Decision Theory Applied to an Instrumental Variables Model
AbstractThis paper applies some general concepts in decision theory to a simple instrumental variables model. There are two endogenous variables linked by a single structural equation; k of the exogenous variables are excluded from this structural equation and provide the instrumental variables (IV). The reduced-form distribution of the endogenous variables conditional on the exogenous variables corresponds to independent draws from a bivariate normal distribution with linear regression functions and a known covariance matrix. A canonical form of the model has parameter vector (rho, phi, omega), where phi is the parameter of interest and is normalized to be a point on the unit circle. The reduced-form coefficients on the instrumental variables are split into a scalar parameter rho and a parameter vector omega, which is normalized to be a point on the (k - 1)-dimensional unit sphere; rho measures the strength of the association between the endogenous variables and the instrumental variables, and omega is a measure of direction. A prior distribution is introduced for the IV model. The parameters phi, rho, and omega are treated as independent random variables. The distribution for phi is uniform on the unit circle; the distribution for omega is uniform on the unit sphere with dimension k-1. These choices arise from the solution of a minimax problem. The prior for rho is left general. It turns out that given any positive value for rho, the Bayes estimator of phi does not depend on rho; it equals the maximum-likelihood estimator. This Bayes estimator has constant risk; because it minimizes average risk with respect to a proper prior, it is minimax. Copyright The Econometric Society 2007.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Econometric Society in its journal Econometrica.
Volume (Year): 75 (2007)
Issue (Month): 3 (05)
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Andrews, Donald W.K. & Moreira, Marcelo J. & Stock, James H., 2008. "Efficient two-sided nonsimilar invariant tests in IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 146(2), pages 241-254, October.
- T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2009. "The Limited Information Maximum Likelihood Estimator as an Angle," CIRJE F-Series CIRJE-F-619, CIRJE, Faculty of Economics, University of Tokyo.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 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.