ABSTRACT In the stepwise procedure of selection of a fixed or a random explanatory variable in a mixed quantitative linear model with errors following a Gaussian stationary autocorrelated process, we have studied the efficiency of five estimators relative to Generalized Least Squares (GLS): Ordinary Least Squares (OLS), Maximum Likelihood (ML), Restricted Maximum Likelihood (REML), First Differences (FD), and First-Difference Ratios (FDR). We have also studied the validity and power of seven derived testing procedures, to assess the significance of the slope of the candidate explanatory variable x2 to enter the model in which there is already one regressor x1. In addition to five testing procedures of the literature, we considered the FDR t-test with n ? 3 df and the modified t-test with n? ? 3 df for partial correlations, where n? is Dutilleul's effective sample size. Efficiency, validity, and power were analyzed by Monte Carlo simulations, as functions of the nature, fixed vs. random (purely random or autocorrelated), of x1 and x2, the sample size and the autocorrelation of random terms in the regression model. We report extensive results for the autocorrelation structure of first-order autoregressive [AR(1)] type, and discuss results we obtained for other autocorrelation structures, such as spherical semivariogram, first-order moving average [MA(1)] and ARMA(1,1), but we could not present because of space constraints. Overall, we found that:
the efficiency of slope estimators and the validity of testing procedures depend primarily on the nature of x2, but not on that of x1;
FDR is the most inefficient slope estimator, regardless of the nature of x1 and x2;
REML is the most efficient of the slope estimators compared relative to GLS, provided the specified autocorrelation structure is correct and the sample size is large enough to ensure the convergence of its optimization algorithm;
the FDR t-test, the modified t-test and the REML t-test are the most valid of the testing procedures compared, despite the inefficiency of the FDR and OLS slope estimators for the former two;
the FDR t-test, however, suffers from a lack of power that varies with the nature of x1 and x2; and
the modified t-test for partial correlations, which does not require the specification of an autocorrelation structure, can be recommended when x1 is fixed or random and x2 is random, whether purely random or autocorrelated. Our results are illustrated by the environmental data that motivated our work.
The article evaluates the relationship between the tax burden on labor and magic quadrangle indicators in the Czech Republic in the years 1993 through 2020. The article examines whether indicators such as the effective rate or tax rate on labor affect the macro-economic indicators of the magic quadrangle. The originality of this study lies in the fact that it deals with the influence of political factors. The analysis shows the strongest correlation between the growth of gross domestic product and the implicit tax rate on labor. Moreover, the study finds that the factor with the most significant – and surprising – bearing on the findings is that fact that right-wing Parliament behaved like left-wing parties. The conclusions reached by this study further underline the significance of the tax burden on labor on the selected magic quadrangle indicators. 相似文献