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SIMULTANEOUS EQUATIONS MODELS WITH HIGHER-ORDER SPATIAL OR SOCIAL NETWORK INTERACTIONS

Published online by Cambridge University Press:  28 March 2022

David M. Drukker ,
Peter H. Egger  and
Ingmar R. Prucha
David M. Drukker
Affiliation:
Department of Economics and International Business, Sam Houston State University
Peter H. Egger
Affiliation:
ETH Zurich
Ingmar R. Prucha*
Affiliation:
Department of Economics, University of Maryland
*
Address correspondence to Ingmar R. Prucha, Department of Economics, University of Maryland, College Park, MD 20742, USA; e-mail: prucha@umd.edu.
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Abstract

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This paper develops an estimation methodology for network data generated from a system of simultaneous equations, which allows for network interdependencies via spatial lags in the endogenous and exogenous variables, as well as in the disturbances. By allowing for higher-order spatial lags, our specification provides important flexibility in modeling network interactions. The estimation methodology builds, among others, on the two-step generalized method of moments estimation approach introduced in Kelejian and Prucha (1998, Journal of Real Estate Finance and Economics 17, 99–121; 1999, International Economic Review 40, 509–533; 2004, Journal of Econometrics 118, 27–50). The paper considers limited and full information estimators, and one- and two-step estimators, and establishes their asymptotic properties. In contrast to some of the earlier two-step estimation literature, our asymptotic results facilitate joint tests for the absence of all forms of network spillovers.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 6: SPECIAL ISSUE IN HONOR OF BENEDIKT M PÖTSCHER , December 2023 , pp. 1154 - 1201
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We are grateful to the editor, a guest editor, and three anonymous referees for their very helpful comments. We gratefully acknowledge financial support from the National Institute of Health through SBIR grants R43 AG027622 and R44 AG027622. We also thank the CESifo for their hospitality.

References

REFERENCES

Anselin, L. (1988) Spatial Econometrics: Methods and Models . Kluwer Academic Publishers.CrossRefGoogle Scholar
Anselin, L. (2010) Thirty years of spatial econometrics. Papers in Regional Science 89, 3–25.CrossRefGoogle Scholar
Anselin, L. & Florax, R. (1995) New Directions in Spatial Econometrics . Springer.CrossRefGoogle Scholar
Audretsch, D.B. & Feldmann, M.P. (1996) R&D spillovers and the geography of innovation and production. American Economic Review 86, 630–640.Google Scholar
Ballester, C., Calvó-Armengol, A., & Zenou, Y. (2006) Who’s who in networks. Wanted: The key player. Econometrica 74, 1403–1417.CrossRefGoogle Scholar
Baltagi, B.H. & Deng, Y. (2015) EC3SLS estimator for a simultaneous system of spatial autoregressive equations with random effects. Econometric Reviews 34, 659–694.CrossRefGoogle Scholar
Baltagi, B.H., Egger, P., & Pfaffermayr, M. (2007) Estimating models of complex FDI: Are there third-country effects? Journal of Econometrics 140, 260–281.CrossRefGoogle Scholar
Baltagi, B.H., Egger, P., & Pfaffermayr, M. (2008) Estimating regional trade agreement effects on FDI in an interdependent world. Journal of Econometrics 145, 194–208.CrossRefGoogle Scholar
Behrens, K., Koch, W., & Ertur, C. (2012) Dual gravity: Using spatial econometrics to control for multilateral resistance. Journal of Applied Econometrics 27, 773–794.CrossRefGoogle Scholar
Bell, K.P. & Bockstael, N.E. (2000) Applying the generalized-moments estimation approach to spatial problems involving microlevel data. Review of Economics and Statistics 82, 72–82.CrossRefGoogle Scholar
Blonigen, B.A., Davies, R.B., Waddell, G.R., & Naughton, H.T. (2007) FDI in space: Spatial autoregressive relationships in foreign direct investment. European Economic Review 51, 1303–1325.CrossRefGoogle Scholar
Blume, L.E., Brock, W.A., Durlauf, S.N., & Ioannides, Y.M. (2011) Identification of social interactions. In Benhabib, J., Bisin, A., & Jackson, M.O. (eds.), Handbook of Social Economics , vol. 1B, pp. 853–964. Elsevier Publisher.Google Scholar
Calvó-Armengol, A., Patacchini, E., & Zenou, Y. (2009) Peer effects and social networks in education. Review of Economic Studies 76, 1239–1267.CrossRefGoogle Scholar
Case, A., Hines, J. Jr., & Rosen, H. (1993) Budget spillovers and fiscal policy independence: Evidence from the States. Journal of Public Economics 52, 285–307.CrossRefGoogle Scholar
Cliff, A. & Ord, J. (1973) Spatial Autocorrelation . Pion.Google Scholar
Cliff, A. & Ord, J. (1981) Spatial Processes, Models and Applications . Pion.Google Scholar
Cohen, J.P. & Morrison Paul, C.J. (2007) Higher order spatial autocorrelation in a system of equations: The impacts of transportation infrastructure on capital asset values. Journal of Regional Science 47, 457–478.CrossRefGoogle Scholar
Cohen-Cole, E., Liu, X., & Zenou, Y. (2018) Multivariate choice and identification of social interactions. Journal of Applied Econometrics 33, 165–178.CrossRefGoogle Scholar
Conley, T.G. & Ligon, E. (2002) Economic distance and cross-country spillovers. Journal of Economic Growth 7, 157–187.CrossRefGoogle Scholar
Cressie, N.A.C. (1993) Statistics of Spatial Data . Wiley.CrossRefGoogle Scholar
Das, D., Kelejian, H.H., & Prucha, I.R. (2003) Finite sample properties of estimators of spatial autoregressive models with autoregressive disturbances. Papers in Regional Science 82, 1–26.CrossRefGoogle Scholar
Devereux, M.P., Lockwood, B., & Redoano, M. (2008) Do countries compete over corporate taxes? Journal of Public Economics 92, 1210–1235.CrossRefGoogle Scholar
Egger, P., Pfaffermayr, M., & Winner, H. (2005) Commodity taxation in a ‘linear’ world: A spatial panel data approach. Regional Science and Urban Economics 35, 527–541.CrossRefGoogle Scholar
Ertur, C. & Koch, W. (2007) Growth, technological interdependence and spatial externalities: Theory and evidence. Journal of Applied Econometrics 22, 1033–1062.CrossRefGoogle Scholar
Holtz-Eakin, D. (1994) Public sector capital and the productivity puzzle. Review of Economics and Statistics 76, 12–21.CrossRefGoogle Scholar
Horn, R.A. & Johnson, C.R. (1985) Matrix Analysis . Cambridge University Press.CrossRefGoogle Scholar
Kapoor, M., Kelejian, H.H., & Prucha, I.R. (2007) Panel data models with spatially correlated error components. Journal of Econometrics 140, 97–130.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. (1998) A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. Journal of Real Estate Finance and Economics 17, 99–121.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. (1999) A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40, 509–533.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. (2004) Estimation of simultaneous systems of spatially interrelated cross sectional equations. Journal of Econometrics 118, 27–50.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. (2010) Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics 157, 53–67.CrossRefGoogle ScholarPubMed
Kuersteiner, G.M. & Prucha, I.R. (2020) Dynamic spatial panel models: Networks, common shocks, and sequential exogeneity. Econometrica 88, 2109–2146.CrossRefGoogle Scholar
Lee, J., Phillips, P.C.B., & Rossi, F. (2021) Specification Testing in Spatial Autoregression. Working Paper.Google Scholar
Lee, L.-F. (2003) Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances. Econometric Reviews 22, 307–335.CrossRefGoogle Scholar
Lee, L.-F. (2007) Identification and estimation of econometric models with group interactions, contextual factors and fixed effects. Journal of Econometrics 140, 333–374.CrossRefGoogle Scholar
Lee, L.-F. & Liu, X. (2010) Efficient GMM estimation of high order spatial autoregrssive models with autoregressive disturbances. Econometric Theory 26, 187–230.CrossRefGoogle Scholar
Liu, X. (2014) Identification and efficient estimation of simultaneous equations network models. Journal of Business & Economic Statistics 32, 516–536.CrossRefGoogle Scholar
Liu, X. (2019) Simultaneous equations with binary outcomes and social interactions. Econometric Reviews 38, 921–937.CrossRefGoogle Scholar
Liu, X. (2020) GMM identification and estimation of peer effects in a system of simultaneous equations. Journal of Spatial Econometrics 1, 2–27.CrossRefGoogle Scholar
Liu, X. & Saraiva, P. (2019) GMM estimation of spatial autoregressive models in a system of simultaneous equations with heteroskedasticity. Econometric Reviews 38, 359–385.CrossRefGoogle Scholar
Pinkse, J. & Slade, M.E. (1998) Contracting in space: An application of spatial statistics to discrete-choice models. Journal of Econometrics 85, 125–154.CrossRefGoogle Scholar
Pinkse, J., Slade, M.E., & Brett, C. (2002) Spatial price competition: A semiparametric approach. Econometrica 70, 1111–1153.CrossRefGoogle Scholar
Pötscher, B.M. & Prucha, I.R. (1997) Dynamic Nonlinear Econometric Models, Asymptotic Theory . Springer Verlag.CrossRefGoogle Scholar
Wang, W., Lee, L.-F., & Bao, Y. (2018) GMM estimation of the spatial autoregressive model in a system of interrelated networks. Regional Science and Urban Economics 69, 167–198.CrossRefGoogle Scholar
Wang, L., Li, K., & Wang, Z. (2014) Quasi Maximum Likelihood Estimation for Simultaneous Spatial Autoregressive Models. MPRA Working Paper 59901.Google Scholar
Whittle, P. (1954) On stationary processes in the plane. Biometrica 41, 434–449.CrossRefGoogle Scholar
Yang, K. & Lee, L.-F. (2017) Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models. Journal of Econometrics 196, 196–214.CrossRefGoogle Scholar
Yang, K. & Lee, L.-F. (2019) Identification and estimation of spatial dynamic panel simultaneous equations models. Regional Science and Urban Economics 76, 32–46.CrossRefGoogle Scholar
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