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Quasi-ML estimation, Marginal Effects and Asymptotics for Spatial Autoregressive Nonlinear Models

Author

Listed:
  • Anna Gloria Billé

    () (Free University of Bozen-Bolzano, Faculty of Economics and Management)

  • Samantha Leorato

    () (University of Rome Tor Vergata, Department of Economics and Finance)

Abstract

In this paper we propose a Partial-MLE for a general spatial nonlinear probit model, i.e. SARAR(1,1)-probit, defined through a SARAR(1,1) latent linear model. This model encompasses the SAE(1)-probit model, considered by Wang et al. (2013), and the more interesting SAR(1)-probit model. We perform a complete asymptotic analysis, and account for the possible finite sum approximation of the covariance matrix (Quasi-MLE) to speed the computation. Moreover, we address the issue of the choice of the groups (couples, in our case) by proposing an algorithm based on a minimum KL-divergence problem. Finally, we provide appropriate definitions of marginal effects for this setting. Finite sample properties of the estimator are studied through a simulation exercise and a real data application. In our simulations, we also consider both sparse and dense matrices for the specification of the true spatial models, and cases of model misspecifications due to different assumed weighting matrices.

Suggested Citation

  • 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.
  • Handle: RePEc:bzn:wpaper:bemps44
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    File URL: http://pro1.unibz.it/projects/economics/repec/bemps44.pdf
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    References listed on IDEAS

    as
    1. Amemiya, Takeshi, 1978. "The Estimation of a Simultaneous Equation Generalized Probit Model," Econometrica, Econometric Society, vol. 46(5), pages 1193-1205, September.
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    More about this item

    Keywords

    spatial autoregressive-regressive probit model; nonlinear modeling; SARAR; partial maximum likelihood; quasi maximum likelihood; marginal effects;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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