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Indirect Inference With(Out) Constraints

Listed author(s):
  • David T. Frazier
  • Eric Renault

The traditional implementation of Indirect Inference (I-I) is to perform inference on structural parameters $\theta$ by matching observed and simulated auxiliary statistics. These auxiliary statistics are consistent estimators of instrumental parameters whose value depends on the value of structural parameters through a binding function. Since instrumental parameters encapsulate the statistical information used for inference about the structural parameters, it sounds paradoxical to constrain these parameters, that is, to restrain the information used for inference. However, there are situations where the definition of instrumental parameters $\beta$ naturally comes with a set of $q$ restrictions. Such situations include: settings where the auxiliary parameters must be estimated subject to $q$ possibly binding strict inequality constraints $g(\cdot) > 0$; cases where the auxiliary model is obtained by imposing $q$ equality constraints $g(\theta) = 0$ on the structural model to define tractable auxiliary parameter estimates of $\beta$ that are seen as an approximation of the true $\theta$, since the simplifying constraints are misspecified; examples where the auxiliary parameters are defined by $q$ estimating equations that overidentify them. We demonstrate that the optimal solution in these settings is to disregard the constrained auxiliary statistics, and perform I-I without these constraints using appropriately modified unconstrained versions of the auxiliary statistics. In each of the above examples, we outline how such unconstrained auxiliary statistics can be constructed and demonstrate that this I-I approach without constraints can be reinterpreted as a standard implementation of I-I through a properly modified binding function.

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File URL: http://arxiv.org/pdf/1607.06163
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Paper provided by arXiv.org in its series Papers with number 1607.06163.

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Date of creation: Jul 2016
Date of revision: Aug 2016
Handle: RePEc:arx:papers:1607.06163
Contact details of provider: Web page: http://arxiv.org/

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  1. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models 2 volume set," Cambridge Books, Cambridge University Press, number 9780521478373, December.
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  3. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, December.
  4. Pinkse, Joris & Slade, Margaret E., 1998. "Contracting in space: An application of spatial statistics to discrete-choice models," Journal of Econometrics, Elsevier, vol. 85(1), pages 125-154, July.
  5. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
  6. Gourieroux, C. & Monfort, A. & Trognon, A., 1985. "A General Approach to Serial Correlation," Econometric Theory, Cambridge University Press, vol. 1(03), pages 315-340, December.
  7. Peñaranda, Francisco & Sentana, Enrique, 2012. "Spanning tests in return and stochastic discount factor mean–variance frontiers: A unifying approach," Journal of Econometrics, Elsevier, vol. 170(2), pages 303-324.
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