| 正文 | In this paper, we study a weak instrumental variables model for longitudinal data. A two stage least-squares estimator (the instrumental variables estimator) is presented. We show that the asymp-totic property for the proposed estimator is different from that for cross-sectional data. Also, similar to Hahn and Kuersteiner (2002), we extend a local-to-zero assumption as in Staiger and Stock (1997) on the coefficients of the instruments in the first stage equation to a more general setting by allowing for different degrees of weakness. Moreover, the consistency and limiting distribution of the proposed estimators are established and the explicit expressions for the asymptotic bias are given. Further, we show that the discontinuity phenomenon observed in Hahn and Kuersteiner (2002) still exists for the longitudinal data case. Finally, we examine the finite sample properties of the proposed estimator by Monte Carlo simulations. |
