My bibliography  Save this paper

# Indirect Inference With(Out) Constraints

## Author

Listed:
• David T. Frazier
• Eric Renault

## Abstract

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.

## Suggested Citation

• David T. Frazier & Eric Renault, 2016. "Indirect Inference With(Out) Constraints," Papers 1607.06163, arXiv.org, revised Aug 2016.
• Handle: RePEc:arx:papers:1607.06163
as

File URL: http://arxiv.org/pdf/1607.06163

## References listed on IDEAS

as
1. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models 2 volume set," Cambridge Books, Cambridge University Press, number 9780521478373.
2. 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.
3. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626.
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.
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as

Cited by:

1. repec:eee:econom:v:205:y:2018:i:1:p:76-111 is not listed on IDEAS
2. repec:eee:econom:v:205:y:2018:i:1:p:55-75 is not listed on IDEAS

### NEP fields

This paper has been announced in the following NEP Reports:

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1607.06163. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.