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First differencing approach to instrumental variables
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First differencing approach to instrumental variables : ウィキペディア英語版
First differencing approach to instrumental variables

When endogeneity is a concern in a dynamic panel data framework, it is possible to exploit the panel data structure of the data to deal with this issue. Examples include (but are not limited to) data over time on capital investment or wage equations. The first differencing approach to instrumental variables, also referred to as First-Difference Two Stage Least Squares (or FD2SLS in short), was first proposed by Anderson and Hsiao (1982)〔Anderson, T. W., and C. Hsiao (1982): Formulation and Estimation of Dynamic Models Using Panel Data. Journal of Econometrics (18), pp.67-82〕 and later extended by Arellano and Bond (1991) 〔Arellano, M. and S. R. Bond (1991): Some Specification Tests for Panel Data: Monte Carlo Evidence and an Application to Employment Equations. Review of Economic Studies (58), pp.277-298.〕 . The key problem the attempt address, is the problem of as predetermined regressors.
Predetermined variables will lead static fixed effects estimators, such as First Differencing or Within-Group Fixed Effects models to be inconsistent. The strict exogeneity assumption fails in dynamic models. Denotee_itas the idiosyncratic part of the error terms (i.e. it does not include the fixed effect ''ai''). Consider the following Fixed Effects model.
''yit=Xit b + ai + eit''

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