Spatial Chow-Lin Methods for Data Completion in Econometric Flow Models

Flow data across regions can be modeled by spatial econometric models, see LeSage and Pace (2009). Recently, regional studies became interested in the aggregation and disaggregation of flow models, because trade data cannot be obtained at a disaggregated level but data are published on an aggregate level. Furthermore, missing data in disaggregated flow models occur quite often since detailed measurements are often not possible at all observation points in time and space. In this paper we develop classical and Bayesian methods to complete flow data. The Chow and Lin (1971) method was developed for completing disaggregated incomplete time series data. We will extend this method in a general framework to spatially correlated flow data using the cross-sectional Chow-Lin method of Polasek et al. (2009). The missing disaggregated data can be obtained either by feasible GLS prediction or by a Bayesian (posterior) predictive density.Missing values in spatial econometrics, MCMC, non-spatial Chow-Lin (CL) and spatial Chow-Lin (SCL) methods, spatial internal flow (SIF) models, origin and destination (OD) data

SPATIAL CHOW-LIN METHODS: BAYESIAN AND ML FORECAST COMPARISONS

Completing data that are collected in disaggregated and heterogeneous spatial units is a quite frequent problem in spatial analyses of regional data. Chow and Lin (1971) (CL) were the rst to develop a uni ed framework for the three problems (interpolation, extrapolation and distribution) of predicting disaggregated times series by so-called indicator series. This paper develops a spatial CL procedure for disaggregating cross-sectional spatial data and compares the Maximum Likelihood and Bayesian spatial CL forecasts with the naive pro rata error distribution. We outline the error covariance structure in a spatial context, derive the BLUE for the ML estimator and the Bayesian estimation procedure by MCMC. Finally we apply the procedure to European regional GDP data and discuss the disaggregation assumptions. For the evaluation of the spatial Chow-Lin procedure we assume that only NUTS 1 GDP is known and predict it at NUTS 2 by using employment and spatial information available at NUTS 2. The spatial neighborhood is de ned by the inverse travel time by car in minutes. Finally, we present the forecast accuracy criteria comparing the predicted values with the actual observations.

Sensitivity Analysis of SAR Estimators: A Simulation Study

Spatial autoregressive models come with a variety of estimators and it is interesting and useful to compare the estimators by location and covariance properties. In this paper, we first study the local sensitivity behavior of the main least squares estimator by using matrix derivatives. We then calculate the Taylor approximation of the least squares estimator in the SAR model up to the second order. Also, we compare the estimators of the spatial autoregression (SAR) model in terms of the covariance structure of the least squares estimators and we make efficiency comparisons using Kantorovich inequalities. Finally, we demonstrate our approach by an example for GDP and employment in 239 European NUTS2 regions. We find a quite good approximation behavior of the SAR estimator in the neighborhood of ρ = 0, i.e. a small spatial correlation.Spatial autoregressive models, least-squares estimators, Taylor approximations, Kantorovich inequality

Aggregate and Regional Economic Effects of New Railway Infrastructure

Economists expect positive returns to investments in infrastructure. However a project with higher national returns might have less favorable effects on a regional level than the alternative. Therefore new infrastructure should also be assessed on a regional level, but econom(etr)ic evalua tion models are scarce, especially in regional science. This paper proposes new approaches to evaluate infrastructure by a dynamic spatial economet ric model that allows long-term predictions. We investigate the regional effects for 2 Austrian railway projects and show that infrastructure returns are positive on an aggregate and at a regional level but spatial variation can be large.Regional growth convergence, traffic accessibility, infrastructure evaluation, spatial econometrics

Bayesian Methods for Completing Data in Space-Time Panel Models

Completing data sets that are collected in heterogeneous units is a quite frequent problem. Chow and Lin (1971) were the first to develop a unified framework for the three problems (interpolation, extrapolation and distribution) of predicting times series by related series (the `indicators'). This paper develops a spatial Chow-Lin procedure for cross-sectional and panel data and compares the classical and Bayesian estimation methods. We outline the error covariance structure in a spatial context and derive the BLUE for the ML and Bayesian MCMC estimation. Finally, we apply the procedure to Spanish regional GDP data between 2000-2004. We assume that only NUTS-2 GDP is known and predict GDP at NUTS-3 level by using socio-economic and spatial information available at NUTS-3. The spatial neighborhood is defined by either km distance, travel time, contiguity and trade relationships. After running some sensitivity analysis, we present the forecast accuracy criteria comparing the predicted values with the observed ones.Interpolation, Spatial panel econometrics, MCMC, Spatial

Bayesian Methods for Completing Data in Space-time Panel Models

Completing data sets that are collected in heterogeneous units is a quite frequent problem. Chow and Lin (1971) were the first to develop a united framework for the three problems (interpolation, extrapolation and distribution) of predicting times series by related series (the 'indicators'). This paper develops a spatial Chow-Lin procedure for cross-sectional and panel data and compares the classical and Bayesian estimation methods. We outline the error covariance structure in a spatial context and derive the BLUE for the ML and Bayesian MCMC estimation. Finally, we apply the procedure to Spanish regional GDP data between 2000-2004. We assume that only NUTS-2 GDP is known and predict GDPat NUTS-3 level by using socio-economic and spatial information available at NUTS-3. The spatial neighborhood is defined by either km distance, travel-time, contiguity and trade relationships. After running some sensitivity analysis, we present the forecast accuracy criteria comparing the predicted with the observed values.Interpolation, Spatial panel econometrics, MCMC, Spatial Chow-Lin, Missing regional data, Spanish provinces, 'Polycentric-periphery' relationship

Sensitivity Analysis of SAR Estimators

Estimators of spatial autoregressive (SAR) models depend in a highly non-linear way on the spatial correlation parameter and least squares (LS) estimators cannot be computed in closed form. We first compare two simple LS estimators by distance and covariance properties and then we study the local sensitivity behavior of these estimators using matrix derivatives. These results allow us to calculate the Taylor approximation of the least squares estimator in the spatial autoregression (SAR) model up to the second order. Using Kantorovich inequalities, we compare the covariance structure of the two estimators and we derive efficiency comparisons by upper bounds. Finally, we demonstrate our approach by an example for GDP and employment in 239 European NUTS2 regions. We find a good approximation behavior of the SAR estimator, evaluated around the non-spatial LS estimators. These results can be used as a basis for diagnostic tools to explore the sensitivity of spatial estimators.Spatial autoregressive models, least squares estimators, sensitivity analysis, Taylor Approximations, Kantorovich inequality

Human Capital and Regional Growth in Switzerland

This paper develops a regional production function model for Swiss cantons that incorporates human capital together with spatial effects. Within a spatial panel framework we find that controlling for time effects the spatial spillover effect becomes insignificant. Our results are sensitive with respect to the human capital proxy. We find that the share of academics in the workforce is the main component of human capital driving productivity growth in Swiss cantons. This is in line with findings of previous studies suggesting that mostly highly skilled workers matter for productivity growth in technologically advanced economies.Production function with human capital, spatial panel, Regional Growth