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SIMPLE MODIFICATION OF THE TWO-STAGE LEAST-SQUARES PROCEDURE FOR UNDERSIZED SAMPLES (FROM STRUCTURAL EQUATION MODELS IN THE SOCIAL SCIENCES, 1973, BY ARTHUR S GOLDBERGER AND OTIS D DUNCAN - SEE NCJ-52004)

NCJ Number
52010
Author(s)
H THEIL
Date Published
1973
Length
17 pages
Annotation
ESTIMATION PROCEDURES BASED ON TWO-STAGE LEAST SQUARES ANALYSIS PROCEDURES FOR UNDERSIZED SAMPLES ARE DESCRIBED AND ILLUSTRATED.
Abstract
IN ECONOMETRICS, ALMOST ALL LARGE MODELS AND MANY MEDIUM-SIZED MODELS HAVE A NUMBER OF PREDETERMINED VARIABLES EXCEEDING THE NUMBER OF OBSERVATIONS. THIS PROBLEM IS NOT CONFINED TO TWO-STAGE LEAST SQUARES ESTIMATION. FULL INFORMATION METHODS SUCH AS THREE-STAGE LEAST SQUARES ANALYSIS AND LINEARIZED MAXIMUM-LIKELIHOOD TECHNIQUES USE TWO-STAGE LEAST SQUARES ESTIMATES AS BASIC INGREDIENTS AND ARE INAPPLICABLE WHEN TWO-STAGE LEAST SQUARES ANALYSIS IS NOT APPROPRIATE. VARIOUS ATTEMPTS TO SOLVE PROBLEMS ASSOCIATED WITH UNDERSIZED SAMPLES ARE REVIEWED, AND A CLASS OF ESTIMATORS FOR UNDERSIZED SAMPLES IS DEVELOPED. CONSIDERATION IS GIVEN TO ASYMPTOTIC VARIANCES AND COVARIANCES. FURTHER INFORMATION ON ESTIMATION PROCEDURES IS APPENDED. SUPPORTING EQUATIIONS ARE INCLUDED. (DEP)

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