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Dynamic Spatial Discrete Choice Using One-step GMM: An Application to Mine Operating Decisions

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  • Joris Pinkse
  • Margaret Slade
  • Lihong Shen

Abstract

Abstract In many spatial applications, agents make discrete choices (e.g. operating or product-line decisions), and applied researchers need econometric techniques that enable them to model such situations. Unfortunately, however, most discrete-choice estimators are invalid when variables and/or errors are spatially dependent. More generally, discrete-choice estimators have difficulty dealing with many common problems such as heteroskedasticity, endogeneity, and measurement error, which render them inconsistent, as well as the inclusion of fixed effects in short panels, which renders them computationally burdensome if not infeasible. In this paper, we introduce a new estimator that can be used to overcome many of the above-mentioned problems. In particular, we show that the one-step (‘continuous updating’) GMM estimator is consistent and asymptotically normal under weak conditions that allow for generic spatial and time series dependence. We use our estimator to study mine operating decisions in a real-options context. To anticipate, we find little support for the real-options model. Instead, the data are found to be more consistent with a conventional mean/variance utility model. RÉSUMÉ Choix Discret Dynamique et Spatial: utiliser le GMM à une étape: Application aux Décisions Opérationnelles dans le Secteur Minier Dans beaucoup d'applications spatiales, les agents font des choix discrets (c'est –à- dire prennent des décisions opérationnelles ou des décisions de production). La recherche appliquée a besoin de techniques économétriques pour modéliser ces situations. Malheureusement, la plupart des indicateurs de choix discret ne signifient rien, lorsque les variables et /ou les erreurs sont spatialement dépendantes. Plus généralement, les indicateurs de choix discret ne gèrent que difficilement la plupart des problèmes rencontrés couramment, comme l'hétéroscédasticité, l'endogénéité et les erreurs de mesure, ce qui les vide de leur sens. Il en est de même avec l'inclusion d'effets fixes dans des panels courts, qui les rend mathématiquement très lourds, si ce n'est irréalisables. Dans cet article, nous introduisons un nouvel indicateur qui peut surmonter les difficultés mentionnées plus haut. En particulier, nous montrons que l'indicateur du GMM à une étape (mise à jour continue) fonctionne et qu'il est normal de façon asymptotique, dans des conditions faibles, qui permettent de rendre dépendantes des séries spatialement et temporellement génériques. Nous utilisons notre indicateur pour étudier les décisions opérationnelles dans le secteur minier dans un contexte d'options réelles. Pour anticiper, nous avons trouvé peu d'arguments en faveur du modèle d'options réelles.Donc, les donnée sont plus parlantes avec un modèle d'utilité conventionelle moyenne/variance. RESUMEN Opción discreta espacial dinámica usando el método MGM de un paso: una aplicación a las decisiones operativas en las minas En muchas aplicaciones espaciales, los agentes optan por elecciones discretas (ej., en las decisiones sobre operaciones o la producción en línea), y para la investigación aplicada se necesitan técnicas econométricas para poder modelar tales situaciones. Por desgracia, la mayoría de los estimadores de elecciones discretas no son válidos cuando las variables, los errores, o ambos, tienen una dependencia espacial. En general, los estimadores de elecciones discretas tienen dificultades para tratar con diferentes problemas tales como la heteroscedasticidad, la endogeneidad, y el error de medición que hacen que sean inconsistentes, así como la inclusión de efectos fijos en paneles cortos que resultan onerosos e incluso imposibles de calcular. En este artículo introducimos un nuevo estimador que puede servir para superar muchos de los problemas antes mentionados. En concreto, demonstramos que el estimador MGM (Método Generalizado de Momentos) de un paso (‘actualización continua’) es consistente y asintóticamente normal en condiciones débiles que permiten una dependencia genérica espacial y temporal. Utilizamos nuesto estimador para estudiar las decisiones operativas en las minas en un contexto de opciones reales. Anticipamos que hallamos poca evidencia a favor del modelo de opciones reales. En cambio, los datos son más consistentes con un modelo de utilidad convencional de media/varianza.

Suggested Citation

  • Joris Pinkse & Margaret Slade & Lihong Shen, 2006. "Dynamic Spatial Discrete Choice Using One-step GMM: An Application to Mine Operating Decisions," Spatial Economic Analysis, Taylor & Francis Journals, vol. 1(1), pages 53-99.
  • Handle: RePEc:taf:specan:v:1:y:2006:i:1:p:53-99
    DOI: 10.1080/17421770600661741
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    References listed on IDEAS

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    2. Pinkse, Joris & Shen, Lihong & Slade, Margaret, 2007. "A central limit theorem for endogenous locations and complex spatial interactions," Journal of Econometrics, Elsevier, vol. 140(1), pages 215-225, September.
    3. Liangjun Su & Zhenlin Yang, 2007. "Instrumental Variable Quantile Estimation of Spatial Autoregressive Models," Development Economics Working Papers 22476, East Asian Bureau of Economic Research.
    4. T. Arduini, 2016. "Distribution Free Estimation of Spatial Autoregressive Binary Choice Panel Data Models," Working Papers wp1052, Dipartimento Scienze Economiche, Universita' di Bologna.
    5. William C. Horrace & Kurt E. Schnier, 2010. "Fixed-Effect Estimation of Highly Mobile Production Technologies," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 92(5), pages 1432-1445.
    6. Iglesias, Emma M. & Phillips, Garry D.A., 2008. "Asymptotic bias of GMM and GEL under possible nonstationary spatial dependence," Economics Letters, Elsevier, vol. 99(2), pages 393-397, May.
    7. Sasaki, Yuya & Xin, Yi, 2017. "Unequal spacing in dynamic panel data: Identification and estimation," Journal of Econometrics, Elsevier, vol. 196(2), pages 320-330.
    8. 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.
    9. Joris Pinkse & Margaret E. Slade, 2010. "The Future Of Spatial Econometrics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 103-117, February.
    10. J. Paul Elhorst & Pim Heijnen & Anna Samarina & Jan P. A. M. Jacobs, 2017. "Transitions at Different Moments in Time: A Spatial Probit Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 422-439, March.
    11. Baltagi, Badi H. & Egger, Peter H. & Kesina, Michaela, 2017. "Determinants of firm-level domestic sales and exports with spillovers: Evidence from China," Journal of Econometrics, Elsevier, vol. 199(2), pages 184-201.
    12. Wang, Honglin & Iglesias, Emma M. & Wooldridge, Jeffrey M., 2013. "Partial maximum likelihood estimation of spatial probit models," Journal of Econometrics, Elsevier, vol. 172(1), pages 77-89.
    13. Smirnov, Oleg A., 2010. "Modeling spatial discrete choice," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 292-298, September.
    14. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2018. "Generalized spatial autocorrelation in a panel-probit model with an application to exporting in China," Empirical Economics, Springer, vol. 55(1), pages 193-211, August.

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    More about this item

    Keywords

    Spatial econometrics; continuous updating; generalized empirical likelihood; GMM; C21; C31;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • 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

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