台灣真實經濟成長率的估計：卡門過濾法之應用

Estimating taiwan's True Economic Growth Rate: An Application of Kalman Filtering

GDP成長率可從生產面、所得面及支出面分開編算，但三面統計結果通常並不相同。目前我國行政院主計總處以支出面結果為準，但究竟哪一種編算結果比較好，是一個值得探討的重要議題。此外，從不同編算結果中擇一的作法有違資訊應極大化運用的原則。本文採用卡門過濾法估計台灣的真實GDP成長率，其特色是融合了生產面與支出面訊息，且為滿足常態分配假設下的最適推估結果。實證結果發現生產面GDP成長率比支出面GDP成長率更貼近真實。此外，為獲取台灣真實GDP成長率估計值來自於生產面與支出面的個別貢獻比重，我們應用組合預測理論求得最適權數。最後以估得的真實GDP成長率當基準，利用效率檢定發現主計總處歷來發布的GDP成長率初步統計數及年修正數滿足理性預測假說。

Quarterly GDP growth rates are typically computed using the data from the production and expenditure sides, but the results may be quite different. The Directorate-General of Budget, Accounting and Statistics (DGBAS) in Taiwan chooses the GDP growth rate based on the expenditure side, yet this choice implies that the information in the production side are completely ignored. This paper applies the Kalman filter to estimate the underlying true GDP growth rate and find that the GDP growth rate from the production side tracks the true GDP growth rate better. In order to approximate shares of the underlying true GDP growth rate contributed from the production and expenditure sides, we also apply the combinded forecast theory to obtain optimal weights. Finally, Mincer-Zarnowitz test reveals that both the preliminary and annual revised GDP growth rates released by the DGBAS are able to rationally forecast the true GDP growth rate.