固定效果動態追蹤資料模型之估計與推論──二階差分動差法

GAUSSIAN INFERENCE IN DYNAMIC PANELS WITH FIXED EFFECTS BASED ON SECOND DIFFERENCING

本文提出一種簡單的二階差分估計式來估計具固定效果的動態追蹤資料模型（dynamic panels with fixed effects），而此方法可避免傳統一般動差法在近單根環境下面臨的弱工具變數問題（weak instrument problem）。特別的是，不論序列為恆定或具單根，隨著橫斷面規模或／和時間序列長度趨近於無窮大，該估計式皆可收斂至常態分配。相較於Han and Phillips（2010）之一階差分估計式，當序列為正自我相關，且序列長度適度地長，二階差分估計式具有較小的漸進變異數；受惠於此，據以發展的單根檢定擁有較佳的檢力。當模型中存在個別趨勢項時，本文提出一種雙重二階差分估計式；同樣地，其於恆定與單根的環境下皆具漸進常態分配。值得注意的是，利用該估計市所建構的單根檢定相較於Han and Phillips（2010），雖然型一誤差略高，但在檢力上卻具有顯著的趨勢。

This paper develops a new approach to estimation in dynamic panel data models with fixed effects and incidental trends, based on second differencing. The proposed estimation method is immune to the weak instrument problem that is known to arise when the conventional GMM is applied to the cases where the autoregressive coefficient (ρ) is close to unity. Similar to the first-difference estimator introduced by Han and Phillips (2010, pp. 119–151), the new estimator has standard Gaussian asymptotics for all values of ρ ∈ (−1, 1] in both panel and time series cases. Given its smaller asymptotic variance when the series exhibit positive or moderate positive autocorrelation, the panel unit root test built on the second-difference estimator is more powerful than that built on Han and Phillips’ counterpart.