First difference or forward demeaning: Implications for the method of moments estimators

ABSTRACT

In this paper, we consider the method of moment estimation for dynamic panel models based on either forward demeaning (FOD) or first difference (FD) transformations to eliminate the individual-specific effects, using either all lags or one lag as instruments. We show that the Arellano–Bond-type generalized method of moment (GMM) based on FD is asymptotically biased of order $\sqrt{c}$ using all lags or one lag as instruments where $c=\frac{T}{N}<\infty$ as N,T→∞. For GMM based on FOD, it is asymptotically biased of order $\sqrt{c}$ when using all lags, but it is asymptotically unbiased when using only fixed number of lags as instruments. We also discuss these findings in light of the simple IV estimator. Monte Carlo simulations confirm our findings in this paper.

KEYWORDS:

• Dynamic panel data model
• first difference
• forward demeaning
• generalized method of moments
• instrumental variable estimation

JEL CLASSIFICATION:

• C01
• C13
• C23
• C33

Acknowledgment

We would like to thank the editors as well as two anonymous referees for helpful comments on this paper. All questions should be addressed to [email protected] Partial support by China NSF grant #71131008 and 71631004 to the first author is gratefully acknowledged.

Notes

¹More specifically, c has to be less than 1 to ensure the estimability of GMM based on FOD [Alvarez and Arellano (2003)].

²Han and Kim (2014) suggest to include the constant term in the instrument set to gain finite sample efficiency of the method of moments estimation. However, addition of the constant instrument does not change the order of asymptotic bias, which is the focus of this paper.

³For the balanced panel, we expect the GMM based on FOD or FD to have the same asymptotical variance, we are not able to show this algebraically. However, we indeed find that (3.7) is very close to the variance term of (3.3) in our simulation (Table 2). We thank a referee for calling our attention to this.