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Continuous updating gmm estimator

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.A data-dependent moment selection method based on minimizing the approximate mean squared error is developed.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.Our simulation results indicate that the subset-continuous-updating GMM estimators outperform their standard two-step counterparts in finite samples in terms of the estimation accuracy on the autoregressive parameter and the size of the Sargan-Hansen test.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.

This paper applies test statistics developed by Stock and Wright [Econometrica 68 (2000) 1055] to examine the two specifications of the New Keynesian Phillips curve in Galı́ and Gertler [Journal of Monetary Economics 44 (1999) 195].Kernel weighting also helps to simplify the problem of selecting the optimal number of instruments.A feasible procedure similar to optimal bandwidth selection is proposed for the kernel-weighted GMM estimator.It is computationally advantageous relative to the continuous-updating estimator in that it replaces a relatively high-dimensional optimization over unbounded intervals by a one-dimensional optimization limited to the stationary domain of the autoregressive parameter.We conduct Monte Carlo experiments and show that the proposed subset-continuous-updating versions of the DIF and SYS GMM estimators outperform their standard two-step counterparts in small samples in terms of the estimation accuracy on the autoregressive parameter and the rejection frequency of the Sargan-Hansen test.However, it was pointed out later on (see Hayakawa [6] and Bun and Windmeijer [7]) that the weak instruments problem still remains in the SYS GMM estimator.Since the increase in the length of the panel leads to a quadratic increase in the number of instruments, the two-step DIF and SYS GMM estimators are both biased due to many weak moment conditions; see Newey and Windmeijer [8].The new test statistics demonstrate the inadequacy of conventional GMM methodology by indicating two features that are neglected by Galı́ and Gertler: observational equivalence in the baseline model and weak identification in the hybrid model.In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.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 [5] argue, this model specification is sufficient to cover most cases that researchers would encounter in linear dynamic panel applications.


  1. GMM for Panel Count Data Models. step GMM estimation results are known to have poor finite. also considers estimation by the continuous updating estimator.

  2. Step ‘continuous updating’ GMM estimator is consistent and asymptotically normal under weak conditions that allow for generic spatial and time series dependence.

  3. Package ‘gmm ’ June 15, 2017. doi10.2307/1912775, the iterated GMM and continuous updated estimator Hansen, Eaton and. # GMM is like GLS for linear.

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