IDEAS home Printed from https://ideas.repec.org/a/wly/japmet/v39y2024i4p640-658.html
   My bibliography  Save this article

Best linear and quadratic moments for spatial econometric models with an application to spatial interdependence patterns of employment growth in US counties

Author

Listed:
  • Fei Jin
  • Lung‐fei Lee
  • Kai Yang

Abstract

We provide a novel analytic procedure to construct best linear and quadratic moments of the generalized method of moments estimation for a large class of cross‐sectional network and spatial econometric models. These moments generate an estimator that is asymptotically more efficient than the quasi‐maximum likelihood estimator when the disturbances follow a non‐normal and unknown distribution. We apply this procedure to a high‐order spatial autoregressive model with spatial errors, where the disturbances are heteroskedastic. Two normality tests of disturbances are developed. We apply the model to employment data in US counties, which demonstrates spatial interdependence patterns of regional employment growth.

Suggested Citation

  • Fei Jin & Lung‐fei Lee & Kai Yang, 2024. "Best linear and quadratic moments for spatial econometric models with an application to spatial interdependence patterns of employment growth in US counties," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(4), pages 640-658, June.
    • Handle: RePEc:wly:japmet:v:39:y:2024:i:4:p:640-658
    DOI: 10.1002/jae.3046
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/jae.3046
    Download Restriction: no
    File URL: https://libkey.io/10.1002/jae.3046?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Thomas de Graaff & Frank G. van Oort & Raymond J.G.M. Florax, 2012. "Regional Population–Employment Dynamics Across Different Sectors Of The Economy," Journal of Regional Science, Wiley Blackwell, vol. 52(1), pages 60-84, February.
    4. Elhorst, J. Paul, 2010. "Dynamic panels with endogenous interaction effects when T is small," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 272-282, September.
    5. Bernard Fingleton, 2008. "A Generalized Method of Moments Estimator for a Spatial Panel Model with an Endogenous Spatial Lag and Spatial Moving Average Errors," Spatial Economic Analysis, Taylor & Francis Journals, vol. 3(1), pages 27-44.
    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. 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.
    8. 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.
    9. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2022. "Bayesian estimation of multivariate panel probits with higher‐order network interdependence and an application to firms' global market participation in Guangdong," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1356-1378, November.
    10. Gupta, Abhimanyu & Robinson, Peter M., 2015. "Inference on higher-order spatial autoregressive models with increasingly many parameters," Journal of Econometrics, Elsevier, vol. 186(1), pages 19-31.
    11. Cem Ertur & Wilfried Koch, 2007. "Growth, technological interdependence and spatial externalities: theory and evidence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1033-1062.
    12. Marcy Burchfield & Henry G. Overman & Diego Puga & Matthew A. Turner, 2006. "Causes of Sprawl: A Portrait from Space," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(2), pages 587-633.
    13. Gilles Duranton & Matthew A. Turner, 2012. "Urban Growth and Transportation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1407-1440.
    14. 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.
    15. Hauptmeier, Sebastian & Mittermaier, Ferdinand & Rincke, Johannes, 2012. "Fiscal competition over taxes and public inputs," Regional Science and Urban Economics, Elsevier, vol. 42(3), pages 407-419.
    16. James P. LeSage & R. Kelley Pace, 2014. "The Biggest Myth in Spatial Econometrics," Econometrics, MDPI, vol. 2(4), pages 1-33, December.
    17. 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.
    18. 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.
    19. Maarten A. Allers & J. Paul Elhorst, 2011. "A Simultaneous Equations Model Of Fiscal Policy Interactions," Journal of Regional Science, Wiley Blackwell, vol. 51(2), pages 271-291, May.
    20. Christopher H. Wheeler, 2003. "Evidence on agglomeration economies, diseconomies, and growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 79-104.
    21. Debarsy, Nicolas & Jin, Fei & Lee, Lung-fei, 2015. "Large sample properties of the matrix exponential spatial specification with an application to FDI," Journal of Econometrics, Elsevier, vol. 188(1), pages 1-21.
    22. 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.
    23. Alexander G. James & Brock Smith, 2020. "Geographic Dispersion of Economic Shocks: Evidence from the Fracking Revolution: Comment," American Economic Review, American Economic Association, vol. 110(6), pages 1905-1913, June.
    24. Schmitt, Bertrand & Henry, Mark S., 2000. "Size and growth of urban centers in French labor market areas: consequences for rural population and employment," Regional Science and Urban Economics, Elsevier, vol. 30(1), pages 1-21, January.
    25. Xiaodong Liu & Paulo Saraiva, 2019. "GMM estimation of spatial autoregressive models in a system of simultaneous equations with heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 38(4), pages 359-385, April.
    26. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    27. James Feyrer & Erin T. Mansur & Bruce Sacerdote, 2017. "Geographic Dispersion of Economic Shocks: Evidence from the Fracking Revolution," American Economic Review, American Economic Association, vol. 107(4), pages 1313-1334, April.
    28. Michael Peters, 2022. "Market Size and Spatial Growth—Evidence From Germany's Post‐War Population Expulsions," Econometrica, Econometric Society, vol. 90(5), pages 2357-2396, September.
    29. Bertrand B. Schmitt & M.S. Henry, 2000. "Size and growth of urban centers in French labor market areas : consequences for rural population and employment [[Taille et croissance des centres urbains dans les bassins d'emplois en France : co," Post-Print hal-02687942, HAL.
    30. Gebremeskel Gebremariam & Tesfa Gebremedhin & Peter Schaeffer, 2010. "Analysis of county employment and income growth in Appalachia: a spatial simultaneous-equations approach," Empirical Economics, Springer, vol. 38(1), pages 23-45, February.
    31. Baltagi, Badi H. & Bresson, Georges, 2011. "Maximum likelihood estimation and Lagrange multiplier tests for panel seemingly unrelated regressions with spatial lag and spatial errors: An application to hedonic housing prices in Paris," Journal of Urban Economics, Elsevier, vol. 69(1), pages 24-42, January.
    32. 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.
    33. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    34. Sandro M. Reia & P. Suresh C. Rao & Marc Barthelemy & Satish V. Ukkusuri, 2022. "Spatial structure of city population growth," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    35. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    36. Christopher H. Wheeler, 2001. "A Note on the Spatial Correlation Structure of County‐Level Growth in the U.S," Journal of Regional Science, Wiley Blackwell, vol. 41(3), pages 433-449, August.
    37. 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.
    38. Süleyman Taşpınar & Osman Doğan & Anil K. Bera, 2019. "Heteroskedasticity-consistent covariance matrix estimators for spatial autoregressive models," Spatial Economic Analysis, Taylor & Francis Journals, vol. 14(2), pages 241-268, April.
    39. Jeanty, P. Wilner & Partridge, Mark & Irwin, Elena, 2010. "Estimation of a spatial simultaneous equation model of population migration and housing price dynamics," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 343-352, September.
    40. 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.
    41. Lee, Lung-fei & Liu, Xiaodong, 2010. "Efficient Gmm Estimation Of High Order Spatial Autoregressive Models With Autoregressive Disturbances," Econometric Theory, Cambridge University Press, vol. 26(1), pages 187-230, February.
    42. Yang, Kai & Lee, Lung-fei, 2017. "Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 196(1), pages 196-214.
    Full references (including those not matched with items on IDEAS)

    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. Marius C. O. Amba & Taoufiki Mbratana & Julie Gallo, 2023. "Spatial panel simultaneous equations models with error components," Empirical Economics, Springer, vol. 65(3), pages 1149-1196, September.
    2. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2022. "Bayesian estimation of multivariate panel probits with higher‐order network interdependence and an application to firms' global market participation in Guangdong," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1356-1378, November.
    3. Yang, Kai & Lee, Lung-fei, 2017. "Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 196(1), pages 196-214.
    4. Debarsy, Nicolas & Ertur, Cem, 2019. "Interaction matrix selection in spatial autoregressive models with an application to growth theory," Regional Science and Urban Economics, Elsevier, vol. 75(C), pages 49-69.
    5. AMBA OYON, Claude Marius & Mbratana, Taoufiki, 2017. "Simultaneous equation models with spatially autocorrelated error components," MPRA Paper 82395, University Library of Munich, Germany.
    6. Lina Lu, 2017. "Simultaneous Spatial Panel Data Models with Common Shocks," Supervisory Research and Analysis Working Papers RPA 17-3, Federal Reserve Bank of Boston.
    7. Wang, Wei & Lee, Lung-Fei & Bao, Yan, 2018. "GMM estimation of the spatial autoregressive model in a system of interrelated networks," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 167-198.
    8. 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.
    9. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    10. Bao, Yong, 2024. "Estimating spatial autoregressions under heteroskedasticity without searching for instruments," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    11. William C. Horrace & Hyunseok Jung & Shane Sanders, 2022. "Network Competition and Team Chemistry in the NBA," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 35-49, January.
    12. Nicolas DEBARSY & Cem ERTUR, 2016. "Interaction matrix selection in spatial econometrics with an application to growth theory," LEO Working Papers / DR LEO 2172, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    13. Malikov, Emir & Sun, Yiguo, 2017. "Semiparametric estimation and testing of smooth coefficient spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 199(1), pages 12-34.
    14. Yang, Kai & Lee, Lung-fei, 2021. "Estimation of dynamic panel spatial vector autoregression: Stability and spatial multivariate cointegration," Journal of Econometrics, Elsevier, vol. 221(2), pages 337-367.
    15. Yong Bao & Xiaotian Liu & Lihong Yang, 2020. "Indirect Inference Estimation of Spatial Autoregressions," Econometrics, MDPI, vol. 8(3), pages 1-26, September.
    16. 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.
    17. 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.
    18. Heather D Gibson & Stephen G Hall & Deborah GeFang & Pavlos Petroulas & George S Tavlas, 2021. "Cross-country spillovers of national financial markets and the effectiveness of ECB policies during the euro-area crisis," Oxford Economic Papers, Oxford University Press, vol. 73(4), pages 1454-1470.
    19. Lee, Lung-fei & Yu, Jihai, 2014. "Efficient GMM estimation of spatial dynamic panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 180(2), pages 174-197.
    20. Elhorst, J. Paul & Emili, Silvia, 2022. "A spatial econometric multivariate model of Okun's law," Regional Science and Urban Economics, Elsevier, vol. 93(C).

    More about this item

    Statistics

    Access and download statistics

    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:wly:japmet:v:39:y:2024:i:4:p:640-658. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0883-7252/ .

    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.