We estabilsh the relationships between certain Bayesian and classical approaches to instrumental variables regression. We determine the form of priors that lead to posteriors for structural paameters that have similar properties as classical 2SLS and LIML and in doing so provide some new insight to the small sample behavior of Bayesian and classical procedures in the limited information simultaneous equations model. Our approach is motivated by the relationship between Bayesian and classical procedures in linear regression models: i.e., Bayesian analysis with a diffuse prior leads to posteriors that are identical in form to the finite sample density of classical least squares estimators. We use the fact that the instrumental variables regression model can be obtained from a reduced rank restriction on a multivariate linear model to determine the priors that give rise to posteriors that have properties similar to classical 2SLS and LIML. As a by-product of this approach we provide a novel way to dtermine the exact finite sample density of the LIML estimator and theprior that corresponds with classical LIML. We show that the traditional Dreze (1976) and a new Bayesian Two Stage approach are similar to 2SLS whereas the approach based on the Jeffreys' prior corresponds to LIML.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. 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.
Publisher Info
Paper provided by EconWPA in its series Econometrics with number
9812002.
Length: 38 pages Date of creation: 31 Dec 1998 Date of revision: Handle: RePEc:wpa:wuwpem:9812002
Note: Type of Document - Adobe Acrobat (.pdf); prepared on IBM PC ; to print on PostScript; pages: 38; figures: included Contact details of provider: Web page: http://129.3.20.41
For technical questions regarding this item, or to correct its listing, contact: (EconWPA).
Find related papers by JEL classification: C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics C5 - Mathematical and Quantitative Methods - - Econometric Modeling C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
This paper has been announced in the following NEP Reports:
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)