A Monte Carlo comparison of alternative estimators for dynamic panel data models

Abstract

This article compares the performance of three recently proposed estimators for dynamic panel data models (LSDV bias-corrected, MLE and MDE) along with GMM. Using Monte Carlo, we find that MLE and bias-corrected estimators have the smallest bias and are good alternatives for the GMM. System-GMM outperforms the rest in ‘difficult’ designs. Unfortunately, bias-corrected estimator is not reliable in these designs which may limit its applicability.

Notes

¹ Stata routine -xtabond2- written by David Roodman, Center for Global Development, Washington, DC is capable of estimating both system and difference GMM. EViews 5.0 release has a difference GMM available. Gauss and PcGive have an original DPD. Limdep 8.0 can estimate difference GMM.

² In particular, Bun and Carree (2005) state that the BC estimator has convergence problems when the signal-to-noise ratio is low for relatively high values of γ (p. 207). Hsiao et al. (2002) state that ‘MLE sometimes breaks down completely … [when T and N are small]’ (p. 132). See the footnote 3 below for our approach to tracking nonconvergence cases.

³ To avoid over- or under-reporting of nonconvergence of the BC estimator, in our version of the program we rely on the exact solution, rather than on the iterative procedure proposed in the original article. The system of Equations 19 and 20 (see original article) can be transformed into a polynomial of power T. We solve this polynomial with respect to γ. Then we use (20) to solve for true β. Note, that when T is odd the polynomial always has at least one real root, when T is even, it may have zero real roots and T complex roots. In our Monte Carlo experiments, for the designs when T = 6 we count the number of cases when the polynomial has no real roots, this is reported in Table 2; in designs when T = 3, when there is at least one real root, we count as nonconvergence those solutions that are smaller than γ-LSDV. The unique solution to the polynomial when T = 3 and the root is less than γ-LSDV is a negative number between −3 and −4. Convergence for MLE has been always achieved. The starting values for MLE were the MDE estimates. We used NLPDD Double Dogleg optimization routine in SAS for MLE and used the outer product of gradient to compute variance. Estimates for MDE are obtained from B.5 based on initial and γ, β from Anderson–Hsiao IV estimator, using y _{i, t−2} and (x _{i, t} − x _{i, t−1}) as instruments.

⁴ The ranking is computed by giving five points for the first place, four for the second and so on in each of the designs and is based on average cumulative score for biases on γ and β.