Spatio-Temporal Models for Labor Force Series of Small Areas

近年來隨著區域均衡發展的推行，公、私部門對於各縣市區域性統計資料的需求與日遽增。然而大型抽樣調查之小區域結果，常因樣本數較少而產生過大的變異，改善上述問題之統計方法稱為「小區域估計」。行政院主計處現行「台灣地區人力資源調查」，以台灣地區23縣市為副母體，按月實施抽樣調查，期能提供縣市人力統計結果。惟受限於經費，致使各縣市按月調查結果因樣本數較少而發生變異過大之現象。本文之目的是以台灣地區人力資源調查為實例，建立適當的小區域時間空間估計模型。首先，檢驗各國普遍採用之複合估計量，建立適合我國的複合估計模型，並以相對效力衡量其估計結果。其次，利用各區域間互相借助力量的方法，結合橫斷面資料與時間序列特性，建構小區域時空混合效果模型；對於缺乏輔助資料以致模型無法建立的問題，亦提出可行的解決方法。此外，本文針對調查之時間、空間特性，建構各區域在時間與空間上互相影響的強度，並據以建立小區域聯合自我迴歸模型。最後，就時間而言，調查結果之改變是緩慢的，因此可利用該特性及貝氏理論建立小區域貝氏估計過程，以經驗貝氏估計減低小區域異常變動的情形。就上述四種小區域估計模型而言，複合估計量已為美國官方統計所採用，但其改善變異過大之效果較為有限；其餘估計方法均能大幅改善小區域異常變動之情形，其中時空混合效果與聯合自我迴歸模型之計算相對較為繁複，且需額外的輔助資料以增進估計的準確度，但較能反應地區特性；至於經驗貝氏估計除可達到預期目標外，更具有計算簡單、迅速之特性，較適合官方統計機構所採用。由於國內許多調查之抽樣設計均以人力資源調查為藍本，因此本文除提供人力資源有效之小區域估計外，亦可為其他調查所使用，以獲致可靠的小區域估計方法。Small area estimation is getting more important because of a growing demand for reliable small area statistics. In Taiwan, labor force series of local governments are likely to yield unacceptably large standard errors due to unduly small size of the sample in the areas. In this paper, we propose four methods to find more accurate estimates for given small areas.First of all, we construct a composite estimator for the labor force series and evaluate it using relative efficiency. Secondly, we develop alternative estimates, mixed effects model and simultaneous auto-regression model, which borrow strength from neighboring small areas. We solve the important problem of small area estimation by creating a mixed effects model for cross-sectional and time series data, and overcome the lack of auxiliary data. Simultaneous auto-regression models are constructed to describe the spatio-temporal relationship between neighboring small areas. Finally, we use Bayes theory and characteristic of the survey design to develop an empirical Bayes estimator.Besides, some discussion and conclusion of the previous methods are given to compare with the current survey estimates. To sum up, mixed effects model and simultaneous auto-regression model can reduce the variation of the current survey estimates, but the computations are relatively complex. The empirical Bayes estimator has three characteristics. First, the assumption is based on the slowly changing of labor force series. Secondly, it achieves the expected goal of variance reduction. Finally, the computation procedure is very simple. Therefore, empirical Bayes estimator is a potential method for small area estimation