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Heterogeneity in spatial growth clusters

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Abstract

This paper sets forth an approach which allows for dealing with both model uncertainty and threshold effects of unknown form in spatial growth regression models. The estimation of threshold effects designates different spatial growth regimes which account for unknown structural heterogeneities in the parameter estimates. Using stochastic search variable selection priors, the paper deals with the issue of model uncertainty in a flexible and computationally efficient way. The paper uses Bayesian Markov chain Monte Carlo to simultaneously account for threshold effects, model uncertainty, and spatial dependence in regional growth regression models. The approach is illustrated for both identifying model covariates and unveiling growth regimes present in pan-European growth data.

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Notes

  1. For specifics on Markov chain Monte Carlo (MCMC) estimation in general, see Koop (2003).

  2. It is worth noting that a diffuse prior specification like in Eq. (23) might result in a growth regime that consists of less observations/regions than explanatory variables, which in turn impedes the identifiability of the model. This concern can be eased by using rejection sampling, which involves simply discarding the respective draws for \({\omega _t}\).

  3. The sample regions include regions located in Austria (nine regions), Belgium (11 regions), Bulgaria (six regions), Czech Republic (eight regions), Denmark (five regions), Estonia (one region), Finland (five regions), France (22 regions), Germany (38 regions), Greece (13 regions), Hungary (seven regions), Italy (21 regions), Latvia (one region), Lithuania (one region), Luxembourg (one region), Netherlands (12 regions), Norway (seven regions), Poland (16 regions), Portugal (five regions), Republic of Ireland (two regions), Romania (eight regions), Slovakia (four regions), Slovenia (two regions), Spain (16 regions), Sweden (eight regions), Switzerland (seven regions), and the UK (37 regions).

  4. ISCED refers to the International Standard Classification of Education.

  5. Robustness checks using different values of k barely affected the results. Results for different number of nearest neighbors are available upon request.

  6. It is, moreover, worth noting that model specifications for \(M>2\) produce very imprecise parameter estimates, since the number of parameters gets very large relative to n. Results for alternative choices of M and \({\varvec{z}}\) are available upon request.

  7. Convergence of the MCMC sampler has been checked using convergence diagnostics proposed by Geweke (1992) and Raftery and Lewis (1992). The convergence diagnostics have been calculated using the MATLAB package coda implemented in the Econometric Toolbox provided by James P. LeSage.

  8. For a detailed discussion on the interpretation of parameter estimates in spatial autoregressive models, see LeSage and Pace (2009).

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  1. Institute for Macroeconomics, Vienna University of Economics and Business, Welthandelsplatz 1, 1020, Vienna, Austria

    Philipp Piribauer

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Piribauer, P. Heterogeneity in spatial growth clusters. Empir Econ 51, 659–680 (2016). https://doi.org/10.1007/s00181-015-1023-y

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  • DOI: https://doi.org/10.1007/s00181-015-1023-y

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