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The two-step GMM estimators of Arellano and Bond (1991) and Blundell and Bond (1998) for dynamic panel data models have been widely used in empirical work; however, neither of them performs well in small samples with weak instruments.
The continuous-updating GMM estimator proposed by Hansen, Heaton, and Yaron (1996) is in principle able to reduce the small-sample bias, but it involves high-dimensional optimizations when the number of regressors is large.
This paper proposes a computationally feasible variation on these standard two-step GMM estimators by applying the idea of continuous-updating to the autoregressive parameter only, given the fact that the absolute value of the autoregressive parameter is less than unity as a necessary requirement for the data-generating process to be stationary.
We show that our subset-continuous-updating method does not alter the asymptotic distribution of the two-step GMM estimators, and it therefore retains consistency.
The interpretation gives some insight into why there is less bias associated with this estimator.
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The method requires that a certain number of moment conditions were specified for the model.
These moment conditions are functions of the model parameters and the data, such that their expectation is zero at the true values of the parameters.
Version control ensures statistical programs will continue to produce the same results no matter when you wrote them.