Smooth Transition Spatial Autoregressive Models

TI 2017-050/III, Tinbergen Institute Discussion Paper

55 Pages Posted: 1 Jun 2017

See all articles by Bo Pieter Johannes Andree

Bo Pieter Johannes Andree

Vrije Universiteit Amsterdam, School of Business and Economics; World Bank; Tinbergen Institute

Francisco Blasques

VU University Amsterdam; Tinbergen Institute

Eric Koomen

VU University Amsterdam - Department of Spatial Economics

Date Written: May 31, 2017

Abstract

This paper introduces a new model for spatial time series in which cross-sectional dependence varies nonlinearly over space by means of smooth transitions. We refer to our model as the Smooth Transition Spatial Autoregressive (ST-SAR). We establish consistency and asymptotic Gaussianity for the MLE under misspecification and provide additional conditions for geometric ergodicity of the model. Simulation results justify the use of limit theory in empirically relevant settings. The model is applied to study spatio-temporal dynamics in two cases that differ in spatial and temporal extent. We study clustering in urban densities in a large number of neighborhoods in the Netherlands over a 10-year period. We pay particular focus to the advantages of the ST-SAR as an alternative to linear spatial models. In our second study, we apply the ST-SAR to monthly long term interest rates of 15 European sovereigns over 25-year period. We develop a strategy to assess financial stability across the Eurozone based on attraction of individual sovereigns toward the common stochastic trend. Our estimates reveal that stability attained a low during the Greek sovereign debt crisis, and that the Eurozone has remained to struggle in attaining stability since the onset of the financial crisis. The results suggest that the European Monetary System has not fully succeeded in aligning the economies of Ireland, Portugal, Italy, Spain, and Greece with the rest of the Eurozone, while attraction between other sovereigns has continued to increase. In our applications linearity of spatial dependence is overwhelmingly rejected in terms of model fit and forecast accuracy, estimates of control variables improve, and residual correlation is better neutralized.

Keywords: Dynamic panel, Threshold models, Spatial heterogeneity, Spatial autocorrelation, Urban Density, Interest Rates, Monetary Stability, Sovereign Debt Crisis

Suggested Citation

Andree, Bo Pieter Johannes and Blasques, Francisco and Blasques, Francisco and Koomen, Eric, Smooth Transition Spatial Autoregressive Models (May 31, 2017). TI 2017-050/III, Tinbergen Institute Discussion Paper , Available at SSRN: https://ssrn.com/abstract=2977830 or http://dx.doi.org/10.2139/ssrn.2977830

Bo Pieter Johannes Andree (Contact Author)

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

World Bank ( email )

1818 H Street, NW
Washington, DC 20433
United States

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Francisco Blasques

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Eric Koomen

VU University Amsterdam - Department of Spatial Economics ( email )

De Boelelaan 1105
1081HV Amsterdam
Netherlands

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