摘要
本博士論文由兩篇關於時間數列分析方法之應用研究的文章所組成。 此二篇文章從不同的角度建立台灣新的總體經濟指標,第一篇的題目是混合不同頻率資料的新景氣現況暨趨向指標,第二篇的題目為台灣真實經濟成長率的估計。 第一篇文章設立經濟計量模型以獲取代表台灣景氣動向的兩項新指： 一是景氣現況指標,另一是景氣趨向指標。此二指標雖與行政院經濟建設委員會 (以下簡稱經建會) 編製同時指標綜合指數暨領先指標綜合指數所要傳遞的訊息相似,但二者產生指標的方法並不相同。本文二項指標設計為每週產生一個新數據,優點是能在較短時間內獲知景氣發展脈動,如此,發布時效可大幅提升。反觀經建會的二個景氣綜合指數均採用指標法編製,亦即各個綜合指數被設定為構成數列的算數平均數,且二個景氣綜合指數均相隔一個月才公布一次數據。因此,本文產生景氣指標的作法與經建會明顯不同。 在模型架構方面,本文延續文獻上最常採用的動態因子模型設定,將景氣狀況視為一個不可觀測的關鍵因子,從眾多可觀測資料中萃取產。 具體而言,本文設定的模型是在 Stock and Watson (1989,1991), Watson~(1994),Mariano and Murasawa (2003),Aruoba et~al.(2009) 及 Aruoba and Diebold~(2009) 的基礎上加入若干修定,主要差異為,相對於 Stock and Watson (1989,1991) 及 Watson 1994) 使用單一種頻率資料 (月資料),以及 Mariano and Murasawa(2003) 的兩種頻率資料 (月資料及季資料),本文使用的資料頻率最多達三種,分別為季資料,月資料及週資料,因此,本文涵蓋的總體經濟面向較為多元。其次是在模型設立上,Mariano and Murasawa (2003) 將國內生產毛額 (GDP) 季資料加在 Stock and Watson(1989,1991) 的單一種資料頻率 (月資料) 模型時,為了得到 GDP 季變動率與其本身月變動率間的線性關係式,將季 GDP 設定為月 GDP 的幾何平均數,惟此作法與一般實務計算季 GDP 為月 GDP 的平均數方式不同。Aruoba et al. (2009) 模型中被解釋變數是移除時間趨勢後的離差值,因未全然達到定態的狀態,致其估計結果出現若干乖離情形。本文對可觀測資料的處理方式,是一律取對數一階差分轉換為變動率形式後再進入模型。此種處理方式的好處是,雖然實際取得的資料數列為低頻變動率 (如 GDP 季增率),但其可以表示為高頻變動率 (如 GDP 月增率) 的線性加總關係,如此可讓模型結構更加簡潔化,亦可免除前述國外文獻模型的缺失。最後本文強調,如果有合適的日資料可供使用,本文模型也可擴展成四種資料頻率的架構。 本文發現經建會之同時指標綜合指數雖納入 7 個構成數列,但有 3 個構成數列貢獻權重偏低。同樣在領先指標綜合指數的構成數列中, 也有 3 個構成數列貢獻權重較低。在刪除權重較低的變數後,透由精簡的模型所估計得的景氣現況指標及景氣趨向指標,仍可適切地達到反映景氣所處狀況與預告景氣未來變化方向的功能。 第二篇文章探討台灣真實經濟成長率的估計。此議題的成因在於GDP 成長率雖可從生產面、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,值得深入探討。本文認為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。因此,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,本文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。
並列摘要
This Ph.D. dissertation comprises two essays on constructing Taiwan's new macroeconomic indexes.The first essay is entitled New Coincident and Leading Indexes from Series with Different Frequencies, while the second estimating Taiwan's True Economic Growth Rates. The purpose of the first essay is to construct new coincident and leading indexes which are able to characterize the fluctuation of Taiwan's business cycle. Although the two new indexes portray similar message to those of the composite coincident and leading indexes compiled by the Council of Economic Planning and Development, abbreviated as CEPD,both construction methods are totally different. Specifically, this paper constructs indexes basing on econometric model, while the CEPD uses an indicator approach, by which the composite indexes are subjectively set to be equally weighted average of their component series. Another difference is that the new indexes are designed to generate data weekly, intending to tract economic movements promptly. On the contrary, the CEPD releases its indexes only once in a month. Consequently, the lag time-length owing to the new indexes can be highly shortened. Following Stock and Watson (1989,1991),Watson (1994), Mariano and Murasawa (2003), Aruoba et al.(2009) and Aruoba and Diebold (2009), this paper views business condition as the key unobserved variable, and adopts the dynamic factor model to extract it from a group of observed cyclical indicators. The main difference between this paper and the afore-mentioned papers is on how to handle the series of cyclical indicators with mixed frequency. Specifically, Stock and Watson (1989, 1991) and Watson (1994) use a single frequency of data (monthly) and lose the information of other indicators measured at different frequencies. Mariano and Murasawa (2003) bring the quarterly GDP series into Stock and Watson (1989, 1991) and Watson (1994). However, to obtain a linear relationship between quarterly and monthly rate of change of GDP, Mariano and Murasawa(2003) specify the level of quarterly GDP as the geometric average of monthly GDP. Their specification obviously violates the general recognition, ie., quarterly flow variable is the summation of its monthly counterparts. Aruoba et al. (2009) incorporate indicators with up to four kinds of data frequencies including quarterly (e.g., GDP), monthly (e.g., industrial production), weekly (e.g., employment), and daily (e.g., term premium). All of these indicators are removed deterministic time trend instead of being taken first order difference to attain stationary forms. However, their data transformation is unable to fulfill stationarity requirement and leads to undesirable characteristics. In this paper, we unanimously take log difference for all the data series before they enter the model. Our data treatment method results in a linear aggregation relationship between quarterly and monthly variable, ie., quarterly growth rate of variable is added up from its monthly counterparts. The biggest benefit is our model framework becomes very concise without the shortcomings of the afore-mentioned papers. Although our model contains three kinds of data frequencies including quarterly, monthly and weekly, it can be easily extended to incorporate daily frequency as long as the relevant daily-based data are available. In this paper, we find three out of seven component series contribute very low share of weights in both of the CEPD's composite coincident and leading indexes. Once removing those low-weight component series, the underlying business factor extracted from the remaining component series by our model performs as well as the one extracted from comprehensive component series. The second essay concerns that 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.