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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク First-difference estimator ： ウィキペディア英語版 First-difference estimator The first-difference (FD) estimator is an approach used to address the problem of omitted variables in econometrics and statistics with panel data. The estimator is obtained by running a pooled OLS estimation for a regression of $\backslash Delta\; y\_$ on $\backslash Delta\; x\_$. The FD estimator wipes out time invariant omitted variables $c\_$ using the repeated observations over time: :$y\_=x\_\backslash beta\; +\; c\_+\; u\_,\; t=1,...T\; ,$ :$y\_=x\_\backslash beta\; +\; c\_+u\_,\; t=2,...T\; .$ Differencing both equations, gives: :$\backslash Delta\; y\_=y\_-y\_=\backslash Delta\; x\_\backslash beta\; +\; \backslash Delta\; u\_,\; t=2,...T\; ,$ which removes the unobserved $c\_$. The FD estimator $\backslash hat\_$ is then simply obtained by regressing changes on changes using OLS: :$\backslash hat\_\; =\; (\backslash Delta\; X\text{'}\backslash Delta\; X)^\backslash Delta\; X\text{'}\; \backslash Delta\; y$ Note that the rank condition must be met for $\backslash Delta\; X\text{'}\backslash Delta\; X$ to be invertible ($rank(X\text{'}\backslash Delta\; X)=k$). Similarly, :$Av\backslash hatr(\backslash hat\_)=\backslash hat^\_(\backslash Delta\; X\text{'}\backslash Delta\; X)^\; ,$ where $\backslash hat^\_$ is given by :$\backslash hat^\_\; =\; ()^\backslash hat\text{'}\backslash hat\; .$ == Properties == Under the assumption of $E()=0$, the FD estimator is unbiased and consistent, i.e. $E()=\backslash beta$ and $plim\; \backslash hat=\backslash beta$. Note that this assumption is less restrictive than the assumption of weak exogeneity required for unbiasedness using the fixed effects (FE) estimator. If the disturbance term $u\_$ follows a random walk, the usual OLS standard errors are asymptotically valid. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「First-difference estimator」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.