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The ABC of Simulation Estimation with Auxiliary Statistics

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  • Jean-Jacques Forneron
  • Serena Ng

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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  • Jean-Jacques Forneron & Serena Ng, 2015. "The ABC of Simulation Estimation with Auxiliary Statistics," Papers 1501.01265, arXiv.org, revised Oct 2017.
    • Handle: RePEc:arx:papers:1501.01265
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    Cited by:

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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. Michael Creel, 2021. "Inference Using Simulated Neural Moments," Econometrics, MDPI, vol. 9(4), pages 1-15, September.
    5. Boucher, Vincent, 2020. "Equilibrium homophily in networks," European Economic Review, Elsevier, vol. 123(C).
    6. 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).
    7. 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.
    8. Lynda Khalaf & Beatriz Peraza López, 2020. "Simultaneous Indirect Inference, Impulse Responses and ARMA Models," Econometrics, MDPI, vol. 8(2), pages 1-26, April.
    9. 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.
    10. Alessandro Casini & Pierre Perron, "undated". "Generalized Laplace Inference in Multiple Change-Points Models," Boston University - Department of Economics - Working Papers Series WP2018-012, Boston University - Department of Economics.
    11. Pongou, Roland & Sidie, Ghislain Junior & Tchuente, Guy & Tondji, Jean-Baptiste, 2022. "Profits, Pandemics, and Lockdown Effectiveness in Nursing Home Networks," GLO Discussion Paper Series 1131, Global Labor Organization (GLO).
    12. 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).
    13. Jean-Jacques Forneron, 2019. "A Scrambled Method of Moments," Papers 1911.09128, arXiv.org.
    14. 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.
    15. 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.
    16. 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.

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    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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