以貝式估計法推估台灣之潛在產出與自然失業率

Bayesian Estimates of Potential Output and the NAIRU for Taiwan

過去文獻指出自然失業率（NAIRU）與潛在產出的推估常伴隨著相當高的不確定性。為了讓模型允許較多的不確定性，本文分別為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 algorithms），同時亦設計了一系列的蒙地卡羅分析以驗證抽樣演算法的正確性與效率性。本文更進一步將此演算法運用於推估台灣未經季節調整的潛在產出與自然失業率，並將季節單根的觀念引入模型中。模擬分析與實證結果均顯示，相對於傳統的最大概似估計法（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。

Previous literature indicates that the NAIRU and potential output are measured with large degree of uncertainty. To account for this large estimate uncertainty, this paper develops the corresponding Bayesian sampling algorithms for Watson’s decomposition method and Apel and Jansson’s systems approach. We assess our algorithms by conducting a series of Monte Carlo simulation experiments. To illustrate the practical relevance of our algorithms, we also apply them to Taiwan’s seasonally unadjusted data and incorporate the idea of seasonal unit root into our Bayesian framework. 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. A Bayesian approach allows for more stochastic variation in the permanent and cyclical components. Our analysis demonstrates 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.