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Quantifying the Computational Advantage of Forward Orthogonal Deviations

Robert F. Phillips

arXiv 17 Aug 2018 · Econometrics · 1 citations (OpenAlex)

arXiv:1808.05995 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Under suitable conditions, one-step generalized method of moments (GMM) based on the first-difference (FD) transformation is numerically equal to one-step GMM based on the forward orthogonal deviations (FOD) transformation. However, when the number of time periods ($T$) is not small, the FOD transformation requires less computational work. This paper shows that the computational complexity of the FD and FOD transformations increases with the number of individuals ($N$) linearly, but the computational complexity of the FOD transformation increases with $T$ at the rate $T^{4}$ increases, while the computational complexity of the FD transformation increases at the rate $T^{6}$ increases. Simulations illustrate that calculations exploiting the FOD transformation are performed orders of magnitude faster than those using the FD transformation. The results in the paper indicate that, when one-step GMM based on the FD and FOD transformations are the same, Monte Carlo experiments can be conducted much faster if the FOD version of the estimator is used.

Citation extraction

6
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distinct cited
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appendix boundary found by appendix_titled_section at “Appendix A: Floating point operations for one-step GMM” · 68% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1(1991) Arellano, M., & Bond, S. (1991)0.64422100%
2(1995) Arellano, M., & Bover, O. (1995)0.51121100%
3(2003) Alvarez, J., & Arellano, M. (2003)0.40511100%
Alvarez and Arellanounmatched citation key Alvarez and Arellano0.000110%
Arellano and Bondunmatched citation key Arellano and Bond0.000110%
Arellano and Boverunmatched citation key Arellano and Bover0.000110%
Hayakawa and Nagataunmatched citation key Hayakawa and Nagata0.000110%
8(2007) Hunger, R. (2007)0.000110%
9(2003) Strang, G. (2003)0.000110%

Showing the top 9 of 9 scored citations. 4 of these could not be matched to a bibliography entry, so only the citation key is shown.