Initial conditions and Blundell–Bond estimators

We place the Blundell–Bond paper in the context of the early development of panel data estimators that accounted for unobserved heterogeneity, dynamics and persistent economic series. The initial work focused on appropriate econometric methods to estimate dynamic models using unbalanced panel data with many firms and/or individuals but covering a small number of time periods. Eliminating the unobserved firm-specific ‘fixed’ effects by taking first-differences and using as instruments suitably lagged values of the dependent variable , and of endogenous or predetermined explanatory variables, led to the first-differenced GMM estimators popularised by Arellano and Bond (1991). This approach was less well suited to models which relate highly persistent series. Following Arellano and Bover (1995) we examined the use of suitably lagged first-differences as instruments for the equations in levels and derived the conditions, particularly on initial conditions, under which first-differences of the dependent variable would or would not be uncorrelated with individual-specific ‘fixed’ effects. An influential contribution was to illustrate the magnitude of the bias when the first-differenced GMM estimator is used to estimate autoregressive models for highly persistent series, and the potential to reduce that bias by using additional valid moment conditions for the equations in levels — thereby popularising the use of these extended or ‘System’ GMM estimators.