Top

Empirical Economics

Published in:

20-03-2020

A Bayesian spatial autoregressive logit model with an empirical application to European regional FDI flows

Authors: Tamás Krisztin, Philipp Piribauer

Published in: Empirical Economics | Issue 1/2021

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, we propose a Bayesian estimation approach for a spatial autoregressive logit specification. Our approach relies on recent advances in Bayesian computing, making use of Pólya–Gamma sampling for Bayesian Markov-chain Monte Carlo algorithms. The proposed specification assumes that the involved log-odds of the model follow a spatial autoregressive process. Pólya–Gamma sampling involves a computationally efficient treatment of the spatial autoregressive logit model, allowing for extensions to the existing baseline specification in an elegant and straightforward way. In a Monte Carlo study we demonstrate that our proposed approach markedly outperforms alternative specifications in terms of parameter precision. The paper moreover illustrates the performance of the proposed spatial autoregressive logit specification using pan-European regional data on foreign direct investments. Our empirical results highlight the importance of accounting for spatial dependence when modelling European regional FDI flows.

previous article No place like home: geography and culture in the dissemination of economic research articles

next article Public perceptions of the tax avoidance of corporations and the wealthy

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

An alternative, however, computationally more intensive approach also frequently used in the spatial econometric literature involves a Metropolis–Hastings step for the spatial autoregressive parameter (see, for example, LeSage and Pace 2009).

R-codes for the proposed spatial autoregressive logit estimation procedure can be found at https://github.com/tkrisztin/spatial-logit.

Convergence of the MCMC algorithm was checked using the convergence diagnostics proposed by Geweke (1991) and Raftery and Lewis (1992). Convergence diagnostics have been calculated using the R package coda.

Detailed R-codes are available from the authors upon request.

The choice for these parameter values, as well as the normally distributed explanatory variables is analogous to the spatial autoregressive probit Monte Carlo study in (LeSage and Pace 2009, Chapter 10, pp 289–291).

Estimates for GMM SAR Logit have been produced using the R package McSpatial. For the SAR data generating process, the spatially lagged variants of the explanatory variables were used as instruments, which correspond to the default setting in the R package. Using the same approach with the SDM, data generating process would lead to perfect collinearity; therefore, we used \(\tilde{\varvec{W}}^2 \tilde{\varvec{X}}\) as the corresponding instruments. However, for high spatial autocorrelation \(\tilde{\rho }=0.8\), GMM SAR Logit appeared to have severe problems to produce any estimates in more than 99% of all simulation runs. We have therefore omitted GMM SAR Logit in the simulation study for \(\tilde{\rho }=0.8\).

Estimates for Linearized GMM SAR Logit have been produced using the R package McSpatial. With regard to instrumental variables, the same considerations and setting apply as in the GMM SAR Logit case. In this setting, however, it is worth noting that estimates of \(\rho \) may exceed unity. In these cases, we have restricted the estimate for \(\rho \) to 0.99 for calculation of spatial impact metrics.

In the empirical application, we have also used alternative values for \(r_K\). The results, however, appeared rather robust for the choice of \(r_K\).

McFadden’s pseudo-\(R^2\) is defined as \(1- \frac{\mathcal {L}_1}{\mathcal {L}_0}\), where \(\mathcal {L}_1\) denotes the posterior log-likelihood of the fitted model and \(\mathcal {L}_0\) the log-likelihood of a null mode containing only an intercept. Based on McFadden (1974), values between 0.2 and 0.4 are considered to be an excellent fit.

Albert JH, Chib S (1993) Bayesian analysis of binary and polychotomous response data. J Am Stat Assoc 88(422):669–679

Anselin L (2002) Under the hood: issues in the specification and interpretation of spatial regression models. Agric Econ 27(2):247–267

Ascani A, Crescenzi R, Iammarino S (2016) Economic institutions and the location strategies of European multinationals in their geographic neighborhood. Econ Geogr 92(4):401–429

Balasubramanyam VN, Salisu M, Sapsford D (1996) Foreign direct investment and growth in EP and IS countries. Econ J 106(434):92–105

Baltagi BH, Egger P, Pfaffermayr M (2007) Estimating models of complex FDI: are there third-country effects? J Econom 140(1):260–281

Bellak C, Leibrecht M (2009) Do low corporate income tax rates attract FDI? Evidence from Central- and East European countries. Appl Econ 41(21):2691–2703

Blomstrom M, Kokko A (2003) The economics of foreign direct investment incentives. Technical report, National Bureau of Economic Research

Blonigen BA, Piger J (2014) Determinants of foreign direct investment. Can J Econ 47(3):775–812

Borensztein E, De Gregorio J, Lee JW (1998) How does foreign direct investment affect economic growth? J Int Econ 45(1):115–135

Brasington D, Flores-Lagunes A, Guci L (2016) A spatial model of school district open enrollment choice. Reg Sci Urban Econ 56:1–18

Burger MJ, van der Knaap B, Wall RS (2012) Revealed competition for greenfield investments between European regions. J Econ Geogr 13(4):619–648

Calabrese R, Elkink JA (2014) Estimators of binary spatial autoregressive models: a Monte Carlo study. J Reg Sci 54(4):664–687

Cameron AC, Trivedi KP (2005) Microeconometrics, 2nd edn. Cambridge University Press, New York

Cornwall GJ, Parent O (2017) Embracing heterogeneity: the spatial autoregressive mixture model. Reg Sci Urban Econ 64:148–161

Crescenzi R, Pietrobelli C, Rabellotti R (2013) Innovation drivers, value chains and the geography of multinational corporations in Europe. J Econ Geogr 14(6):1053–1086

Crespo Cuaresma J, Doppelhofer G, Feldkircher M (2014) The determinants of economic growth in European regions. Reg Stud 48(1):44–67

Crespo Cuaresma J, Doppelhofer G, Huber F, Piribauer P (2018) Human capital accumulation and long-term income growth projections for European regions. J Reg Sci 58(1):81–99

Defever F (2006) Functional fragmentation and the location of multinational firms in the enlarged Europe. Reg Sci Urban Econ 36(5):658–677

Dimitropoulou D, McCann P, Burke SP (2013) The determinants of the location of foreign direct investment in UK regions. Appl Econ 45(27):3853–3862

Duranton G, Puga D (2005) From sectoral to functional urban specialisation. J Urban Econ 57(2):343–370

Eicher TS, Helfman L, Lenkoski A (2012) Robust FDI determinants: Bayesian model averaging in the presence of selection bias. J Macroecon 34(3):637–651

Ekholm K, Forslid R, Markusen JR (2007) Export-platform foreign direct investment. J Eur Econ Assoc 5(4):776–795

Fallon G, Cook M (2014) Explaining manufacturing and non-manufacturing inbound FDI location in five UK regions. Tijdschrift voor Economische en Sociale Geografie 105(3):331–348

Fischer MM, LeSage JP (2015) A Bayesian space-time approach to identifying and interpreting regional convergence clubs in Europe. Pap Reg Sci 94(4):677–702

Frühwirth-Schnatter S, Frühwirth R (2010) Data augmentation and MCMC for binary and multinomial logit models. In: Kneib T, Tutz G (eds) Statistical modelling and regression structures. Springer, Berlin, pp 111–132

Geweke J (1991) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, volume 196. Federal Reserve Bank of Minneapolis, Research Department Minneapolis, MN, USA

Gramacy RB, Polson NG et al (2012) Simulation-based regularized logistic regression. Bayesian Anal 7(3):567–590

Halleck Vega S, Elhorst JP (2015) The SLX model. J Reg Sci 55(3):339–363

Henderson JV, Ono Y (2008) Where do manufacturing firms locate their headquarters? J Urban Econ 63(2):431–450

Holmes CC, Held L et al (2006) Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Anal 1(1):145–168

Huber F, Fischer MM, Piribauer P (2017) The role of US based FDI flows for global output dynamics. Macroecon Dyn (forthcoming)

Klier T, McMillen DP (2008) Clustering of auto supplier plants in the United States: generalized method of moments spatial logit for large samples. J Bus Econ Stat 26(4):460–471

Koch M, Krisztin T (2011) Applications for asynchronous multi-agent teams in nonlinear applied spatial econometrics. J Internet Technol 12(6):1007–1014

Krisztin T (2017) The determinants of regional freight transport: a spatial, semiparametric approach. Geogr Anal 49(3):268–308

Krisztin T (2018) Semi-parametric spatial autoregressive models in freight generation modeling. Transp Res Part E Logist Transp Rev 114(September 2017):121–143

Laurini MP (2017) A spatial error model with continuous random effects and an application to growth convergence. J Geogr Syst 19(4):371–398

LeSage JP (1997) Bayesian estimation of spatial autoregressive models. Int Reg Sci Rev 20(1):113–129

LeSage JP (2000) Bayesian estimation of limited dependent variable spatial autoregressive models. Geogr Anal 32(1):19–35

LeSage JP, Chih YY (2018) A Bayesian spatial panel model with heterogeneous coefficients. Reg Sci Urban Econ 72:58–73

LeSage JP, Fischer MM (2008) Spatial growth regressions: model specification, estimation and interpretation. Spat Econ Anal 3(3):275–304

LeSage JP, Fischer MM (2012) Estimates of the impact of static and dynamic knowledge spillovers on regional factor productivity. Int Reg Sci Rev 35(1):103–127

LeSage JP, Kelley Pace R, Lam N, Campanella R, Liu X (2011) New Orleans business recovery in the aftermath of Hurricane Katrina. J R Stat Soc Ser A Stat Soc 174(4):1007–1027

LeSage JP, Pace RK (2007) A matrix exponential spatial specification. J Econom 140:190–214

LeSage JP, Pace RK (2009) Introduction to spatial econometrics. CRC Press, Boca Raton

LeSage JP, Pace RK (2018) Spatial econometric Monte Carlo studies: raising the bar. Empir Econ 55(1):17–34

Markusen JR, Venables AJ (2000) The theory of endowment, intra-industry and multi-national trade. J Int Econ 52(2):209–234

McFadden D (1974) Conditional logit analysis of qualitative choice behavior. In: Zarembka P (ed) Frontiers in econometrics. Academic Press, New York, pp 105–142

McMillen DP (1992) Probit with spatial autocorrelation. J Reg Sci 32(3):335–348

Pfarrhofer M, Piribauer P (2019) Flexible shrinkage in high-dimensional Bayesian spatial autoregressive models. Spat Stat 29(1):109–128

Pintar N, Sargant B, Fischer MM (2016) Austrian outbound foreign direct investment in Europe: a spatial econometric study. Romanian J Reg Sci 10(1):1–22

Piribauer P (2016) Heterogeneity in spatial growth clusters. Empir Econ 51(2):659–680

Piribauer P, Crespo Cuaresma J (2016) Bayesian variable selection in spatial autoregressive models. Spat Econ Anal 11(4):457–479

Polson NG, Scott JG, Windle J (2013) Bayesian inference for logistic models using Polya–Gamma latent variables. J Am Stat Assoc 108(504):1339–1349

Raftery AE, Lewis S (1992) How many iterations in the Gibbs sampler? In: Bernardo JM, Berger J, Dawid AP, Smith AFM (eds) Bayesian statistics 4. Oxford University Press, Oxford, pp 763–773

Ritter C, Tanner MA (1992) Facilitating the Gibbs sampler: the Gibbs stopper and the Griddy–Gibbs sampler. J Am Stat Assoc 87(419):861–868

Rodriguez-Clare A (1996) Multinationals, linkages, and economic development. Am Econ Rev 86(4):852–873

Smirnov OA (2010) Modeling spatial discrete choice. Reg Sci Urban Econ 40(5):292–298

Smith TE, LeSage JP (2004) A Bayesian probit model with spatial dependencies. In: LeSage JP, Pace RK (eds) Spatial and spatiotemporal econometrics. Emerald Group Publishing Limited, Bingley, pp 127–160

Strauss-Kahn V, Vives X (2009) Why and where do headquarters move? Reg Sci Urban Econ 39(2):168–186

Sturgeon TJ (2008) Mapping integrative trade: conceptualising and measuring global value chains. Int J Technol Learn Innov Dev 1(3):237–257

Windle J, Polson NG, Scott JG (2014) Sampling Polya–Gamma random variates: alternate and approximate techniques. arXiv preprint arXiv:1405.0506

Xu B (2000) Multinational enterprises, technology diffusion, and host country productivity growth. J Dev Econ 62(2):477–493

Title: A Bayesian spatial autoregressive logit model with an empirical application to European regional FDI flows
Authors: Tamás Krisztin
Philipp Piribauer
Publication date: 20-03-2020
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 1/2021
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-020-01856-w

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 1/2021

Measuring monetary policy: rules versus discretion

No place like home: geography and culture in the dissemination of economic research articles

Sup-ADF-style bubble-detection methods under test

Higher frequency hedonic property price indices: a state-space approach

The robustness of forecast combination in unstable environments: a Monte Carlo study of advanced algorithms

Public perceptions of the tax avoidance of corporations and the wealthy