0, such as, when I‐I is based on GARCH auxiliary models. In these settings, we propose a novel I‐I approach that uses appropriately modified unconstrained auxiliary statistics, which are simple to compute and always exists. We state the relevant asymptotic theory for this I‐I approach without constraints and show that it can be reinterpreted as a standard implementation of I‐I through a properly modified binding function. Several examples that have featured in the literature illustrate our approach."> 0, such as, when I‐I is based on GARCH auxiliary models. In these settings, we propose a novel I‐I approach that uses appropriately modified unconstrained auxiliary statistics, which are simple to compute and always exists. We state the relevant asymptotic theory for this I‐I approach without constraints and show that it can be reinterpreted as a standard implementation of I‐I through a properly modified binding function. Several examples that have featured in the literature illustrate our approach.">
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Indirect inference with(out) constraints

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  • David T. Frazier
  • Eric Renault
Abstract
Indirect Inference (I‐I) estimation of structural parameters θ requires matching observed and simulated statistics, which are most often generated using an auxiliary model that depends on instrumental parameters β. The estimators of the instrumental parameters will encapsulate the statistical information used for inference about the structural parameters. As such, artificially constraining these parameters may restrict the ability of the auxiliary model to accurately replicate features in the structural data, which may lead to a range of issues, such as a loss of identification. However, in certain situations the parameters β naturally come with a set of q restrictions. Examples include settings where β must be estimated subject to q possibly strict inequality constraints g(β)>0, such as, when I‐I is based on GARCH auxiliary models. In these settings, we propose a novel I‐I approach that uses appropriately modified unconstrained auxiliary statistics, which are simple to compute and always exists. We state the relevant asymptotic theory for this I‐I approach without constraints and show that it can be reinterpreted as a standard implementation of I‐I through a properly modified binding function. Several examples that have featured in the literature illustrate our approach.

Suggested Citation

  • David T. Frazier & Eric Renault, 2020. "Indirect inference with(out) constraints," Quantitative Economics, Econometric Society, vol. 11(1), pages 113-159, January.
    • Handle: RePEc:wly:quante:v:11:y:2020:i:1:p:113-159
    DOI: 10.3982/QE986
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    Cited by:

    1. Gregory Fletcher Cox, 2024. "A Simple and Adaptive Confidence Interval when Nuisance Parameters Satisfy an Inequality," Papers 2409.09962, arXiv.org.
    2. Czellar, Veronika & Frazier, David T. & Renault, Eric, 2022. "Approximate maximum likelihood for complex structural models," Journal of Econometrics, Elsevier, vol. 231(2), pages 432-456.

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