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Covariates impacts in spatial autoregressive models for compositional data

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  • Thomas-Agnan, Christine
  • Laurent, Thibault
  • Ruiz-Gazen, Anne

Abstract

Spatial simultaneous autoregressive models have been adapted to model data with both a geographic and a compositional nature. Interpretation of parameters in such a model is intricate. Indeed, when the model involves a spatial lag of the dependent variable, this interpretation must focus on the so-called impacts rather than on parameters and when moreover the dependent variable of this model is of a compositional nature, this interpretation should be based on elasticities or semi-elasticities. Combining the two difficulties, we provide exact formulas for the evaluation of these elasticity-based impact measures which have been only approximated so far in some applications. We also discuss their decomposition into direct and indirect impacts taking into account the compositional nature of the dependent variable. Finally, we also propose more local summary measures as exploratory tools that we illustrate on a toy data set and a case study.

Suggested Citation

  • Thomas-Agnan, Christine & Laurent, Thibault & Ruiz-Gazen, Anne, 2020. "Covariates impacts in spatial autoregressive models for compositional data," TSE Working Papers 20-1162, Toulouse School of Economics (TSE), revised Oct 2021.
    • Handle: RePEc:tse:wpaper:124927
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    References listed on IDEAS

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    1. Thi Huong An Nguyen & Christine Thomas-Agnan & Thibault Laurent & Anne Ruiz-Gazen, 2021. "A simultaneous spatial autoregressive model for compositional data," Spatial Economic Analysis, Taylor & Francis Journals, vol. 16(2), pages 161-175, April.
    2. J. Paul Elhorst & Marco Gross & Eugen Tereanu, 2021. "Cross‐Sectional Dependence And Spillovers In Space And Time: Where Spatial Econometrics And Global Var Models Meet," Journal of Economic Surveys, Wiley Blackwell, vol. 35(1), pages 192-226, February.
    3. Thibault Laurent & Christine Thomas-Agnan & Anne Ruiz-Gazen, 2023. "Covariates impacts in spatial autoregressive models for compositional data," Journal of Spatial Econometrics, Springer, vol. 4(1), pages 1-23, December.
    4. Takahiro Yoshida & Morito Tsutsumi, 2018. "On the effects of spatial relationships in spatial compositional multivariate models," Letters in Spatial and Resource Sciences, Springer, vol. 11(1), pages 57-70, March.
    5. 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.
    6. Thomas-Agnan, Christine & Laurent, Thibault & Ruiz-Gazen, Anne & Nguyen, T.H.A & Chakir, Raja & Lungarska, Anna, 2020. "Spatial simultaneous autoregressive models for compositional data: Application to land use," TSE Working Papers 20-1098, Toulouse School of Economics (TSE).
    7. LeSage, James P. & Chih, Yao-Yu, 2016. "Interpreting heterogeneous coefficient spatial autoregressive panel models," Economics Letters, Elsevier, vol. 142(C), pages 1-5.
    8. Joanna Morais & Christine Thomas-Agnan & Michel Simioni, 2017. "Interpretation of explanatory variables impacts in compositional regression models," Working Papers hal-01563362, HAL.
    9. Joanna Morais & Christine Thomas-Agnan, 2021. "Impact of covariates in compositional models and simplicial derivatives," Post-Print hal-03180682, HAL.
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    Cited by:

    1. Dargel, Lukas & Thomas-Agnan, Christine, 2023. "Share-ratio interpretations of compositional regression models," TSE Working Papers 23-1456, Toulouse School of Economics (TSE), revised 20 Sep 2023.
    2. Thibault Laurent & Christine Thomas-Agnan & Anne Ruiz-Gazen, 2023. "Covariates impacts in spatial autoregressive models for compositional data," Journal of Spatial Econometrics, Springer, vol. 4(1), pages 1-23, December.
    3. Dargel, Lukas & Thomas-Agnan, Christine, 2024. "Pairwise share ratio interpretations of compositional regression models," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).

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    More about this item

    Keywords

    Elasticities; direct impact; local impact; indirect impact; semi-elasticities; simplicial regression;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing
    • Q15 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Land Ownership and Tenure; Land Reform; Land Use; Irrigation; Agriculture and Environment

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