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Given the fact that the absolute value of the autoregressive parameter must be less than unity as a necessary requirement for the data-generating process to be stationary, we propose a computationally feasible variation on the two-step DIF and SYS GMM estimators, in which the idea of continuous-updating is applied solely to the autoregressive parameter; these two new estimators are denoted “SCUDIF” and “SCUSYS” below.
Following the jackknife interpretation of the continuous-updating estimator in the work of Donald and Newey , we show that the subset-continuous-updating method that we propose in this paper does not alter the asymptotic distribution of the two-step GMM estimators, and it hence retains consistency.
The layout of the paper is as follows: Section 2 describes the model specification and our proposed subset-continuous-updating method; Section 3 describes the Monte Carlo experiments and presents the results; and Section 4 concludes the paper.-dimensional column vector of remaining coefficients.
As Blundell, Bond, and Windmeijer  argue, this model specification is sufficient to cover most cases that researchers would encounter in linear dynamic panel applications.
The interpretation gives some insight into why there is less bias associated with this estimator.
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.
This paper analyzes the higher-order asymptotic properties of generalized method of moments (GMM) estimators for linear time series models using many lags as instruments.
We show that the continuous updating estimator can be interpreted as jackknife estimator.
The resulting system (SYS) GMM estimator has been shown to perform much better than the DIF GMM estimator in terms of finite sample bias and mean squared error, as well as with regard to coefficient estimator standard errors since the instruments used for the level equation are still informative as the autoregressive coefficient approaches unity (see Blundell and Bond  and Blundell, Bond, and Windmeijer ).
As a result, the SYS GMM estimator has been widely used for estimation of production functions, demand for addictive goods, empirical growth models, etc.
Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the distribution function of the data may not be known, and therefore maximum likelihood estimation is not applicable.
The method requires that a certain number of moment conditions were specified for the model.