Analysis and control of macroeconomic trends based on the Leontief model
|
1 Abstract 3
2 Introduction 4
3 Static input-output model 8
3.1 The basic structure of China’s input-output table 8
3.1.1 The three quadrants of input-output table 8
3.1.2 Interrelation of value-added input-output table .... 9
3.1.3 Direct consumption coefficient 11
3.1.4 Complete consumption coefficient 13
3.1.5 Influence coefficient 14
3.2 Aggregation, reduction and inter-sectoral integration calculation of input-output table 15
3.2.1 Aggregation 15
3.2.2 Reduction 17
3.2.3 Calculation of the degree of integration between ad
vanced manufacturing industry and modern service industry 20
3.3 Analysis of the integration status between China’s modern
service industry and advanced manufacturing industry 22
3.3.1 One-way integration degree 22
3.3.2 Comprehensive integration degree 24
3.3.3 Interactive degree of integration 25
3.4 The conclusion of the static model 29
4 The dynamic input-output model of equilibrium economy 30
4.1 Introduction 30
4.2 Construct the system of differential equation 35
4.3 China’s dynamic input-output analysis 38
4.3.1 Predict China’s capital density 38
4.3.2 Predicting GDP and the total output of maximum
aggregation 41
4.4 Dynamic input-output analysis of the United States 43
4.4.1 Predicting US Capital density 44
4.4.2 Predicting the US GDP and the total output among
sectors 45
4.5 Comparison between China and the United States 46
5 Program control of equilibrium economy 48
5.1 Program control problem statement 48
5.2 Program control algorithm 49
5.3 The united states input-output program control 50
6 Input-output model of saddle point equilibrium strategy 52
6.1 The game model of dynamic input-output system 53
6.2 Optimal control construction 55
7 Conclusion 57
2 Introduction 4
3 Static input-output model 8
3.1 The basic structure of China’s input-output table 8
3.1.1 The three quadrants of input-output table 8
3.1.2 Interrelation of value-added input-output table .... 9
3.1.3 Direct consumption coefficient 11
3.1.4 Complete consumption coefficient 13
3.1.5 Influence coefficient 14
3.2 Aggregation, reduction and inter-sectoral integration calculation of input-output table 15
3.2.1 Aggregation 15
3.2.2 Reduction 17
3.2.3 Calculation of the degree of integration between ad
vanced manufacturing industry and modern service industry 20
3.3 Analysis of the integration status between China’s modern
service industry and advanced manufacturing industry 22
3.3.1 One-way integration degree 22
3.3.2 Comprehensive integration degree 24
3.3.3 Interactive degree of integration 25
3.4 The conclusion of the static model 29
4 The dynamic input-output model of equilibrium economy 30
4.1 Introduction 30
4.2 Construct the system of differential equation 35
4.3 China’s dynamic input-output analysis 38
4.3.1 Predict China’s capital density 38
4.3.2 Predicting GDP and the total output of maximum
aggregation 41
4.4 Dynamic input-output analysis of the United States 43
4.4.1 Predicting US Capital density 44
4.4.2 Predicting the US GDP and the total output among
sectors 45
4.5 Comparison between China and the United States 46
5 Program control of equilibrium economy 48
5.1 Program control problem statement 48
5.2 Program control algorithm 49
5.3 The united states input-output program control 50
6 Input-output model of saddle point equilibrium strategy 52
6.1 The game model of dynamic input-output system 53
6.2 Optimal control construction 55
7 Conclusion 57
Input-output analysis, proposed by Leontief in 1936, has been widely applied in economic analysis and continuously improved and developed in practice. As a crucial quantitative tool, input-output analysis can reflect the interdependence between input and output of multi-sector in the national economy and can be applied in economic analysis, policy simulation, economic forecasting and decision-making, and economic control.
Based on the input-output tables released by the National Bureau of Statistics of China in 2002, 2005, 2007, 2010, 2012, 2015, 2017, 2018, and 2020, the third part of this thesis establishes a static inputoutput model and provides relevant balance equations. One considers the direct consumption coefficient of m industries and analyzed the oneway integration degree, comprehensive integration degree, and interactive degree of integration. Through multidimensional quantification of China’s "modern service industry" and "advanced manufacturing industry," one finds that the integration of the "two industries" has achieved some results, but the contribution of the modern service industry to the advanced manufacturing industry is still limited. The influence of the "two industries" is differentiated, and traditional advantageous industries still exist. To address this issue, it is necessary to construct a sound domestic demand system for the modern service industry, connect the "dual circulation" of the "two industries," strengthen the industrial connection, enhance the innovation connection between the "two industries," and thus achieve deep integration of the "two industries."
According to, the modern service industry can drive technological progress in related industries to a certain extent and promote industrial structure upgrading. [Sun,2020] believes that the modern service industry includes modern logistics, information transportation, computer services and software industry, scientific research, technology services, and geological exploration. Based on the "Thirteenth Five-Year Plan" for the transformation of scientific and technological innovation in China’s modern service industry in 2017, this paper divides the modern service industry in combination with Sun’s viewpoint.
According to the advanced manufacturing industry refers to industries that primarily use emerging technologies as the primary means. and believe that advanced manufacturing includes six industries: electronic equipment manufacturing, general and special-purpose equipment manufacturing, instrumentation and meter manufacturing, computer and electronic equipment manufacturing, and transportation equipment manufacturing. Based on the "End-of-year Reserve Policy for Advanced Manufacturing Industry (2021)" published by the Chinese Tax Bureau, this paper divides the advanced manufacturing industry along with Li and Hua’s perspective.
In the research of industrial integration, [Xia,2020] measured the integration of the productive service industry and manufacturing industry by using the ratio of intermediate input to total output. [Ma,2011] proposed to measure the degree of integration by the proportion of the input to the total intermediate input. [Peng,2019] pointed out the comprehensive integration degree in industrial coupling. In this section, we combine the views of Xia and Ma and use the degree of service-oriented of the advanced manufacturing industry and the degree of manufacturing-oriented of the modern service industry as indicators of a one-way integration degree. One also considers Peng’s view to measure the comprehensive integration degree.
As the economic structure is a constantly changing and developing dynamic process, static input-output models cannot accurately reflect the actual situation of expanding social product reproduction. Therefore, many scholars have explored the construction of dynamic input-output models. For example, [Leontief,1956] proposed the "dynamic inverse model", laying the foundation for dynamic input-output models. [Miller, 2009] incorporated the time factor into the input-output analysis. [Smirnov,2021] considered GDP as the (n + 1)th variable in the input-output equilibrium equation, defining total output as the derivative for time.
...
Based on the input-output tables released by the National Bureau of Statistics of China in 2002, 2005, 2007, 2010, 2012, 2015, 2017, 2018, and 2020, the third part of this thesis establishes a static inputoutput model and provides relevant balance equations. One considers the direct consumption coefficient of m industries and analyzed the oneway integration degree, comprehensive integration degree, and interactive degree of integration. Through multidimensional quantification of China’s "modern service industry" and "advanced manufacturing industry," one finds that the integration of the "two industries" has achieved some results, but the contribution of the modern service industry to the advanced manufacturing industry is still limited. The influence of the "two industries" is differentiated, and traditional advantageous industries still exist. To address this issue, it is necessary to construct a sound domestic demand system for the modern service industry, connect the "dual circulation" of the "two industries," strengthen the industrial connection, enhance the innovation connection between the "two industries," and thus achieve deep integration of the "two industries."
According to, the modern service industry can drive technological progress in related industries to a certain extent and promote industrial structure upgrading. [Sun,2020] believes that the modern service industry includes modern logistics, information transportation, computer services and software industry, scientific research, technology services, and geological exploration. Based on the "Thirteenth Five-Year Plan" for the transformation of scientific and technological innovation in China’s modern service industry in 2017, this paper divides the modern service industry in combination with Sun’s viewpoint.
According to the advanced manufacturing industry refers to industries that primarily use emerging technologies as the primary means. and believe that advanced manufacturing includes six industries: electronic equipment manufacturing, general and special-purpose equipment manufacturing, instrumentation and meter manufacturing, computer and electronic equipment manufacturing, and transportation equipment manufacturing. Based on the "End-of-year Reserve Policy for Advanced Manufacturing Industry (2021)" published by the Chinese Tax Bureau, this paper divides the advanced manufacturing industry along with Li and Hua’s perspective.
In the research of industrial integration, [Xia,2020] measured the integration of the productive service industry and manufacturing industry by using the ratio of intermediate input to total output. [Ma,2011] proposed to measure the degree of integration by the proportion of the input to the total intermediate input. [Peng,2019] pointed out the comprehensive integration degree in industrial coupling. In this section, we combine the views of Xia and Ma and use the degree of service-oriented of the advanced manufacturing industry and the degree of manufacturing-oriented of the modern service industry as indicators of a one-way integration degree. One also considers Peng’s view to measure the comprehensive integration degree.
As the economic structure is a constantly changing and developing dynamic process, static input-output models cannot accurately reflect the actual situation of expanding social product reproduction. Therefore, many scholars have explored the construction of dynamic input-output models. For example, [Leontief,1956] proposed the "dynamic inverse model", laying the foundation for dynamic input-output models. [Miller, 2009] incorporated the time factor into the input-output analysis. [Smirnov,2021] considered GDP as the (n + 1)th variable in the input-output equilibrium equation, defining total output as the derivative for time.
...
This master thesis first establishes a static input-output model in the third part based on the input-output table issued by the National Bureau of Statistics of China. I considered the direct consumption coefficients of m departments and analyzed the one-way fusion degree, fusion interaction degree, and comprehensive fusion degree. Through the multi-dimensional quantification of China’s "modern service industry" and "advanced manufacturing industry", I found that the integration of "two industries" has achieved some results, but the contribution of the modern service industry to the advanced manufacturing industry is still limited; traditional advantageous industries are still promising. In this regard, a modern service industry demand system should be built and improved to open up the double cycle of "two industries"; through strengthening industrial linkages and strengthening the innovation linkages of "two industries", the deep integration of "two industries" should be realized.
The fourth part of this article establishes the dynamic input-output model of China and the United States based on the OECD. Through this model and the least squares method, the capital density of the two countries underinflation and non-inflation is predicted. For China’s inputoutput table, Considering the maximum aggregated total output, use the time series to predict the maximum aggregated total output and the development trend of GDP from 2019 to 2024; similarly, the same is true for the US input-output table, and finally compare the differences between the two countries. Through my research, I found that the contribution of the modern service industry in the United States to GDP is higher than that of advanced manufacturing, and the opposite is true in China. For China, it is even more necessary to maintain an open and shared attitude and actively promote digital transformation and upgrading, increase investment in modern service industries such as science and technology, and promote industrial transformation and upgrading. For the United States, it should relax trade controls, actively promote international economic and technological cooperation, and promote sound economic development.
The classical program control theory is employed in the fifth section of this study. Based on the linear non-homogeneous differential equation including three sectors and GDP, I exerted control on the aggregated advanced manufacturing industry in the United States from 2017 to 2018, obtained the control equation of multi-factor influence, and used Python to verify the program control through numerical calculation effectiveness.
Finally, the continuous optimal strategy design problem is presented based on Leontief’s dynamic input-output model. The dynamic inputoutput system is abstracted as a saddle point equilibrium theory, and a new approach for addressing the dynamic input-output problem is created utilizing the saddle point equilibrium strategy.
The fourth part of this article establishes the dynamic input-output model of China and the United States based on the OECD. Through this model and the least squares method, the capital density of the two countries underinflation and non-inflation is predicted. For China’s inputoutput table, Considering the maximum aggregated total output, use the time series to predict the maximum aggregated total output and the development trend of GDP from 2019 to 2024; similarly, the same is true for the US input-output table, and finally compare the differences between the two countries. Through my research, I found that the contribution of the modern service industry in the United States to GDP is higher than that of advanced manufacturing, and the opposite is true in China. For China, it is even more necessary to maintain an open and shared attitude and actively promote digital transformation and upgrading, increase investment in modern service industries such as science and technology, and promote industrial transformation and upgrading. For the United States, it should relax trade controls, actively promote international economic and technological cooperation, and promote sound economic development.
The classical program control theory is employed in the fifth section of this study. Based on the linear non-homogeneous differential equation including three sectors and GDP, I exerted control on the aggregated advanced manufacturing industry in the United States from 2017 to 2018, obtained the control equation of multi-factor influence, and used Python to verify the program control through numerical calculation effectiveness.
Finally, the continuous optimal strategy design problem is presented based on Leontief’s dynamic input-output model. The dynamic inputoutput system is abstracted as a saddle point equilibrium theory, and a new approach for addressing the dynamic input-output problem is created utilizing the saddle point equilibrium strategy.
