Comparison of Small Area Estimation Methods for Estimating Unemployment Rate

Extended Abstract. In recent years, needs for small area estimations have been greatly increased for large surveys particularly household surveys in Sta­ tistical Centre of Iran (SCI), because of the costs and respondent burden. The lack of suitable auxiliary variables between two decennial housing and popula­ tion census is a challenge for SCI in using these methods. In general, the small area estimators can be classified into three categories: direct estimators, indirect estimators, and their combination. The direct estimators are those estimators using just data falling into small areas for estimating parameter of interest in small areas. The indirect estimators use data collected from both small areas of interest and other areas to estimate the parameters. The small area estimators used in this paper are indirect estimators with a combination of direct and indirect estimators. Three well­known small area estimators, i.e. synthetic estimator, composite estimator, and adjusted regression estimator are introduced and calculated under various conditions. First, a linear systematic sample with a size of 15,400 was selected from active population in the 1996 Census at 0.95 confidence level and a 0.05 maximum relative error. To calculate quality indices in order to assess small area estimators, 1000 sample were selected from the population. Sample size in each province (small area) is a random variable since it varies in each replication. Since the employment information has been collected in the 1996 Census, the true unemployment rate is known for each province. The small area estimators use auxiliary variables from previous census or large scale surveys and because of the long intercensal period, auxiliary variables tend to be out of date. So, for evaluating the effect of out­of­date auxiliary variables on performance of small area estimators, auxiliary variables of 1986 Census were used. For this purpose we have used suitable auxiliary variables from 1986 Census file in each province. There are four quality measures for comparison of small area methods, including bias, mean squared error (MSE), average of relative errors (ARE), and average of squared errors (ASE). Using these measures, four estimators are chosen as the selected methods: p(C­Sy­Av): Composite estimator with synthetic estimator and mean of group weights, p(C­Al­Av): Composite estimator with synthetic alternative estimator and mean of group weights, p(JS­Sy): James­Stein estimator with synthetic estimator, and p(JS­Al): James­Stein estimator with synthetic alternative estimator. MSE charts show that if we assign a fixed value as a minimum sample size in each small area, we can always be assure to have acceptable MSE's in using the above methods. Also p(JS­Al) leads to smaller values of ARE and ASE, and in maximum relative error point of view, p(C­Al­Av) has smaller values than the other selected estimators.