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Use of Auxiliary Information to Evaluate a Synthetic Estimator

John L. Eltinge, Julie B. Gershunskaya, and Larry L. Huff


The Bureau of Labor Statistics has considerable interest in estimation of total monthly employment for small domains defined by the intersection of metropolitan statistical area and major industrial division, based on data from the Current Employment Survey (CES). One of several possible elementary estimators is a synthetic estimator based on state-level changes in employment within a major industrial division. It is important to evaluate empirically the magnitude of the bias of this estimator, relative to the magnitude of the standard error of this estimator, and relative to the magnitudes of the biases and standard errors of other candidate-elementary small-domain estimators. This paper studies the extent to which this type of evaluation may be enhanced through the use of auxiliary data from the Quarterly Census of Employment and Wages (ES-202) Program, a nominal census of employment that provides data several months after production of CES estimates. Principal attention is devoted to evaluation of components of mean-squared error attributable, respectively, to: 1.) lack of fit in the implicit synthetic model; 2.) sampling error in the CES data; and 3.) nonsampling error in the CES data.