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Estimation of a SAR model with endogenous spatial weights constructed by bilateral variables

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  • Qu, Xi
  • Lee, Lung-fei
  • Yang, Chao

Abstract

This paper studies the estimation of a cross-sectional spatial autoregressive (SAR) model with spatial weights constructed by bilateral variables like the trade or investment between regions. We model the possible endogeneity in spatial weights due to the correlation between the error term in the SAR model and unobserved interactive fixed effects in bilateral variables. Using a control function approach, we propose two-stage estimation methods and establish their consistency and asymptotic normality. Finite sample properties are investigated by a Monte Carlo study. We further apply our method to an empirical study of interactions among different US industries through production networks.

Suggested Citation

  • Qu, Xi & Lee, Lung-fei & Yang, Chao, 2021. "Estimation of a SAR model with endogenous spatial weights constructed by bilateral variables," Journal of Econometrics, Elsevier, vol. 221(1), pages 180-197.
    • Handle: RePEc:eee:econom:v:221:y:2021:i:1:p:180-197
    DOI: 10.1016/j.jeconom.2020.05.011
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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Dong, Feng & Wen, Yi, 2019. "Long and Plosser meet Bewley and Lucas," Journal of Monetary Economics, Elsevier, vol. 102(C), pages 70-92.
    3. James E. Anderson & Eric van Wincoop, 2003. "Gravity with Gravitas: A Solution to the Border Puzzle," American Economic Review, American Economic Association, vol. 93(1), pages 170-192, March.
    4. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    5. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    6. Daron Acemoglu & Vasco M. Carvalho & Asuman Ozdaglar & Alireza Tahbaz‐Salehi, 2012. "The Network Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 80(5), pages 1977-2016, September.
    7. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    8. Daron Acemoglu & Pablo D. Azar, 2020. "Endogenous Production Networks," Econometrica, Econometric Society, vol. 88(1), pages 33-82, January.
    9. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    10. Daron Acemoglu & Ufuk Akcigit & William Kerr, 2016. "Networks and the Macroeconomy: An Empirical Exploration," NBER Macroeconomics Annual, University of Chicago Press, vol. 30(1), pages 273-335.
    11. Giuliodori, Massimo & Beetsma, Roel, 2008. "On the relationship between fiscal plans in the European Union: An empirical analysis based on real-time data," Journal of Comparative Economics, Elsevier, vol. 36(2), pages 221-242, June.
    12. Maarten Allers & J. Elhorst, 2005. "Tax Mimicking and Yardstick Competition Among Local Governments in the Netherlands," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 12(4), pages 493-513, August.
    13. Cem Ertur & Wilfried Koch, 2011. "A contribution to the theory and empirics of Schumpeterian growth with worldwide interactions," Journal of Economic Growth, Springer, vol. 16(3), pages 215-255, September.
    14. Baltagi, Badi H. & Fingleton, Bernard & Pirotte, Alain, 2014. "Spatial lag models with nested random effects: An instrumental variable procedure with an application to English house prices," Journal of Urban Economics, Elsevier, vol. 80(C), pages 76-86.
    15. Liu, Xiaodong & Lee, Lung-fei, 2010. "GMM estimation of social interaction models with centrality," Journal of Econometrics, Elsevier, vol. 159(1), pages 99-115, November.
    16. Cheng, Wei & Lee, Lung-fei, 2017. "Testing endogeneity of spatial and social networks," Regional Science and Urban Economics, Elsevier, vol. 64(C), pages 81-97.
    17. Qu, Xi & Lee, Lung-fei & Yu, Jihai, 2017. "QML estimation of spatial dynamic panel data models with endogenous time varying spatial weights matrices," Journal of Econometrics, Elsevier, vol. 197(2), pages 173-201.
    18. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
    19. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    20. Baicker, Katherine, 2005. "The spillover effects of state spending," Journal of Public Economics, Elsevier, vol. 89(2-3), pages 529-544, February.
    21. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    22. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    23. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    24. Kelejian, Harry H. & Piras, Gianfranco, 2014. "Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes," Regional Science and Urban Economics, Elsevier, vol. 46(C), pages 140-149.
    25. Xi Qu & Xiaoliang Wang & Lung‐fei Lee, 2016. "Instrumental variable estimation of a spatial dynamic panel model with endogenous spatial weights when T is small," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 261-290, October.
    26. Qu, Xi & Lee, Lung-fei, 2015. "Estimating a spatial autoregressive model with an endogenous spatial weight matrix," Journal of Econometrics, Elsevier, vol. 184(2), pages 209-232.
    27. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    28. Bordignon, Massimo & Cerniglia, Floriana & Revelli, Federico, 2003. "In search of yardstick competition: a spatial analysis of Italian municipality property tax setting," Journal of Urban Economics, Elsevier, vol. 54(2), pages 199-217, September.
    29. Ho, Chun-Yu & Wang, Wei & Yu, Jihai, 2013. "Growth spillover through trade: A spatial dynamic panel data approach," Economics Letters, Elsevier, vol. 120(3), pages 450-453.
    30. J. Elhorst, 2010. "Applied Spatial Econometrics: Raising the Bar," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 9-28.
    31. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    32. Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
    33. Ida Johnsson & Hyungsik Roger Moon, 2017. "Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach," Papers 1709.10024, arXiv.org, revised Jul 2019.
    34. Joris Pinkse & Margaret E. Slade, 2010. "The Future Of Spatial Econometrics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 103-117, February.
    35. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
    36. Xu Lin, 2010. "Identifying Peer Effects in Student Academic Achievement by Spatial Autoregressive Models with Group Unobservables," Journal of Labor Economics, University of Chicago Press, vol. 28(4), pages 825-860, October.
    37. Lung-fei Lee & Xiaodong Liu & Xu Lin, 2010. "Specification and estimation of social interaction models with network structures," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 145-176, July.
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    3. Marko Mlikota, 2022. "Cross-Sectional Dynamics Under Network Structure: Theory and Macroeconomic Applications," Papers 2211.13610, arXiv.org, revised Dec 2023.
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    8. Huijuan Xiao & Sheng Bao & Jingzheng Ren & Zhenci Xu & Song Xue & Jianguo Liu, 2024. "Global transboundary synergies and trade-offs among Sustainable Development Goals from an integrated sustainability perspective," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    9. Rezgar FEIZI & Sahar AMIDI & Thais NUNEZ-ROCHA & Isabelle RABAUD, 2022. "Carbon Tax and Emissions Transfer: a Spatial Analysis," LEO Working Papers / DR LEO 2965, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    10. Mohamad Adfar & Patta Tope & Muchtar Lutfi, 2022. "Analysis of Resource Ownership of Small Medium Industry and Their Effect on Natural Disaster Preparedness in the Beach Area (Study on SMEs Food Industry Branch)," International Journal of Research and Innovation in Social Science, International Journal of Research and Innovation in Social Science (IJRISS), vol. 6(02), pages 146-156, February.

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    More about this item

    Keywords

    Spatial autoregressive model; Endogenous spatial weight matrix; Bilateral variables;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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