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The ABC of simulation estimation with auxiliary statistics

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  • Forneron, Jean-Jacques
  • Ng, Serena

Abstract

The frequentist method of simulated minimum distance (SMD) is widely used in economics to estimate complex models with an intractable likelihood. In other disciplines, a Bayesian approach known as Approximate Bayesian Computation (ABC) is far more popular. This paper connects these two seemingly related approaches to likelihood-free estimation by means of a Reverse Sampler that uses both optimization and importance weighting to target the posterior distribution. Its hybrid features enable us to analyze an ABC estimate from the perspective of SMD. We show that an ideal ABC estimate can be obtained as a weighted average of a sequence of SMD modes, each being the minimizer of the deviations between the data and the model. This contrasts with the SMD, which is the mode of the average deviations. Using stochastic expansions, we provide a general characterization of frequentist estimators and those based on Bayesian computations including Laplace-type estimators. Their differences are illustrated using analytical examples and a simulation study of the dynamic panel model.

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  • Forneron, Jean-Jacques & Ng, Serena, 2018. "The ABC of simulation estimation with auxiliary statistics," Journal of Econometrics, Elsevier, vol. 205(1), pages 112-139.
    • Handle: RePEc:eee:econom:v:205:y:2018:i:1:p:112-139
    DOI: 10.1016/j.jeconom.2018.03.007
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    3. Casini, Alessandro & Perron, Pierre, 2022. "Generalized Laplace Inference In Multiple Change-Points Models," Econometric Theory, Cambridge University Press, vol. 38(1), pages 35-65, February.
    4. Lynda Khalaf & Beatriz Peraza López, 2020. "Simultaneous Indirect Inference, Impulse Responses and ARMA Models," Econometrics, MDPI, vol. 8(2), pages 1-26, April.
    5. Baey, Charlotte & Smith, Henrik G. & Rundlöf, Maj & Olsson, Ola & Clough, Yann & Sahlin, Ullrika, 2023. "Calibration of a bumble bee foraging model using Approximate Bayesian Computation," Ecological Modelling, Elsevier, vol. 477(C).
    6. Georgios Tsiotas, 2022. "Regression Analysis Using Asymmetric Losses: A Bayesian Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(2), pages 311-327, June.
    7. KANO, Takashi, 2023. "Posterior Inferences on Incomplete Structural Models : The Minimal Econometric Interpretation," Discussion paper series HIAS-E-128, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    8. Bao, Yong & Yu, Xuewen, 2023. "Indirect inference estimation of dynamic panel data models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1027-1053.
    9. Casini, Alessandro & Perron, Pierre, 2021. "Continuous record Laplace-based inference about the break date in structural change models," Journal of Econometrics, Elsevier, vol. 224(1), pages 3-21.
    10. Roland Pongou & Guy Tchuente & Jean-Baptiste Tondji, 2023. "Optimal interventions in networks during a pandemic," Journal of Population Economics, Springer;European Society for Population Economics, vol. 36(2), pages 847-883, April.
    11. Jean-Jacques Forneron, 2019. "A Scrambled Method of Moments," Papers 1911.09128, arXiv.org.
    12. Pouliot, Guillaume Allaire, 2023. "Spatial econometrics for misaligned data," Journal of Econometrics, Elsevier, vol. 232(1), pages 168-190.
    13. Michael Creel, 2021. "Inference Using Simulated Neural Moments," Econometrics, MDPI, vol. 9(4), pages 1-15, September.
    14. Pongou, Roland & Tchuente, Guy & Tondji, Jean-Baptiste, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," GLO Discussion Paper Series 957, Global Labor Organization (GLO).
    15. Boucher, Vincent, 2020. "Equilibrium homophily in networks," European Economic Review, Elsevier, vol. 123(C).
    16. Roland Pongou & Guy Tchuente & Jean-Baptiste Tondji, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," Papers 2110.10230, arXiv.org.

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    More about this item

    Keywords

    Indirect Inference; Synthetic likelihood; Auxiliary statistics; Laplace type estimator;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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