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Variance Measures for Seasonally Adjusted Employment and Employment Change

Stuart Scott, Daniel Pfeffermann, and M. Sverchkov


The Pfeffermann method of variance estimation for X-11 seasonal adjustment is applied to series from the U.S. Bureau of Labor Statistics Current Employment Statistics (CES) program and the Current Population Survey (CPS). The method builds from the linear approximation to X-11. Change across one or more months also has a linear approximation, so the method extends easily to a variance measure for seasonally adjusted change. Employment exhibits very high correlation across time in CES, a huge monthly establishment survey. Ratio estimates are made and tied to benchmark values, which become available with roughly a nine-month lag. Balanced repeated replication provides estimates of sampling error variances and autocovariances. The treatment of sampling error for this survey should have wide applicability, due to the similarity of its estimator to typical index series estimators. Results are also obtained for CPS household employment series. Sampling error variances are estimated from generalized variance functions and autocorrelations from balanced repeated replication estimates.