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- Title
CONSISTENT SETS OF ESTIMATES FOR REGRESSIONS WITH ERRORS IN ALL VARIABLES.
- Authors
Klepper, Steven; Leamer, Edward E.
- Abstract
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 if 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.
- Subjects
REGRESSION analysis; MEASUREMENT errors; ECONOMETRICS; MATHEMATICAL statistics; ERRORS; ERROR analysis in mathematics; STATISTICAL bias; STATISTICAL reliability; MATHEMATICAL economics
- Publication
Econometrica, 1984, Vol 52, Issue 1, p163
- ISSN
0012-9682
- Publication type
Article
- DOI
10.2307/1911466