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A new sampling design for the Swiss Earnings Structure Survey (308181)*Lionel Qualité, Swiss Federal Statistical Office
Keywords: Poisson sampling, Optimal allocation, Median income
The Swiss Federal Statistical Office undertook to revise the sampling design of its biennial Earnings Structure Survey (ESS) for 2018. The new design uses administrative data on incomes, collected by the Swiss Compensation Office (SCO) for social insurance purposes, as proxy variables. The ESS provides information on wages and salaries paid by businesses in relation to the jobs and individual characteristics of employees. Its main products are median standardized wages for a range of population or business domains and total rewards within activity sections. The sampling design revision aimed at improving efficiency by using the SCO incomes and adapting the allocation procedure to the survey objectives: multiple medians and totals. The sampling design used for previous surveys targeted best precision on the overall average earnings under a cost constraint. A linearization technique allows replacing the estimation variance of a median with that of an estimator of total in the allocation problem. We compared results of different linearization procedures using simulations on the SCO incomes matched with the business register. The multi-objective nature of the problem required to scale up the allocation procedure for the case of several hundred interest variables. This is done in two steps: limit values for the coefficient of variation of each interest estimator in the ESS are computed taking into account the maximum achievable precision under full census and a non-response scenario. These limits are set to the publication thresholds of 3% or 5% when possible. Then, a new allocation procedure of ‘sample sizes within strata’, adapted to the ESS sampling design, aims for the minimum overall sample size under constraint that no estimator coefficient of variation exceeds its assigned limit value. The result is a sample size reduced by 10% (approx. 5’000 businesses) for the ESS2018 over the ESS2016 sample and a better control on precisions of the most relevant estimates.