Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jan, 1984, Volume 52, Issue 1

Consistent Sets of Estimates for Regressions with Errors in All Variables<163:CSOEFR>2.0.CO;2-L
p. 163-184

Edward E. Leamer, Steven Klepper

We consider the nature of the inferences that can be made when all variables in a linear regression are measured with error. Assuming that the measurement errors are orthogonal to each other and the unobserved correctly measured regressors, we demonstrate that the true regression coefficient vector can be restricted to the convex hull of all possible regressions iff all these regressions yield coefficient vectors lying in the same orthant. Otherwise, the set of feasible coefficient vectors is unbounded. For the unbounded case, we demonstrate that prior information concerning the "seriousness" of the measurement errors in the variables can bound the feasible region. Two diagnostics are proposed to indicate the sensitivity of conventional inferences to measurement error in the regressors, and an illustrative example is presented.

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