implies that it is important to not over-interpret a model, estimated on one specific static split of the data.

Cross-Region Knowledge Spillovers and Total Factor Productivity: European Evidence Using a Spatial Panel Data Model

This paper concentrates on the central link between productivity and knowledge capital, and shifts attention from firms and industries to regions. The objective is to measure knowledge elasticity effects within a regional Cobb-Douglas production function framework, with an emphasis on knowledge spillovers. The analysis uses a panel of 203 European regions to estimate the effects over the period 1997-2002. The dependent variable is total factor productivity (TFP). We use a region-level relative TFP index as an approximation to the true TFP measure. This index describes how efficiently each region transforms physical capital and labour into outputs. The explanatory variables are internal and out-of-region stocks of knowledge, the latter capturing the contribution of interregional knowledge spillovers. We use patents to measure knowledge capital. Patent stocks are constructed such that patents applied at the European Patent Office in one year add to the stock in the following and then depreciate throughout the patents effective life according to a rate of knowledge obsolescence. A random effects panel data spatial error model is advocated and implemented for analyzing the productivity effects. The findings provide a fairly remarkable confirmation of the role of knowledge capital contributing to productivity differences among regions, and adding an important dimension to the discussion, showing that knowledge spillover effects increase with geographic proximity.