IDEAS home Printed from https://ideas.repec.org/a/gam/jecnmx/v1y2013i1p71-114d26028.html
   My bibliography  Save this article

Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments

Author

Listed:
  • Fei Jin

    (School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China)

  • Lung-fei Lee

    (Department of Economics, The Ohio State University, Columbus, OH 43210, USA)

Abstract

This paper studies the generalized spatial two stage least squares (GS2SLS) estimation of spatial autoregressive models with autoregressive disturbances when there are endogenous regressors with many valid instruments. Using many instruments may improve the efficiency of estimators asymptotically, but the bias might be large in finite samples, making the inference inaccurate. We consider the case that the number of instruments K increases with, but at a rate slower than, the sample size, and derive the approximate mean square errors (MSE) that account for the trade-offs between the bias and variance, for both the GS2SLS estimator and a bias-corrected GS2SLS estimator. A criterion function for the optimal K selection can be based on the approximate MSEs. Monte Carlo experiments are provided to show the performance of our procedure of choosing K.

Suggested Citation

  • Fei Jin & Lung-fei Lee, 2013. "Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments," Econometrics, MDPI, vol. 1(1), pages 1-44, May.
    • Handle: RePEc:gam:jecnmx:v:1:y:2013:i:1:p:71-114:d:26028
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2225-1146/1/1/71/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2225-1146/1/1/71/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kelejian, Harry H. & Prucha, Ingmar R., 2004. "Estimation of simultaneous systems of spatially interrelated cross sectional equations," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 27-50.
    2. 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.
    3. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    4. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    5. Xiaodong Liu & Lung-Fei Lee, 2013. "Two-Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 734-753, August.
    6. 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.
    7. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    8. 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.
    9. Besley, Timothy & Case, Anne, 1995. "Incumbent Behavior: Vote-Seeking, Tax-Setting, and Yardstick Competition," American Economic Review, American Economic Association, vol. 85(1), pages 25-45, March.
    10. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2012. "Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration," Journal of Econometrics, Elsevier, vol. 167(1), pages 16-37.
    11. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    12. Martin Benirschka & James K. Binkley, 1994. "Land Price Volatility in a Geographically Dispersed Market," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 76(2), pages 185-195.
    13. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    14. 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.
    15. David M. Drukker & Peter Egger & Ingmar R. Prucha, 2013. "On Two-Step Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances and Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 686-733, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guy Tchuente, 2016. "Estimation of social interaction models using regularization," Studies in Economics 1607, School of Economics, University of Kent.
    2. Xiaodong Liu, 2020. "GMM identification and estimation of peer effects in a system of simultaneous equations," Journal of Spatial Econometrics, Springer, vol. 1(1), pages 1-27, December.
    3. You, Jing & Huang, Yongfu, 2013. "Green-to-Grey China: Determinants and Forecasts of its Green Growth," MPRA Paper 57468, University Library of Munich, Germany, revised 16 Jul 2014.
    4. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    5. Simplice A. Asongu & Samba Diop, 2021. "Human development and governance in Africa: do good fences make good neighbours?," Research Africa Network Working Papers 21/051, Research Africa Network (RAN).
    6. Nestor Garza & Colin Lizieri, 2019. "An empirical approach to urban land monopoly: A case study of the city of Barranquilla, Colombia," Urban Studies, Urban Studies Journal Limited, vol. 56(10), pages 1931-1950, August.
    7. Tadao Hoshino, 2018. "Semiparametric Spatial Autoregressive Models With Endogenous Regressors: With an Application to Crime Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 160-172, January.
    8. Chalermpong, Saksith & Ratanawaraha, Apiwat & Anuchitchanchai, Ornicha, 2023. "Motorcycle taxis' varying degrees of complementarity and substitution with public transit in Bangkok," Journal of Transport Geography, Elsevier, vol. 108(C).
    9. Liu, Xiaodong & Saraiva, Paulo, 2015. "GMM estimation of SAR models with endogenous regressors," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 68-79.
    10. Povilas Lastauskas & Eirini Tatsi, 2013. "Spatial Nexus in Crime and unemployment in Times of crisis: Evidence from Germany," Cambridge Working Papers in Economics 1359, Faculty of Economics, University of Cambridge.
    11. Bernard Fingleton, 2023. "Estimating dynamic spatial panel data models with endogenous regressors using synthetic instruments," Journal of Geographical Systems, Springer, vol. 25(1), pages 121-152, January.
    12. Solmaria Halleck Vega & J. Paul Elhorst, 2015. "The Slx Model," Journal of Regional Science, Wiley Blackwell, vol. 55(3), pages 339-363, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    2. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
    3. Zhenlin Yang, 2006. "On Joint Modelling and Testing for Local and Global Spatial Externalities," Working Papers 25-2006, Singapore Management University, School of Economics.
    4. 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.
    5. repec:rri:wpaper:201302 is not listed on IDEAS
    6. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    7. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    8. Gibbons, Steve & Overman, Henry G. & Patacchini, Eleonora, 2015. "Spatial Methods," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 115-168, Elsevier.
    9. Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    10. Liu, Shew Fan & Yang, Zhenlin, 2015. "Modified QML estimation of spatial autoregressive models with unknown heteroskedasticity and nonnormality," Regional Science and Urban Economics, Elsevier, vol. 52(C), pages 50-70.
    11. repec:esx:essedp:772 is not listed on IDEAS
    12. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    13. Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2021. "Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 18-44, January.
    14. Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 178-200.
    15. Harald Badinger & Peter Egger, 2015. "Fixed Effects and Random Effects Estimation of Higher-order Spatial Autoregressive Models with Spatial Autoregressive and Heteroscedastic Disturbances," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(1), pages 11-35, March.
    16. Roger Bivand & Giovanni Millo & Gianfranco Piras, 2021. "A Review of Software for Spatial Econometrics in R," Mathematics, MDPI, vol. 9(11), pages 1-40, June.
    17. repec:asg:wpaper:1013 is not listed on IDEAS
    18. Gianfranco Piras & Paolo Postiglione & Patricio Aroca, 2012. "Specialization, R&D and productivity growth: evidence from EU regions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 49(1), pages 35-51, August.
    19. Anselin, Luc, 2002. "Under the hood : Issues in the specification and interpretation of spatial regression models," Agricultural Economics, Blackwell, vol. 27(3), pages 247-267, November.
    20. Harald Badinger & Peter Egger, 2008. "GM Estimation of Higher-Order Spatial Autoregressive Processes in Cross-Section Models with Heteroskedastic Disturbances," CESifo Working Paper Series 2356, CESifo.
    21. David M. Drukker & Peter Egger & Ingmar R. Prucha, 2013. "On Two-Step Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances and Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 686-733, August.
    22. Guy Tchuente, 2016. "Estimation of social interaction models using regularization," Studies in Economics 1607, School of Economics, University of Kent.
    23. Guido M. Kuersteiner & Ingmar R. Prucha, 2020. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," Econometrica, Econometric Society, vol. 88(5), pages 2109-2146, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jecnmx:v:1:y:2013:i:1:p:71-114:d:26028. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.