Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments

Jean-Marie Dufour () and Mohamed Taamouti

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

Abstract: It is well known that standard asymptotic theory is not valid or is extremely unreliable in models with identification problems or weak instruments [Dufour (1997, Econometrica), Staiger and Stock (1997, Econometrica), Wang and Zivot (1998, Econometrica), Stock and Wright (2000, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. One possible way out consists here in using a variant of the Anderson-Rubin (1949, Ann. Math. Stat.) procedure. The latter, however, allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation, which in general does not allow for individual coefficients. This problem may in principle be overcome by using projection techniques [Dufour (1997, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. AR-types are emphasized because they are robust to both weak instruments and instrument exclusion. However, these techniques can be implemented only by using costly numerical techniques. In this paper, we provide a complete analytic solution to the problem of building projection-based confidence sets from Anderson-Rubin-type confidence sets. The latter involves the geometric properties of “quadrics” and can be viewed as an extension of usual confidence intervals and ellipsoids. Only least squares techniques are required for building the confidence intervals. We also study by simulation how “conservative” projection-based confidence sets are. Finally, we illustrate the methods proposed by applying them to three different examples: the relationship between trade and growth in a cross-section of countries, returns to education, and a study of production functions in the U.S. economy.

Keywords: Simultaneous equations; structural model; instrumental variable; weak instrument; confidence interval; testing; ojection; simultaneous inference; exact inference; asymotic theory. (search for similar items in EconPapers)
Pages: 46 pages
Date: 2003
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/1866/499 (application/pdf)

Related works:
Journal Article: Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments (2005)
Working Paper: Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments (2003)
Working Paper: Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments (2003)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:mtl:montde:2003-10

Access Statistics for this paper

More papers in Cahiers de recherche from Universite de Montreal, Departement de sciences economiques Contact information at EDIRC.
Bibliographic data for series maintained by Sharon BREWER ().