  We use identification robust tests to show that difference, level and
non-linear moment conditions, as proposed by Arellano and Bond (1991), Arellano
and Bover (1995), Blundell and Bond (1998) and Ahn and Schmidt (1995) 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 difference, level
and non-linear 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) LM
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.
