考虑生产时滞的Leontief逆矩阵时间序列模型

Leontief逆矩阵是投入产出模型的核心, 常用以计算部门间拉动关系以及最终需求变动的影响. 经典的Leontief逆矩阵完全没有考虑传导过程所需要的时间, 但由于部门内部生产周期和部门间流通周期的存在, 使其在有限期间内对部门间拉动效应作出不切实际的估计. 本文研究部门内部存在生产时滞时, 部门间需求拉动的水平与传导规律, 即Leontief逆矩阵的形式. 以生产周期作为生产时滞的度量指标, 并建立生产周期特征矩阵对部门分类. 按照给定时段实现的需求系数和诱发的需求系数间的转换关系进行上下时序间变量的迭代, 得到各时段的完全需求系数. 迭代变量包括: ① 实现的需求系数; ② 完全需求系数; ③ 诱发的需求系数. 模型应用的效果在于合理的生产周期的设定.

Time series Leontief inverse considering production delay

As the key of input-output model, Leontief inverse has usually been applied to calculate backward and forward effect and to estimate the effect of the change in final demand. Traditional Leontief inverse do not take account of the time-lag of transmission at all. Due to the existence of production cycle and distribution cycle, however, traditional Leontief inverse may generate unrealistic estimation regarding the inter-sectoral pull effects, especially in a limited period. This paper presents a new Leontief inverse formula which considers production delay. We firstly employ production cycle as the indicator of production delay, then establish a production cycle eigen matrix to represent sectors. In the following, we conduct a temporal iteration to estimate the new Leontief inverse (i.e. total requirement coefficients) for each period, according to the relationship between direct requirement coefficients and induced requirement coefficients. The iteration variables include: ① direct requirement coefficients; ② total requirement coefficients; ③ induced requirement coefficients. The key of model application is to set a reasonable production cycle.