IDEAS home Printed from https://ideas.repec.org/p/pae/wpaper/10-5.html
   My bibliography  Save this paper

A Two-Step Estimator For A Spatial Lag Model Of Counts: Theory, Small Sample Performance And An Application

Author

Listed:
  • Dayton M. Lambert

    () (Dept. of Agricultural Economics, University of Tennessee)

  • Jason P. Brown

    () (USDA, Economic Research Service, Washington, D.C.)

  • Raymond J.G.M. Florax

    () (Dept. of Agricultural Economics, Purdue University)

Abstract

Several spatial econometric approaches are available to model spatially correlated disturbances in count models, but there are at present no structurally consistent count models incorporating spatial lag autocorrelation. A two-step, limited information maximum likelihood estimator is proposed to fill this gap. The estimator is developed assuming a Poisson distribution, but can be extended to other count distributions. The small sample properties of the estimator are evaluated with Monte Carlo experiments. Simulation results suggest that the spatial lag count estimator achieves gains in terms of bias over the aspatial version as spatial lag autocorrelation and sample size increase. An empirical example deals with the location choice of single-unit start-up firms in the manufacturing industry in the US between 2000 and 2004. The empirical results suggest that in the dynamic process of firm formation, counties dominated by firms exhibiting (internal) increasing returns to scale are at a relative disadvantage even if localization economies are present

Suggested Citation

  • Dayton M. Lambert & Jason P. Brown & Raymond J.G.M. Florax, 2010. "A Two-Step Estimator For A Spatial Lag Model Of Counts: Theory, Small Sample Performance And An Application," Working Papers 10-5, Purdue University, College of Agriculture, Department of Agricultural Economics.
  • Handle: RePEc:pae:wpaper:10-5
    as

    Download full text from publisher

    File URL: http://ageconsearch.umn.edu/bitstream/59780/2/10-5.pdf
    Download Restriction: no

    Other versions of 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. Timothy J. Bartik, 2010. "Small Business Start-Ups in the United States: Estimates of the Effects of Characteristics of States," Book chapters authored by Upjohn Institute researchers,in: Zolton Acs (ed.), Entrepreneurship and regional Development, pages 155-169 W.E. Upjohn Institute for Employment Research.
    3. Paulo Guimarães & Octávio Figueirdo & Douglas Woodward, 2003. "A Tractable Approach to the Firm Location Decision Problem," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 201-204, February.
    4. Göran Therborn & K.C. Ho, 2009. "Introduction," City, Taylor & Francis Journals, vol. 13(1), pages 53-62, March.
    5. Lambert, Dayton M. & McNamara, Kevin T. & Garrett, Megan I., 2006. "An Application of Spatial Poisson Models to Manufacturing Investment Location Analysis," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 38(01), April.
    6. Carlson, Virginia, 2000. "Studying Firm Locations: Survey Responses vs. Econometric Models," Journal of Regional Analysis and Policy, Mid-Continent Regional Science Association, vol. 30(1).
    7. Edward Glaeser & Janet Kohlhase, 2003. "Cities, regions and the decline of transport costs," Economics of Governance, Springer, vol. 83(1), pages 197-228, October.
    8. Blundell, Richard & Griffith, Rachel & Windmeijer, Frank, 2002. "Individual effects and dynamics in count data models," Journal of Econometrics, Elsevier, vol. 108(1), pages 113-131, May.
    9. Florax, Raymond J. G. M. & Folmer, Hendrik & Rey, Sergio J., 2003. "Specification searches in spatial econometrics: the relevance of Hendry's methodology," Regional Science and Urban Economics, Elsevier, vol. 33(5), pages 557-579, September.
    10. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    11. Bernard Fingleton & Julie Le Gallo, 2008. "Estimating spatial models with endogenous variables, a spatial lag and spatially dependent disturbances: Finite sample properties," Papers in Regional Science, Wiley Blackwell, vol. 87(3), pages 319-339, August.
    12. Dayton M. Lambert & Kevin T. McNamara, 2009. "Location determinants of food manufacturers in the United States, 2000-2004: are nonmetropolitan counties competitive?," Agricultural Economics, International Association of Agricultural Economists, vol. 40(6), pages 617-630, November.
    13. Paulo Guimaraes & Octávio Figueiredo & Douglas Woodward, 2004. "Industrial Location Modeling: Extending the Random Utility Framework," Journal of Regional Science, Wiley Blackwell, vol. 44(1), pages 1-20.
    14. Stephan J. Goetz, 1997. "State- and County-Level Determinants of Food Manufacturing Establishment Growth: 1987–93," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 79(3), pages 838-850.
    15. Josep Maria Arauzo Carod & Miguel C. ManjÛn AntolÌn, 2004. "Firm Size and Geographical Aggregation: An Empirical Appraisal in Industrial Location," Small Business Economics, Springer, vol. 22(3_4), pages 299-312, April.
    16. Schmenner, Roger W. & Huber, Joel C. & Cook, Randall L., 1987. "Geographic differences and the location of new manufacturing facilities," Journal of Urban Economics, Elsevier, vol. 21(1), pages 83-104, January.
    17. Cameron,A. Colin & Trivedi,Pravin K., 2008. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9787111235767, March.
    18. Smith, Eldon D. & Deaton, Brady J. & Kelch, David R., 1978. "Location Determinants Of Manufacturing Industry In Rural Areas," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 10(01), July.
    19. James P. LeSage & Manfred M. Fischer & Thomas Scherngell, 2007. "Knowledge spillovers across Europe: Evidence from a Poisson spatial interaction model with spatial effects," Papers in Regional Science, Wiley Blackwell, vol. 86(3), pages 393-421, August.
    20. Fotopoulos, Georgios & Louri, Helen, 2000. "Location and Survival of New Entry," Small Business Economics, Springer, vol. 14(4), pages 311-321, June.
    21. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
    22. Davis, David E. & Schluter, Gerald E., 2005. "Labor-Force Heterogeneity as a Source of Agglomeration Economies in an Empirical Analysis of County-Level Determinants of Food Plant Entry," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 30(03), December.
    23. Pinkse, Joris & Slade, Margaret E., 1998. "Contracting in space: An application of spatial statistics to discrete-choice models," Journal of Econometrics, Elsevier, vol. 85(1), pages 125-154, July.
    24. Cletus C. Coughlin & Eran Segev, 2000. "Location Determinants of New Foreign-Owned Manufacturing Plants," Journal of Regional Science, Wiley Blackwell, vol. 40(2), pages 323-351.
    25. Anselin, Luc, 2002. "Under the hood Issues in the specification and interpretation of spatial regression models," Agricultural Economics of Agricultural Economists, International Association of Agricultural Economists, vol. 27(3), November.
    26. Kaiser, Mark S. & Cressie, Noel, 1997. "Modeling Poisson variables with positive spatial dependence," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 423-432, November.
    27. Wojan, Timothy R. & McGranahan, David A., 2007. "Ambient Returns: Creative Capital's Contribution to Local Manufacturing Competitiveness," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 36(1), April.
    28. Lambert, Dayton M. & McNamara, Kevin T. & Garrett, Megan I., 2006. "Food Industry Investment Flows: Implications for Rural Development," The Review of Regional Studies, Southern Regional Science Association, vol. 36(2), pages 140-162.
    29. repec:eee:ecomod:v:220:y:2009:i:15:p:1797-1809 is not listed on IDEAS
    30. Josep Maria Arauzo Carod, 2005. "Determinants of industrial location: An application for Catalan municipalities," Papers in Regional Science, Wiley Blackwell, vol. 84(1), pages 105-120, March.
    31. Hisham S. El-Osta & Ashok K. Mishra & Mitchell J. Morehart, 2007. "Determinants of economic well-being among U.S. farm operator households," Agricultural Economics, International Association of Agricultural Economists, vol. 36(3), pages 291-304, May.
    32. Henderson, Jason R. & McNamara, Kevin T., 2000. "The Location Of Food Manufacturing Plant Investments In Corn Belt Counties," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 25(02), December.
    33. Klier, Thomas & McMillen, Daniel P, 2008. "Clustering of Auto Supplier Plants in the United States," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 460-471.
    34. 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.
    35. J. Barkley Rosser, 2009. "Introduction," Chapters,in: Handbook of Research on Complexity, chapter 1 Edward Elgar Publishing.
    36. Todd M. Gabe & Kathleen P. Bell, 2004. "Tradeoffs between Local Taxes and Government Spending as Determinants of Business Location," Journal of Regional Science, Wiley Blackwell, vol. 44(1), pages 21-41.
    37. Griffith, Daniel A., 2002. "A spatial filtering specification for the auto-Poisson model," Statistics & Probability Letters, Elsevier, vol. 58(3), pages 245-251, July.
    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. Jean-François Richard, 2015. "Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables," Working Paper 5778, Department of Economics, University of Pittsburgh.
    2. Qu, Xi & Lee, Lung-fei, 2012. "LM tests for spatial correlation in spatial models with limited dependent variables," Regional Science and Urban Economics, Elsevier, vol. 42(3), pages 430-445.
    3. Buczkowska, Sabina & de Lapparent, Matthieu, 2014. "Location choices of newly created establishments: Spatial patterns at the aggregate level," Regional Science and Urban Economics, Elsevier, vol. 48(C), pages 68-81.
    4. Sabina Buczkowska & Nicolas Coulombel & Matthieu de Lapparent, 2015. "Euclidean distance versus travel time in business location: A probabilistic mixture of hurdle-Poisson models," ERSA conference papers ersa15p1060, European Regional Science Association.
    5. Rodolfo Metulini & Roberto Patuelli & Daniel A. Griffith, 2018. "A Spatial-Filtering Zero-Inflated Approach to the Estimation of the Gravity Model of Trade," Econometrics, MDPI, Open Access Journal, vol. 6(1), pages 1-15, February.
    6. repec:eee:respol:v:47:y:2018:i:1:p:139-157 is not listed on IDEAS
    7. Liesenfeld, Roman & Richard, Jean-François & Vogler, Jan, 2013. "Analysis of discrete dependent variable models with spatial correlation," Economics Working Papers 2013-01, Christian-Albrechts-University of Kiel, Department of Economics.
    8. Sandro Montresor & Francesco Quatraro, 2015. "Smart Specialization Strategies and Key Enabling Technologies. Regional evidence from European patent data," Papers in Evolutionary Economic Geography (PEEG) 1525, Utrecht University, Department of Human Geography and Spatial Planning, Group Economic Geography, revised Aug 2015.
    9. Anna Gloria Billé & Samantha Leorato, 2017. "Quasi-ML estimation, Marginal Effects and Asymptotics for Spatial Autoregressive Nonlinear Models," BEMPS - Bozen Economics & Management Paper Series BEMPS44, Faculty of Economics and Management at the Free University of Bozen.
    10. Roberto Patuelli & Daniel A. Griffith & Michael Tiefelsdorf & Peter Nijkamp, 2009. "Spatial Filtering and Eigenvector Stability: Space-Time Models for German Unemployment Data," Quaderni della facoltà di Scienze economiche dell'Università di Lugano 0902, USI Università della Svizzera italiana.
    11. Brown, Jason & Lambert, Dayton, 2014. "Location decisions of natural gas extraction establishments: a smooth transition count model approach," Research Working Paper RWP 14-5, Federal Reserve Bank of Kansas City.
    12. Daniel Griffith & Manfred Fischer, 2013. "Constrained variants of the gravity model and spatial dependence: model specification and estimation issues," Journal of Geographical Systems, Springer, vol. 15(3), pages 291-317, July.
    13. Daniel Arribas-Bel & Julia Koschinsky & Pedro Amaral, 2012. "Improving the multi-dimensional comparison of simulation results: a spatial visualization approach," Letters in Spatial and Resource Sciences, Springer, vol. 5(2), pages 55-63, July.
    14. Oscar Martinez Ibañez & Miguel Manjón Antolín & Josep-Maria Arauzo-Carod, 2013. "The Geographical Scope of Industrial Location Determinants: An Alternative Approach," Tijdschrift voor Economische en Sociale Geografie, Royal Dutch Geographical Society KNAG, vol. 104(2), pages 194-214, April.
    15. Andrea Bonaccorsi & Massimo Colombo & Massimiliano Guerini & Cristina Rossi-Lamastra, 2013. "University specialization and new firm creation across industries," Small Business Economics, Springer, vol. 41(4), pages 837-863, December.
    16. Arauzo-Carod, Josep-Maria & Manjón-Antolín, Miguel & Martínez , Óscar, 2015. "The Relocation of R&D Establishments in France: An Empirical Analysis," INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, Asociación Española de Ciencia Regional, issue 33, pages 97-119.
    17. Jason P. Brown & Dayton M. Lambert & Raymond J. G. M. Florax, 2013. "The Birth, Death, and Persistence of Firms: Creative Destruction and the Spatial Distribution of U.S. Manufacturing Establishments, 2000–2006," Economic Geography, Clark University, vol. 89(3), pages 203-226, July.
    18. Magnus Söderberg & Makoto Tanaka, 2012. "Spatial price homogeneity as a mechanism to reduce the threat of regulatory intervention in locally monopolistic sectors," Working Papers hal-00659458, HAL.
    19. Teodora Corsatea & Hubert Jayet, 2014. "Spatial patterns of innovation activities in France: market’s role versus public research efforts," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(3), pages 739-762, May.
    20. Koster, Hans R.A. & van Ommeren, Jos & Rietveld, Piet, 2014. "Estimation of semiparametric sorting models: Explaining geographical concentration of business services," Regional Science and Urban Economics, Elsevier, vol. 44(C), pages 14-28.
    21. repec:gam:jecnmx:v:5:y:2017:i:2:p:24-:d:101618 is not listed on IDEAS
    22. Dayton M. Lambert & Wan Xu & Raymond J. G. M. Florax, 2014. "Partial Adjustment Analysis of Income and Jobs, and Growth Regimes in the Appalachian Region with Smooth Transition Spatial Process Models," International Regional Science Review, , vol. 37(3), pages 328-364, July.

    More about this item

    Keywords

    count model; location choice; manufacturing; Poisson; spatial econometrics;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R30 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pae:wpaper:10-5. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Debby Weber). General contact details of provider: http://edirc.repec.org/data/dapurus.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.