We use identification robust tests to show that difference (Dif), level (Lev), and nonlinear (NL) moment conditions, as proposed by Arellano and Bond (1991, Review of Economic Studies 58, 277–297), Ahn and Schmidt (1995, Journal of Econometrics 68, 5–27), Arellano and Bover (1995, Journal of Econometrics 68, 29–51), and Blundell and Bond (1998, Journal of Econometrics 87, 115–143) for the linear dynamic panel data model, do not separately identify the autoregressive parameter when its true value is close to one and the variance of the initial observations is large. We prove that combinations of these moment conditions, however, do so when there are more than three time series observations. This identification then solely results from a set of, so-called, robust moment conditions. These robust moments are spanned by the combined Dif, Lev, and NL moment conditions and only depend on differenced data. We show that, when only the robust moments contain identifying information on the autoregressive parameter, the discriminatory power of the Kleibergen (2005, Econometrica 73, 1103–1124) Lagrange multiplier (KLM) test using the combined moments is identical to the largest rejection frequencies that can be obtained from solely using the robust moments. This shows that the KLM test implicitly uses the robust moments when only they contain information on the autoregressive parameter.

正如 Arellano 和 Bond (1991, Review of Economic Studies 58, 277–297)、Ahn 和 Schmidt ( 1995, Journal of Econometrics 68, 5–27), Arellano and Bover (1995, Journal of Econometrics 68, 29–51), Blundell and Bond (1998, Journal of Econometrics87, 115-143) 对于线性动态面板数据模型，当自回归参数的真实值接近 1 且初始观测值的方差较大时，不要单独识别自回归参数。然而，我们证明了当有超过三个时间序列观察时，这些矩条件的组合会这样做。然后，这种识别仅来自一组所谓的稳健矩条件。这些稳健矩由组合的 Dif、Lev 和 NL 矩条件跨越，并且仅取决于差分数据。我们表明，当只有稳健矩包含关于自回归参数的识别信息时，Kleibergen (2005, Econometrica73, 1103–1124) 使用组合矩的拉格朗日乘数 (KLM) 测试与仅使用稳健矩可获得的最大拒绝频率相同。这表明 KLM 测试隐含地使用了仅包含自回归参数信息的稳健矩。