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For the last several decades, the US Census Bureau has been using the AKcomposite estimation method to produce statistics on employment from theCurrent Population Survey (CPS) data. The CPS uses a rotating design and AKestimators are linear combinations of monthly survey weighted averages (calledmonth-in-sample estimates) in each rotation groups. Denoting by $X$ the vectorof month-in-sample estimates and by $\Sigma$ its design based variance, thecoefficients of the linear combination were optimized by the Census Bureauafter substituting $\Sigma$ by an estimate and under unrealistic stationarityassumptions. To show the limits of this approach, we compared the AK estimatorwith different competitors using three different synthetic populations thatmimics the Current Population Survey (CPS) data and a simplified sample designthat mimics the CPS design. In our simulation setup, empirically bestestimators have larger mean square error than simple averages. In the real dataanalysis, the AK estimates are constantly below the survey-weighted estimates,indicating potential bias. Any attempt to improve on the estimated optimalestimator in either class would require a thorough investigation of the highlynon-trivial problem of estimation of $\Sigma$ for a complex setting like theCPS (we did not entertain this problem in this paper). A different approach isto use a variant of the regression composite estimator used by StatisticsCanada. The regression composite estimator does not require estimation of$\Sigma$ and is less sensitive to the rotation group bias in our simulations.Our study demonstrates that there is a great potential for improving theestimation of levels and month to month changes in the unemployment rates byusing the regression composite estimator.

An Evaluation of Design-based Properties of Different Composite Estimators