An official website of the United States government
United States Department of Labor
United States Department of Labor
The .gov means it's official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information,
make sure you're on a federal government site.
The site is secure.
The
https:// ensures that you are connecting to the official website and that any
information you provide is encrypted and transmitted securely.
Office of Survey Methods Research
SHARE ON:
More Information
Published Year: 1999
Survey/Program(s): N/A
Catalog: Economic Working Paper
WP Number: WP-321
Publication Status / Disposition: See Econometrica, Vol. 69, No. 1, January 2001, pp. 221-222.
Download PDF
Constructing Instruments for Regressions With Measurement Error When No Additional Data Are Available: Comment
Abstract
Lewbel (1997) has ingeniously shown that linear instrumental variables estimators for the errors-in-variables model can be constructed using functions of the dependent variable, proxy, and perfectly measured regressors as instruments. He proves consistency for the estimator and then asserts that "standard limiting distribution theory for TSLS can now be applied." In this note I assume that "standard theory" is given by White (1982), the source of the standard errors used by Professor Lewbel in his empirical application. I show that when White's formulas are applied to Lewbel's instruments, they give an inefficient estimator, an incorrect asymptotic covariance matrix, and an inconsistent covariance matrix estimator. These results stem from a subtle violation of the familiar instrumental variable orthogonality condition. Specifically, only one of Lewbel's instruments can be measured from an arbitrary origin and satisfy the orthogonality condition; the remaining instruments satisfy orthogonality only if measured as deviations from their population means. The substitution of sample means therefore generates a nonstandard asymptotic covariance matrix of the type described by Newey and McFadden (1994) in their discussion of ``plug-in'' estimators. I apply the theory for such estimators to Lewbel's instruments to obtain an efficient estimator, the correct asymptotic covariance matrix, and a consistent covariance matrix estimator.