标题： 量化前向正交偏差的计算优势 显示英文标题

标题： Quantifying the Computational Advantage of Forward Orthogonal Deviations

摘要： 在适当条件下，基于一阶差分（FD）变换的一步广义矩方法（GMM）在数值上等于基于前向正交偏差（FOD）变换的一步GMM。 然而，当时间周期数（$T$）不是很小的时候，FOD变换需要较少的计算工作量。 本文表明，FD和FOD变换的计算复杂度随着个体数量（$N$）线性增加，但FOD变换的计算复杂度随着$T$以$T^{4}$增加的速度增加，而FD变换的计算复杂度随着$T^{6}$增加的速度增加。 模拟结果说明，利用FOD变换的计算比使用FD变换的计算快几个数量级。 论文中的结果表明，当基于FD和FOD变换的一步GMM是相同的时，如果使用FOD版本的估计量，蒙特卡洛实验可以更快地进行。 显示英文摘要

摘要： 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.