Lag Augmentation in Dynamic Econometric Models

众所周知，在具有非平稳回归变量的动态模型中，参数的Wald检验统计量有时具有非标准渐近分布。为了克服这一困难，提出了一种估计动态模型的滞后增强(LA)方法。与其他先进而复杂的方法相比，这是一种非常有用的方法，因为LA方法产生的Wald统计量服从渐近卡方分布。1998年，我们证明了LA方法适用于常见的动态回归模型，尽管该方法最初只适用于向量自回归(VAR)模型。此外，我们发现Wald检验统计量往往具有更高的功率，滞后变量的滞后长度更长，而不是1个滞后。1999年，在综合实验的基础上，我们提出了基于系数参数估计方差-协方差矩阵的广义方差来选择合适的滞后长度的准则。此外，我们还将LA方法推广到回归项和误差项相关的联立方程组。结果表明，LA与仪器变量(IV)法相结合是适用的。蒙特卡罗实验表明了本研究方法的有效性。

It has been widely known that the Wald test statistic for parameters in a dynamic model with non-stationary regressors occasionally has a non-standard asymptotic distribution. To cope with this difficulty, the lag augmentation (LA) approach has been proposed for estimating a dynamic model. It is known to be quite useful compared with other advanced but complicated methods, since the LA approach produces the Wald statistic with asymptotically chi-square distribution.In 1998, we showed that the LA approach is applicable to usual dynamic regression models, although the method was originally developed solely for vector autoregressive (VAR) models. Further, we found that the Wald test statistic tends to have higher power with a lagged variable of a longer lag length rather than that of one lag. In 1999, based upon the comprehensive experiments, we have proposed the criteria for selecting a suitable lag length, which is based upon a generalized variance of an estimated variance-covariance matrix of coefficient parameters. Further, we have generalized the application of the LA approach to simultaneous equation systems where regressors and error terms are correlated. Thus, it has been shown that the LA is applicable in conjunction with the instrumental variable (IV) method. The Monte Carlo experiment has revealed the effectiveness of approaches proposed in the present research.