2018/08/17 by Robert F. Phillips, Phillips, Robert F. · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Algorithm #Applied mathematics #Computational complexity theory #Computer science #Econometrics (econ.EM) #Efficiency Analysis Using DEA #Estimator #FOS: Economics and business #Generalized method of moments #Mathematics #Monetary Policy and Economic Impact #Monte Carlo method #Orthogonal transformation #Physics #Quantum mechanics #Spatial and Panel Data Analysis #Statistics #Transformation (genetics) #Work (physics) #econ.EM
paper · pdf · doi:10.48550/arxiv.1808.05995
published in arXiv (Cornell University) (Cornell University)
arxiv created 2018/08/17 · openalex publication_date 2018/08/17 · arxiv updated 2018/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 T4 increases, while the computational complexity of the FD transformation increases at the rate T6 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.