IF A STRUCTURAL EQUATION IS OVERIDENTIFIED, THERE ARE ALTERNATIVE DISTINCT ESTIMATORS OF ITS PARAMETERS. EFFICIENT ESTIMATION IN OVERIDENTIFIED MODELS INVOLVES THE CONSTRUCTION OF APPROPRIATELY WEIGHTED AVERAGES OF BASIC ESTIMATORS. RESTRICTED ESTIMATES MAY BE INTERPRETED AS WEIGHTED AVERAGES OF UNRESTRICTED ESTIMATES. MINIMUM VARIANCE CONSIDERATIONS DICTATE THE CHOICE OF WEIGHTS, AND AN EFFICIENT ESTIMATOR HAS AN INVARIANCE PROPERTY IN THAT IT CAN BE OBTAINED BY THE APPLICATION OF A SINGLE PRINCIPLE TO SEVERAL DIFFERENT ARRANGEMENTS OF OBSERVED DATA. SINCE OVERIDENTIFICATION IS A GENERAL CONCEPT, ILLUSTRATIONS IN THE ARTICLE REFER TO LINEAR REGRESSION WITH LINEAR CONSTRAINTS, MULTIVARIATE REGRESSION, PATH ANALYSIS, AND SIMULTANEOUS EQUATION MODELS. THE GENERALIZED LEAST SQUARES PRINCIPLE IS MOST FAMILIAR IN THE CONTEXT OF LINEAR REGRESSION WITH AUTOCORRELATED AND/OR HETEROSCEDASTIC DISTURBANCES. EXAMPLES OF OVERIDENTIFIED MODELS ARE DETAILED, ALONG WITH PROCEDURES FOR COMBINING ESTIMATING EQUATIONS AND COMBINING ESTIMATES. SUPPORTING EQUATIONS ARE GIVEN. (DEP)