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Marginal Densities of Instrumental Variable Estimators in the General Single Equation Case

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Abstract

A method of extracting marginal density approximations using the multivariate version of the Laplace formula is given and applied to instrumental variable estimators. Some leading exact distributions are derived for the general single equation case which lead to computable formulae and generalize all known results for marginal densities. These results are related to earlier work by Basmann (1963), Kabe (1964) and Phillips (1980b). Some general issues bearing on the current development of small sample theory and its application in empirical work are discussed in the introduction to the paper.

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File URL: http://cowles.econ.yale.edu/P/cd/d06a/d0609.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 609.

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Length: 34 pages
Date of creation: Oct 1981
Date of revision:
Publication status: Published in Advances in Econometrics, Vol. 2, JAI Press, 1983, pp. 1-24
Handle: RePEc:cwl:cwldpp:609

Note: CFP 582.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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References

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  1. Phillips, Peter C B, 1977. "A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators," Econometrica, Econometric Society, vol. 45(6), pages 1517-34, September.
  2. Phillips, P C B, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 183-224, January.
  3. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-48, May.
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Cited by:
  1. Chao, John C. & Phillips, Peter C. B., 2002. "Jeffreys prior analysis of the simultaneous equations model in the case with n+1 endogenous variables," Journal of Econometrics, Elsevier, vol. 111(2), pages 251-283, December.
  2. Peter C.B. Phillips & R.C. Reiss, 1984. "Testing for Serial Correlation and Unit Roots Using a Computer Function Routine Bases on ERA's," Cowles Foundation Discussion Papers 721, Cowles Foundation for Research in Economics, Yale University.
  3. Phillips, P C B, 1991. "Bayesian Routes and Unit Roots: De Rebus Prioribus Semper Est Disputandum," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 435-73, Oct.-Dec..
  4. Eric Zivot & Peter C.B. Phillips, 1991. "A Bayesian Analysis of Trend Determination in Economic Time Series," Cowles Foundation Discussion Papers 1002, Cowles Foundation for Research in Economics, Yale University.
  5. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec..
  6. Peter C.B. Phillips & Werner Ploberger, 1992. "Time Series Modeling with a Bayesian Frame of Reference: Concepts, Illustrations and Asymptotics," Cowles Foundation Discussion Papers 1038, Cowles Foundation for Research in Economics, Yale University.
  7. John C. Chao & Peter C.B. Phillips, 1996. "Bayesian Posterior Distributions in Limited Information Analysis of the Simultaneous Equations Model Using the Jeffreys Prior," Cowles Foundation Discussion Papers 1137, Cowles Foundation for Research in Economics, Yale University.

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