Identification robust inference for moments based analysis of linear dynamic panel data models

TL;DR

This paper demonstrates that traditional moment conditions in linear dynamic panel data models may fail to identify the autoregressive parameter near one, but a set of robust moments can reliably do so, especially with more than three time points.

Contribution

The paper introduces a set of robust moment conditions that ensure identification of the autoregressive parameter in dynamic panel models when traditional conditions fail.

Findings

Robust moments can identify the autoregressive parameter near one.

The Kleibergen LM test effectively uses robust moments for inference.

More than three time series observations are needed for identification with robust moments.

Abstract

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.