Some Decompositions of OLSEs and BLUEs Under a Partitioned Linear Model

We consider in this paper a partitioned linear model { y , X ₁ β ₁ + X ₂ β ₂ , σ ² σ } and two corresponding small models { y , X ₁ β ₁ , σ ² σ } and { y , X ₂ β ₂ , σ ² σ } . We derive necessary and sufficient conditions for (i) the ordinary least squares estimator under the full model to be the sum of the ordinary least squares estimators under the two small models; (ii) the best linear unbiased estimator under the full model to be the sum of the best linear unbiased estimators under the two small models; (iii) the best linear unbiased estimator under the full model to be the sum of the ordinary least squares estimators under the two small models. The proofs of the main results in this paper also demonstrate how to use the matrix rank method for characterizing various equalities of estimators under general linear models.     

Dynamically evaluating the comprehensive efficiency of technological innovation and low-carbon economy in China's industrial sectors

Technological innovation and low-carbon economy are significant for the high-quality development of China's industrial sectors. However, few scholars combine the two stages closely and discuss their coordinated development. This paper establishes an evaluation index system of technological innovation and low-carbon economy in China's industrial sectors. The technological innovation efficiency, low-carbon economy efficiency, and comprehensive efficiency of technological innovation and low-carbon economy are dynamically investigated by the two-stage data envelopment analysis (DEA) model and the DEA window analysis with 35 subsectors panel data during 1996–2018. The inter-industrial differences in the technological innovation efficiency and low-carbon economy efficiency are considered, and the influencing factors of the comprehensive efficiency of technological innovation and low-carbon economy are studied by the bootstrap truncation regression. The results show that: (1) The development of the technological innovation and low-carbon economy is uncoordinated, and the low-carbon economy efficiency needs improvement; (2) There is heterogeneous of the technological innovation efficiency and low-carbon economy efficiency in the 35 subsectors; (3) The density of science and technology institutions, and the average enterprises scale are positive to the comprehensive efficiency of technological innovation and low-carbon economy, while excessive reliance on technology introduction has a negative impaction. The corresponding suggestions are provided for promoting technological innovation efficiency and low-carbon economy efficiency of industrial sectors.     

Akaike-type criteria and the reliability of inference: Model selection versus statistical model specification

Since the 1990s, the Akaike Information Criterion (AIC) and its various modifications/extensions, including BIC, have found wide applicability in econometrics as objective procedures that can be used to select parsimonious statistical models. The aim of this paper is to argue that these model selection procedures invariably give rise to unreliable inferences, primarily because their choice within a prespecified family of models (a) assumes away the problem of model validation, and (b) ignores the relevant error probabilities. This paper argues for a return to the original statistical model specification problem, as envisaged by Fisher (1922), where the task is understood as one of selecting a statistical model in such a way as to render the particular data a truly typical realization of the stochastic process specified by the model in question. The key to addressing this problem is to replace trading goodness-of-fit against parsimony with statistical adequacy as the sole criterion for when a fitted model accounts for the regularities in the data.