Studies On Several Problems Of Input-Output Models

The input-output analysis and the DEA theory, which is mainly used to analyze the efficiency of double input and output, have been developed and perfected in practice. This thesis covers three fields: the establishment of stochastic input-output models and the derivation of related theories; the expansion of DEA model; and the application of the expanded DEA model to the practical analysis on the relative efficiency of the technological input in many areas in China.As for the establishment of stochastic input-output models and the derivation of related theories, there are three points to be mentioned: firstly, the theoretical basis on which the ultimate requirements must comply with the index movement is given; secondly, the output control model is offered, which is based on the idea that the ultimate requirement is an index stochastic variable. Under this model, a control equation is derived, which can satisfy the outputs with reliability; finally, the stochastic input-output models where direct coefficient of consumption and ultimate requirements are index stochastic variables are derived. Under the model, a definite equal-value equation that meets outputs with reliability is derived.For the study of the expansion of DEA model, a geometrical explanation is made for the fact that the DEA model with single input and output may cover the advanced technology; a DEA model based on output lagging is offered; and three improved DEA models are provided through revising some limited parts in traditional DEA model, that is, an effective DEA model determined by input, a DEA model with output only and a complex DEA model.For the practical analysis of the output efficiency of technological input in many areas in China, a statistic method determining the establishment of index system is presented through the application of the DEA model based on output lagging. Therefore, a basic condition of relative efficiency of technological input in China is acquired, that is, the use of technology in eastern areas is actively effective and relatively low in western areas but with a tendency to increase.