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Cross-sectional dependence model specifications in a static trade panel data setting

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Abstract

The focus is on cross-sectional dependence in panel trade flow models. We propose alternative specifications for modeling time-invariant factors such as sociocultural indicator variables, e.g., common language and currency. These are typically treated as a source of heterogeneity that is eliminated using fixed effects transformations, but we find evidence of cross-sectional dependence after eliminating country-specific and time-specific effects. These findings suggest use of alternative simultaneous dependence model specifications that accommodate cross-sectional dependence, which we set forth along with Bayesian estimation methods. Ignoring cross-sectional dependence implies biased estimates from panel trade flow models that rely on fixed effects.

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Notes

  1. We deal only with the case where the number of importing and exporting countries is the same.

  2. We exclude exports from country i to itself, which would be on the main diagonal of the trade flow matrix, since we have no information on intra-country flows, resulting in \(N-1\).

  3. We do not introduce an intercept vector and associated parameter since use of the within transformation to eliminate fixed effects precludes an intercept.

  4. A value of −1 is often used in practice as this ensures that the matrix inverse \((I_{(N-1)T} - \rho (I_T \otimes W_c))^{-1}\) exists. This has the advantage that we do not have to calculate the minimum eigenvalue of \(W_c\) which changes as a function of the values taken by \(\gamma\).

  5. In the case of maximum likelihood estimation, parameters (say 1000) are drawn from a normal distribution using the mean estimates and estimated covariance matrix based on a numerical or analytical Hessian.

  6. Note also that we pre-compute My prior to MCMC sampling.

  7. See Debarsy and LeSage (2018) for a discussion of the reversible jump nature of this procedure.

  8. Specifically, \(T_1 = y' M' My\), \(T_2 = y' M' Z\), \(T_3 = Z' M y\), \(T_4 =Z' Z\) can be calculated since they consist of known quantities (sample data), so the quadratic forms are: \(e'e = \omega (\Gamma )' T_1 \omega (\Gamma ) - \omega (\Gamma )' T_2 \delta - \delta ' T_3 \omega (\Gamma ) + \delta ' T_4 \delta\). As noted, \(\omega (\Gamma )\) indicates that \(\omega (\Gamma )' = \left( \begin{array}{ccccc} 1&-\rho \gamma _1&-\rho \gamma _2&\cdots&-\rho \gamma _L \end{array} \right)\), where the parameter \(\rho\) is conditioned on (fixed).

  9. Elhorst (2013) points out that the effects for static spatial panel data models such as ours are the same as those developed by LeSage and Pace (2009) for the cross-sectional model, because the weight matrices and parameters do not vary over time periods.

  10. In addition, we eliminated countries from our sample that had one or more zero rows in any of the five weight matrices. As noted earlier, this is necessary to ensure that the matrix \(W_c\) does not contain zero rows, when we allow individual \(\gamma _{\ell }, \ell = 1,\ldots ,L\) parameters to take values of zero. This resulted in a few countries such as South Korea and Japan for which data were available to be excluded from our sample.

  11. Technically, although we allow for the open interval \((0< \gamma < 1)\), we consider a lower 0.05 value above 0.01 for the MCMC draws to be nonzero.

References

  • Anderson JE, van Wincoop E (2003) Gravity with gravitas: a solution to the border puzzle. Am Econ Rev 93(1):170–192

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Baltagi BH, Egger P, Pfaffermayr M (2008) Estimating regional trade agreement effects of FDI in an interdependent world. J Econom 145(1–2):194–208

    Article  Google Scholar 

  • Baltagi BH, Egger P, Pfaffermayr M (2014) Panel data gravity models of international trade, 31 Jan 2014. CESifo Working Paper Series No. 4616. SSRN: http://ssrn.com/abstract=2398292

  • Behrens K, Ertur C, Koch W (2012) Dual gravity: using spatial econometrics to control for multilateral resistance. J Appl Econom 27(5):773–794

    Article  Google Scholar 

  • Debarsy N, LeSage JP (2018) Flexible dependence modeling using convex combinations of different types of connectivity structures. Reg Sci Urban Econ 69(2):46–68

    Google Scholar 

  • Elhorst P (2013) Spatial econometrics: from cross-sectional data to spatial panels. Springer, Berlin Heidelberg

    Google Scholar 

  • Feenstra RC, Lipsey RE, Deng H, Ma AC, Mo H (2005) World trade flows: 1962–2000. NBER Working Paper Series 11040. http://www.nber.org/papers/w11040

  • Golub GH, van Loan CF (1996) Matrix computations. John Hopkins University Press, Baltimore

    Google Scholar 

  • Hazir CS, LeSage JP, Autant-Bernard C (2018) The role of R&D collaboration networks on regional innovation performance. Pap Reg Sci 97(3):549–567

    Article  Google Scholar 

  • Koch W, LeSage JP (2015) Latent multilateral trade resistance indices: theory and evidence. Scott J Polit Econ 62(3):264–290

    Article  Google Scholar 

  • Krisztin T, Fischer MM (2015) The gravity model for international trade: specification and estimation issues. Spat Econ Anal 10(4):451–470

    Article  Google Scholar 

  • Lebreton M, Roi L (2011) A spatial interaction model with spatial dependence for trade flows in Oceania: a preliminary analysis. Unpublished manuscript, Université Montesquieu Bordeaxu IV

  • Lee L-F, Yu J (2010) Estimation of spatial autoregressive panel data models with fixed effects. J Econom 154(2):165–185

    Article  Google Scholar 

  • LeSage JP (2019) Fast MCMC estimation of multiple W-matrix spatial regression models and Metropolis-Hastings Monte Carlo log.marginal likelihoods. J Geogr Syst. https://doi.org/10.1007/s10109-019-00294-2

    Article  Google Scholar 

  • LeSage JP, Fischer MM (2016) Spatial regression-based model specifications for exogenous and endogenous spatial interaction. In: Patuelli R, Arbia G (eds) Spatial econometric interaction modelling. Springer, Berlin, pp 37–68

    Google Scholar 

  • LeSage JP, Pace RK (2008) Spatial econometric modeling of origin-destination flows. J Reg Sci 48(5):941–967

    Article  Google Scholar 

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

    Book  Google Scholar 

  • LeSage JP, Thomas-Agnan C (2015) Interpreting spatial econometric origin-destination flow models. J Reg Sci 55(2):188–208

    Article  Google Scholar 

  • LeSage JP, Chih Y-Y, Vance C (2018) Spatial dynamic panel models for large samples. Paper presented at the North American Meetings of the Regional Science Association International, San Antonio, TX, November 2018

  • Pace RK, LeSage JP (2002) Semiparametric maximum likelihood estimates of spatial dependence. Geogr Anal 34(1):75–90

    Article  Google Scholar 

  • Porojan A (2001) Trade flows, spatial effects: the gravity model revisited. Open Econ Rev 12(3):265–280

    Article  Google Scholar 

  • World Bank (2002) World development indicators. WTO

  • WTO (2014) WTO Regional trade agreements database. WTO, Geneva

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Authors and Affiliations

  1. Texas State University, San Marcos, TX, USA

    James Paul LeSage

  2. Vienna University of Economics and Business , 1020, Vienna, Austria

    Manfred M. Fischer

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  1. James Paul LeSage
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  2. Manfred M. Fischer
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Correspondence to James Paul LeSage.

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Appendix

Appendix

See Tables 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

Table 4 SDM model \(\gamma\) estimates for Wspace import and export flow models
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Table 5 SDM model \(\gamma\) estimates for Wcurrency import and export flow models
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Table 6 SDM model \(\gamma\) estimates for Wlanguage import and export flow models
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Table 7 SDM model \(\gamma\) estimates for Wtrade import and export flow models
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Table 8 SDM model \(\gamma\) estimates for Wcolonial ties import and export flow models
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Table 9 List of countries
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Table 10 Language ties: Common official and second languages (Krisztin and Fischer 2015)
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Table 11 Free trade and stronger forms of agreements in 2000 (Krisztin and Fischer 2015)
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Table 12 Common currency ties
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Table 13 Direct colonial ties
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LeSage, J.P., Fischer, M.M. Cross-sectional dependence model specifications in a static trade panel data setting. J Geogr Syst 22, 5–46 (2020). https://doi.org/10.1007/s10109-019-00298-y

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