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題名：推估潛在產出與自然失業率：卡爾曼濾波器與貝式估計法
作者：陳馨蕙
作者(外文)：Shin-Hui Chen
校院名稱：國立東華大學
系所名稱：經濟學系
指導教授：林金龍
蕭朝興
學位類別：博士
出版日期：2011
主題關鍵詞：潛在產出；卡爾曼濾波器；貝式估計法；季節單根；產出缺口；自然失業率；Potential GDP；Output gap；Seasonal unit root；NAIRU；Okun's law；Phillips curve；State Space model；Kalman Filter；Taiwanese Economy；Bayesian Approach
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正確且有效評估潛在產出與產出缺口一直是施行貨幣與財政政策的重要環節。本論文為三篇獨立的文章連結而成，主要針對台灣與大陸的潛在產出與自然失業率（NAIRU）提供適當且合理的估計方式。
過去文獻中用以估計潛在產出的方法大多假設在潛在產出與NAIRU中存在一般單根（regular unit root）。然而，這樣的假設並不適用於估計台灣未經季節調整的潛在產出。有鑑於此，本論文的第一篇文章以 Watson’s (1981) decomposition與 Apel and Jansson’s（1997）system approach為例，以季節單根取代一般單根，從而考量更多的季節波動於模型中。同時，為了驗證模型的可靠性（robustness）以及更為有效評估台灣的潛在產出與NAIRU，我們亦嘗試對NAIRU與失業缺口（unemployment gap）作不同的模型設定。實證結果顯示在一般單根假設下，亦即模型未考量季節波動時，資料本身的季節波動嚴重干擾估計結果且無法提供有用的訊息；反之，以季節單根取代一般單根後即能有效評估台灣的潛在產出與NAIRU。
考量到估計潛在產出與NAIRU時有相當高的不確定性，在第二篇文章中，我們利用貝式估計法來重新檢視台灣的潛在產出與NAIRU。我們分別為Watson’s decomposition與Apel and Jansson’s system approach建立了相對應的貝式抽樣演算法 (sampling algorithm)。為了驗證抽樣演算法的正確性與效率性，我們設計了一系列的蒙地卡羅模擬(Monte Carlo simulation)分析。本文更進一步將此演算法運用於台灣的潛在產出與NAIRU之估計。模擬分析與實證結果均顯示，相對於傳統的最大概式估計法 (maximum likelihood estimate)，貝式估計法允許參數有較大的隨機變異 (stochastic variation)，且後驗分佈(posterior distribution)確實能容許較高程度的不確定性，並提供更為攸關的訊息供台灣政府執行政策之參考。
由於台灣與大陸間存在密切的經濟與金融聯繫，在最後一篇文章中，我們將貝式演算法運用於估計大陸的潛在產出與產出缺口，並進一步將中國大陸的產出缺口與台灣的產出缺口作比較。中國大陸自1970年代晚期起進行了一系列的市場改革開放政策，導致其產出缺口出現多次結構性的轉變。換言之，中國大陸的潛在產出在估計上具有相當高的不確定性。然而，透過貝式估計法，我們能較為有效的估計中國大陸此一轉型經濟體 (transition economy)的潛在產出與產出缺口。本文實證顯示，相對於台灣在2000年代面臨的兩次景氣蕭條，中國大陸在2002年後進入了一個新的景氣擴張期。而在2008年重創台灣的金融危機則對中國大陸的潛在產出有較輕微的影響，中國大陸的潛在產出在2008年遭受金融危機的重挫後，隨即反彈回到金融危機前的產出水準；然而，台灣的潛在產出卻依然停留在遠低於其1990年代的產出水準。
Potential output and non-accelerating inflation rate of unemployment (NAIRU) are defined as the level of output and unemployment rate consistent with a stable rate of inflation. Output gap is defined as the difference between actual output and potential output. When the actual output level (unemployment rate) is higher (lower) than potential output (NAIRU), excess demand drives up inflation rate and vice versa. Output gap is also an important part of Taylor rules for interest rates determination. Thus, precise estimates of potential GDP and NAIRU are essential for the conduct of monetary and fiscal policies. This dissertation, consists of three independent essays, aims at providing appropriate measures of potential output and the NAIRU for Taiwan and China.
Since most macroeconomic data in Taiwan are seasonally unadjusted, in the first essay, we switch from regular unit root to seasonal unit root ofWatson’s (1986) decomposition method and Apel and Jansson’s (1999) systems approach to allow for seasonal variation. To check robustness and investigate how sensitive the results are to further changes in the specification of the NAIRU and unemployment gap, distinct classes of NAIRU and unemployment gap concept are implemented. Empirical analysis confirms the importance of seasonal behavior. Switching from regular unit root to seasonal unit root improves the efficiency of measuring potential GDP and the NAIRU for Taiwan.
In the first essay, we find that that there appears to be a rising trend in the Taiwan’s unemployment gap, possibly as a result of structural changes or the periodicity of the cycle become longer. Thus, distinct classes of NAIRU specifications are implemented to mitigate the concern about implausible estimates and misspecification. To allow for more parameter uncertainty and avoid potential model misspecifications, the second essay develops the corresponding Bayesian sampling algorithms for Watson’s decomposition method and Apel and Jansson’s systems approach. With appropriate priors, prior information about the structure of the economy can be embedded in the model.
Simulation and empirical analyses show that our Bayesian sampling algorithms are flexible and do not merely duplicate the maximum likelihood estimates. We find that the maximum likelihood estimate generally understates the parameter variability and puts too little weight on the variance. While a Bayesian approach allows for more stochastic variation in the permanent and cyclical components. Further analyses demonstrate that the posterior distribution facilitates assessment of the parameter uncertainty such that a Bayesian approach is rich enough to cope with model specification issues and provides more relevant information for conducting monetary and fiscal policies.
Since there exist strong economic and financial linkages between China and Taiwan, in the last essay, we utilize our Bayesian sampling algorithms to estimate potential output and the output gap for China. A comparison with the Taiwanese Output Gap is also provided in this paper. Since the late 1970s, the Chinese government has implemented a series of macroeconomic and structural reform policies and induced a sequence of structural changes in the behavior of real and potential GDP. As a transition economy, China’s GDP tends to fluctuate greatly with external or domestic shocks. The volatility and uncertainty of potential output are higher than that in developed economies.
Empirical analysis confirms that a Bayesian approach indeed provides more appropriate estimates for transition economies undertaking large structural changes. We find that China has experienced three expansionary periods, interrupted by several sharp but short periods of slowdown. The gradual easing of the output gap fluctuation during post-reform period demonstrates that China has successfully achieved the soft landing without causing big swings in the overall economic growth. Compared to the two severe recessions that occurred to the Taiwan economy during the 2000s, China appeared to enter a period of economic upswing after year 2002. Moreover, the financial crisis of 2008 has minor impact on the Chinese economy. The Chinese output gap rebounded with a short lag behind the financial crisis and returned to levels that prevailed before 2008 while Taiwan’s potential output is sill at a lower level than in the 1990s.
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