Quantifying the Computational Advantage of Forward Orthogonal Deviations
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Comparison of First-Difference and Forward Orthogonal Deviations GMM
This paper provides a necessary and sufficient instruments condition assuring two-step generalized method of moments (GMM) based on the forward orthogonal deviations transformation is numerically equivalent to two-step G…
Forward Orthogonal Deviations GMM and the Absence of Large Sample Bias
It is well known that generalized method of moments (GMM) estimators of dynamic panel data regressions can have significant bias when the number of time periods ($T$) is not small compared to the number of cross-sectiona…
l1-norm Penalized Orthogonal Forward Regression
A l1-norm penalized orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leaveone- out mean square error (LOOMSE). Firstly, a new l1-norm penalized cost function is defined in the constru…
regressionNorm-preserving Orthogonal Permutation Linear Unit Activation Functions (OPLU)
We propose a novel activation function that implements piece-wise orthogonal non-linear mappings based on permutations. It is straightforward to implement, and very computationally efficient, also it has little memory re…
Forward Only Learning for Orthogonal Neural Networks of any Depth
Backpropagation is still the de facto algorithm used today to train neural networks. With the exponential growth of recent architectures, the computational cost of this algorithm also becomes a burden. The recent PEPITA …