# Analysis of Factors Affecting Freight Demand Based on Input-Output Model

Authors: Changxiang Lu; Shaochuan Fu; Jiaqi Fang; Jikai Huang; Yong Ye
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

Freight demand is a highly variable process over economic and industrial structure, and accurate freight demand forecasting is the basis of transportation planning. In order to clarify the influencing factors of freight volume so as to analyze and predict the change trend of freight volume accurately, this paper analyzes the impact of changes in economic, industrial structure, and complete consumption coefficients on freight demand, through constructing an input-output model for transportation value analysis and forecasting freight volume by fitting data of transportation value and freight traffic. Studies have shown that the growth in economic aggregate is the main reason for the increase in the value of transportation, and the change in the complete consumption coefficient is the main reason for the increase in freight traffic.


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## Body

## 1. Introduction

Freight demand forecasting is the basis of transportation planning. The wrong forecast of freight demand may lead to the advanced construction of transportation and waste of resources, such as Japan in the 1980s, or cause the delayed construction and the loss of freight transportation congestion, such as Iraq in the 1970s. Therefore, freight demand forecasting has aroused the interest of the transportation sector and many scholars. This paper attempts to describe and analyze the driving factors that affect China’s freight demand in order to better study the future development trend of freight.In the past, researchers believed that there was a linear relationship between freight transportation demand and GDP [1–3]. The nature of the industry, such as the proportions of primary, secondary, and tertiary industries, has different effects on freight intensity [4]. Alises and Vassallo[5] show that the economic elasticity of freight transportation is gradually decreasing. However, Zhang et al. [6] believe that economic factors are still the main factors affecting freight volume. Wang et al. [7] believe that freight volume is affected by macroeconomics, industrial structure, and supply capacity. The research of Sun et al. [8] shows that resource and population distribution and investment in fixed assets are the main factors influencing railway freight volume. In addition, supply chain management strategies will also affect freight volume, such as inventory management strategies [9–13] and replenishment strategies [14]. Previous studies have analyzed the influencing factors of freight volume from many aspects, but because of the lack of comparative analysis of influencing factors, the importance and relevance of influencing factors cannot be reflected.Many research models are established, such as developing and applying transportation market shares models [15], transportation supply chain models [16], spatial accounting models [17], and multiple regression models [18]. However, such methods are found difficult to predict the growth of freight volume accurately due to the complexity of the economic system and the rapid development of the service economy.Input-output (IO) analysis method was proposed by American economist Leontief in 1925. The input-output model can analyze and investigate the quantitative dependence relationship between the freight transportation sector and other sectors in the national economy [19, 20]. The IO model captures the nature of interindustry interaction, has relatively low data requirements, and is easy to implement [21]. Based on the expression of intersectoral multiplier effects, the IO model allows us to describe the effects on the transport system caused by shocks in the economic system, both from a theoretical and an application point of view.This paper considers an aggregate level of freight transportation, correlates the freight volume with the operation of the economic system, and then constructs the IO model. The model is structured on two levels: the first level forecasts the output value of the production department according to the exogenous demand and the second forecasts the tonnage of goods transported according to the relationship between the value of freight demand and freight volume in the economic system. Through the elaboration of time series of input-output tables for China, the model is validated and used to formulate forecasts for different future scenarios and then the influencing factors of freight traffic are analyzed.This paper tries to answer the following two questions: (1) the relationship between economic development and transportation demand and (2) influencing factors of freight volume growth. The novel contribution of this paper is as follows: (1) the national freight volume was predicted by the input-output model. In order to reflect the impact of changes in industrial structure on freight volume better, this paper subdivides the industrial structure into 42 sectors, and the impact of 42 sectors on freight volume was analyzed, which is more specific than the previous division of the three industries; (2) comparative analysis of the influencing factors of freight value and freight volume was carried out through the complete decomposition model, and the influence degree of economic aggregate, industrial structure, and complete consumption coefficient on freight value and freight volume was obtained, so as to obtain the changing trend of freight volume accurately.


## 2. Literature Review

The literature related to this paper can be divided into three parts: (1) factors affecting freight demand, (2) input-output model, and (3) freight volume forecast.


### 2.1. Factors Affecting Freight Demand

Robert et al. [22] have identified and evaluated the factors of freight demand. Their research shows that population, economic activities, fuel prices, environment, and policies are the main influencing factors, among which GDP and GDP per capita are commonly used indicators of economic activity. Fite et al. [23] conducted regression analysis on 107 indexes related to freight volume and believed that the producer commodity price index of construction materials and equipment (PCPI-CM&E) was the most relevant parameter. Agnolucci and Bonilla [24] conducted a study on the relationship between freight volume and GDP in the UK from 1956 to 2003. Their research found that the decoupling of freight volume and GDP accelerated, and the price and income elasticity also decreased to 18% and 65%. Wang et al. [25] proposed a hierarchical model. The model shows that the demand for truck freight can be estimated by truck traffic, population, number of companies, and income. Short et al. [26] studied the relationship between Sweden’s economic activities and freight volume. The study found that, in the short and medium term, changes in imports and exports led to large fluctuations in freight demand; in the long run, freight demand and GDP are coupled, and there is no sign of decoupling. Wijeweera et al. [27] studied the impact of freight prices, international trade, and business cycles on Australia’s rail freight demand. Their study shows that the fluctuation of freight rates and the Australian dollar was the most important factor affecting Australian rail freight. Alises and Vassallo [28] studied the impact of economic growth, industrial structure, and road transport intensity on the demand for road freight. The results show that, overall, the growth of total road transport demand is mainly driven by economic activities. Patil and Sahu [29] used regression and time series models to estimate the freight demand of Mumbai ports. Their research concluded that GDP and crude oil production are the most important factors affecting freight. Wang et al. [30] analyzed the relationship between freight demand and economic development. They believe that China’s overall economic development is decoupled from freight development, and the intensity of transportation is declining. Khan and Khan [31] analyzed the demand for rail freight in Pakistan. The study showed that GDP and freight are the two most important determinants of rail freight demand. Table 1 shows the comparison between some studies and this paper.Table 1
Comparison of some research studies and this paper.
References/Influencing factorsTransportation supply characteristicsTransport demand characteristicsOtherFreight costFreight timeReliabilityCargo damage costTransport distanceTransport frequencyCargo capacityProduct sizeProduct typesCommodity valueIndustryInventory costDelivery frequencyInteractive termTerminal accessibilityDewey et al. [32]☆☆☆Holguín-Veras [33]☆☆☆☆Kim [34]☆☆☆Norojono and Young [35]☆☆☆☆☆☆☆Train and Wilson [36]☆☆☆Arunotayanun and Polak [37]☆☆☆☆☆☆☆Patterson et al. [38]☆☆☆☆De Jong [39]☆☆☆☆☆☆☆Cavalcante and Roorda [40]☆☆☆Windisch et al. [41]☆☆☆☆☆☆Samimi et al. [42]☆☆☆☆Lloret-Batlle and Combes [43]☆☆☆☆☆☆Pourabdollahi et al. [44]☆☆☆☆Abate and de Jong [45]☆☆☆Stinson et al. [46]☆☆☆☆Roman et al. [47]☆☆☆☆Kim et al. [48]☆☆☆☆Larranaga et al. [49]☆☆☆Abate et al. [50]☆☆☆☆☆☆Jensen et al. [51]☆☆☆☆☆Keya et al. [52]☆☆☆☆☆☆☆Comi and Polimeni [53]☆☆☆☆This paperTransport economic valueFreight volumeIndustrial structureComplete consumption factor


### 2.2. Input-Output Model

There are three main types of input-output models: inter-regional model-IRIO [54, 55], multiple model-MRIO [56], and multiregional econometrics model [57, 58]. Izard et al. [59] proposed an inter-regional input-output model, which introduced a trade coefficient, which represents the proportion of product m produced and used in region j used in the production and use of product n in the region. Because the proportion of trade is difficult to estimate, Moses [60] simplified the calculation of the trade coefficient, considering only the trade flow and no longer the destination. The wrong estimation of the trade coefficient may cause a large deviation in the forecast of freight traffic, which requires multiple corrections [61]. Miller [62] gave a detailed application explanation of the input-output model and constructed a fitting model of transportation and economy. Voigtlaender [63] applied a dynamic input-output model to forecast freight demand in the United States. Rey [64] discussed the application of econometrics in the input-output table model and studied the alternative methods and models of the input-output model. Havenga and Simpson [65] used an economic input-output (I-O) model as a platform, supplemented by actual data, developed supply and demand data classified by space and sector, and converted the supply and demand of South African freight into a freight flow through a gravity model. The above literature has conducted a lot of research on the application of input-output models from the perspective of theory and practice and provided theoretical and methodological support for the research of this paper.


### 2.3. Forecast of Freight Traffic

Freight forecasting models can be grouped into five classes: the economic activity model, the four-step commodity model, the Origin-Destination (O-D) factoring method, the Flow Factoring Method (FFM), and the truck model. Many kinds of literature have used a variety of methods and models to predict freight volume from the national level, such as Daugherty [66], Picard and Nguyen [67], Mazzarino [68], and Regan and Garrido [69]. There are multiple measurement standards for freight traffic, and the common measurement standards are tons, ton-kilometers, and transportation costs (transportation costs or prices paid for transportation services). The accuracy of forecasting freight volume depends on the classification and aggregation of data and the estimated model [70, 71]. Among the influencing factors of freight demand, the most important influencing factors are consumer demand, production structure, and trade mode [72, 73]. Castro-Neto et al. [74] used the online support vector regression algorithm to predict the traffic flow of the road with good prediction accuracy. Chen [75] constructed a comprehensive transportation network, organically combined multiple transportation modes, and improved the accuracy of travel choice model prediction. Ahn et al. [76] combined Bayesian classifier and vector regression to predict the traffic demand of expressways and predicted and analyzed the expressway freight volume of Korea. Garrido and Mahmassani [77] developed a multinomial probit (MNP) model, which predicts freight volume based on time and space changes in transportation. Studies have shown that the model is more accurate. Pompigna and Mauro [78] used Italian economic data from 2000 to 2014 as the basis and used the macro-input-output method to analyze freight demand and forecasted Italian freight volume in 2027. The above research uses a variety of models and methods to forecast freight traffic. Generally speaking, national freight volume forecasting models are the integration of macroeconomic models.


## 2.1. Factors Affecting Freight Demand

Robert et al. [22] have identified and evaluated the factors of freight demand. Their research shows that population, economic activities, fuel prices, environment, and policies are the main influencing factors, among which GDP and GDP per capita are commonly used indicators of economic activity. Fite et al. [23] conducted regression analysis on 107 indexes related to freight volume and believed that the producer commodity price index of construction materials and equipment (PCPI-CM&E) was the most relevant parameter. Agnolucci and Bonilla [24] conducted a study on the relationship between freight volume and GDP in the UK from 1956 to 2003. Their research found that the decoupling of freight volume and GDP accelerated, and the price and income elasticity also decreased to 18% and 65%. Wang et al. [25] proposed a hierarchical model. The model shows that the demand for truck freight can be estimated by truck traffic, population, number of companies, and income. Short et al. [26] studied the relationship between Sweden’s economic activities and freight volume. The study found that, in the short and medium term, changes in imports and exports led to large fluctuations in freight demand; in the long run, freight demand and GDP are coupled, and there is no sign of decoupling. Wijeweera et al. [27] studied the impact of freight prices, international trade, and business cycles on Australia’s rail freight demand. Their study shows that the fluctuation of freight rates and the Australian dollar was the most important factor affecting Australian rail freight. Alises and Vassallo [28] studied the impact of economic growth, industrial structure, and road transport intensity on the demand for road freight. The results show that, overall, the growth of total road transport demand is mainly driven by economic activities. Patil and Sahu [29] used regression and time series models to estimate the freight demand of Mumbai ports. Their research concluded that GDP and crude oil production are the most important factors affecting freight. Wang et al. [30] analyzed the relationship between freight demand and economic development. They believe that China’s overall economic development is decoupled from freight development, and the intensity of transportation is declining. Khan and Khan [31] analyzed the demand for rail freight in Pakistan. The study showed that GDP and freight are the two most important determinants of rail freight demand. Table 1 shows the comparison between some studies and this paper.Table 1
Comparison of some research studies and this paper.
References/Influencing factorsTransportation supply characteristicsTransport demand characteristicsOtherFreight costFreight timeReliabilityCargo damage costTransport distanceTransport frequencyCargo capacityProduct sizeProduct typesCommodity valueIndustryInventory costDelivery frequencyInteractive termTerminal accessibilityDewey et al. [32]☆☆☆Holguín-Veras [33]☆☆☆☆Kim [34]☆☆☆Norojono and Young [35]☆☆☆☆☆☆☆Train and Wilson [36]☆☆☆Arunotayanun and Polak [37]☆☆☆☆☆☆☆Patterson et al. [38]☆☆☆☆De Jong [39]☆☆☆☆☆☆☆Cavalcante and Roorda [40]☆☆☆Windisch et al. [41]☆☆☆☆☆☆Samimi et al. [42]☆☆☆☆Lloret-Batlle and Combes [43]☆☆☆☆☆☆Pourabdollahi et al. [44]☆☆☆☆Abate and de Jong [45]☆☆☆Stinson et al. [46]☆☆☆☆Roman et al. [47]☆☆☆☆Kim et al. [48]☆☆☆☆Larranaga et al. [49]☆☆☆Abate et al. [50]☆☆☆☆☆☆Jensen et al. [51]☆☆☆☆☆Keya et al. [52]☆☆☆☆☆☆☆Comi and Polimeni [53]☆☆☆☆This paperTransport economic valueFreight volumeIndustrial structureComplete consumption factor


## 2.2. Input-Output Model

There are three main types of input-output models: inter-regional model-IRIO [54, 55], multiple model-MRIO [56], and multiregional econometrics model [57, 58]. Izard et al. [59] proposed an inter-regional input-output model, which introduced a trade coefficient, which represents the proportion of product m produced and used in region j used in the production and use of product n in the region. Because the proportion of trade is difficult to estimate, Moses [60] simplified the calculation of the trade coefficient, considering only the trade flow and no longer the destination. The wrong estimation of the trade coefficient may cause a large deviation in the forecast of freight traffic, which requires multiple corrections [61]. Miller [62] gave a detailed application explanation of the input-output model and constructed a fitting model of transportation and economy. Voigtlaender [63] applied a dynamic input-output model to forecast freight demand in the United States. Rey [64] discussed the application of econometrics in the input-output table model and studied the alternative methods and models of the input-output model. Havenga and Simpson [65] used an economic input-output (I-O) model as a platform, supplemented by actual data, developed supply and demand data classified by space and sector, and converted the supply and demand of South African freight into a freight flow through a gravity model. The above literature has conducted a lot of research on the application of input-output models from the perspective of theory and practice and provided theoretical and methodological support for the research of this paper.


## 2.3. Forecast of Freight Traffic

Freight forecasting models can be grouped into five classes: the economic activity model, the four-step commodity model, the Origin-Destination (O-D) factoring method, the Flow Factoring Method (FFM), and the truck model. Many kinds of literature have used a variety of methods and models to predict freight volume from the national level, such as Daugherty [66], Picard and Nguyen [67], Mazzarino [68], and Regan and Garrido [69]. There are multiple measurement standards for freight traffic, and the common measurement standards are tons, ton-kilometers, and transportation costs (transportation costs or prices paid for transportation services). The accuracy of forecasting freight volume depends on the classification and aggregation of data and the estimated model [70, 71]. Among the influencing factors of freight demand, the most important influencing factors are consumer demand, production structure, and trade mode [72, 73]. Castro-Neto et al. [74] used the online support vector regression algorithm to predict the traffic flow of the road with good prediction accuracy. Chen [75] constructed a comprehensive transportation network, organically combined multiple transportation modes, and improved the accuracy of travel choice model prediction. Ahn et al. [76] combined Bayesian classifier and vector regression to predict the traffic demand of expressways and predicted and analyzed the expressway freight volume of Korea. Garrido and Mahmassani [77] developed a multinomial probit (MNP) model, which predicts freight volume based on time and space changes in transportation. Studies have shown that the model is more accurate. Pompigna and Mauro [78] used Italian economic data from 2000 to 2014 as the basis and used the macro-input-output method to analyze freight demand and forecasted Italian freight volume in 2027. The above research uses a variety of models and methods to forecast freight traffic. Generally speaking, national freight volume forecasting models are the integration of macroeconomic models.


## 3. Problem Description and Modelling

### 3.1. Model Description

The basic composition of the model is(1)
Direct consumption coefficient: the direct consumption coefficient refers to the value of the unit’s total output of thejth product sector directly consumed by the ith product sector in the production process, usually recorded as aiji,j=1,2,…,n. The formula of aij is(1)aij=xijXj,wherexij represents the input amount provided by the ith sector as an intermediate product to the jth sector and Xj represents the total investment of the jth sector.(2)
Complete consumption coefficient: the complete consumption coefficient is the number of products completely consumed by thejth sector when producing a unit product. It is called the complete consumption coefficient of the jth sector for the first sector, usually denoted as bij. The complete consumption coefficient is the sum of direct consumption and all indirect consumption, and the calculation formula is(2)bij=aij+∑k=1nakjbjk.The matrix formula isB = A + BA, and the formula for solving the complete consumption matrix can be obtained:(3)B=I−A−1−I.(3)
Balance formula: the input-output table has two important balance relationships, namely, row balance and column balance. Line balance: intermediate use + final use = total output:(4)∑j=1naijxij+Yi=Xi,i=1,2,…,n,whereYi represents the final use amount provided by the ith sector andXi represents the total output of the ith sector.Its matrix is expressed asAX+Y=X.Column balance: initial investment + intermediate investment = total investment:(5)∑i=1nxij+Nj=Xj,j=1,2,…,n,where Nj represents the added value of the jth sector.


### 3.2. Model Assumptions

The basis of the input-output theory is Walras’ general equilibrium theory, which involves the following basic assumptions.


#### 3.2.1. Homogeneity Assumption

Assume that each industrial sector produces only one homogeneous product. That is, the product is completely replaceable in this department but irreplaceable in other departments.


#### 3.2.2. Proportionality Assumption

The input and output of the department are directly proportional, that is, there is a linear relationship between input and output.


#### 3.2.3. Stability Assumption

The technology, production process, and management level are relatively stable.


### 3.3. Division of Departments

This paper uses the input-output tables compiled by China from 2002 to 2017 as the basic data. To facilitate model processing and analysis, the 135 departments, 149 departments, and 41 departments in different years have been uniformly adjusted to 42 departments. The specific divisions are shown in Table2.Table 2
42 sectors of the three industries.
NumberingIndustry name1Agriculture, forestry, animal husbandry, and fishery2Coal mining and washing industry3Oil and gas extraction industry4Metal mining and dressing industry5Nonmetallic minerals and other mining and dressing industries6Food manufacturing and tobacco processing industry7Textile industry8Textile, clothing, shoes, hats, leather down, and its products’ industry9Wood processing and furniture manufacturing10Papermaking, printing and cultural, educational, and sporting goods manufacturing11Petroleum processing, coking, and nuclear fuel processing industry12Chemical industry13Nonmetallic mineral products’ industry14Metal smelting and rolling processing industry15Metal products’ industry16General and special equipment manufacturing industry17Transportation equipment manufacturing18Electrical machinery and equipment manufacturing19Communication equipment, computer, and other electronic equipment manufacturing20Instrumentation and cultural office machinery manufacturing21Crafts and other manufacturing22Scrap23Electricity and heat production and supply industry24Gas production and supply industry25Water production and supply industry26Construction industry27Transportation and storage industry28Postal industry29Information transmission, computer service, and software industry30Wholesale and retail31Accommodation and catering industry32Financial industry33Real estate34Leasing and business services35Research and rxperimental development36Comprehensive technical service industry37Water conservancy, environment, and public facilities management industry38Resident services and other services39Education40Health, social security, and social welfare industries41Culture, sports, and entertainment industry42Public administration and Social OrganizationData source: National Bureau of Statistics of China.


### 3.4. Decomposition of the Input-Output Model

According to the construction principle of the input-output table, the growth of transportation demand can be decomposed into three parts: increase in transportation demand caused by economic growth, industrial relevance and changes in production technology lead to the increase in transportation demand caused by changes in the complete consumption coefficient, and changes in transportation demand caused by the upgrading of industrial structure. Since the input-output table uses the value as the unit of measurement, the formula for calculating the economic valueQ of transportation can be expressed as(6)Q=Z∗X,where Z represents transportation intensity and X represents the total output.Taking the derivative of the above formula, we can obtain(7)∂Q=X∂Z+Z∂X.BecauseZ=Q/X=∑bjXj/X=∑bjsj, where bj represents the complete consumption coefficient of each department for transportation, Xj represents the total output of each department, and sj represents the proportion of each department’s output to the total output.The matrix of the above formula is expressed asZ = B × S, where B is the complete consumption coefficient matrix and S is the structural variable.Taking the derivative of formulas (3)–(8), we can obtain(8)∂Z=S∂B+B∂S.Putting formulas (8) and (9) into (7), we can obtain(9)∂Q=SX∂B+XB∂S+BS∂X,where SX∂B represents the changes in the transportation economy caused by changes in the complete consumption coefficient, XB∂S represents the changes in the transportation economy caused by changes in the industrial structure, and BS∂X represents the changes in the transportation economy caused by changes in the total economic scale.In the time period [0,t], the change of the economic value of transportation is(10)ΔQ=Qt−Q0=BtStXt−B0S0X0.LetBt=B0+ΔB, St=S0+ΔS, and Xt=X0+ΔX, and formula (11) can be expressed as follows:(11)ΔQ=Qt−Q0=ΔBS0X0+B0ΔSX0+B0S0ΔX+B0ΔSΔX+ΔBS0ΔX+ΔBΔSX0+ΔBΔSΔX,with Q=ZX=∑bjsjX, the demand for transportation value caused by different departments can be obtained as(12)Qj=bjsjX.Letbjt=bj0+Δbj, sjt=sj0+Δsj, and Xt=X0+ΔX; then, in the period [0, t], the changes in the economic value of transportation caused by different sectors are(13)ΔQj=Qjt−Qj0=bjtsjtXt−bj0sj0X0=Δbjsj0X0+bj0ΔsjX0+bj0sj0ΔX+bj0ΔsjΔX+Δbjsj0ΔX+ΔbjΔsjX0+ΔbjΔsjΔX.Combining the factors that cause the economic value of transportation into similar items and decomposing them according to the complete consumption coefficient change, industrial structure change, and total output change, the change in the economic value of transportation can be expressed as(14)ΔQj=bjq+sjq+Xjq,bjq=Δbjsj0ΔX+12Δbjsj0ΔX+ΔbjΔsjX0+13ΔbjΔsjΔX,sjq=bj0ΔsjX0+12bj0ΔsjΔX+ΔbjΔsjX0+13ΔbjΔsjΔX,Xjq=bj0sj0ΔX+12bj0ΔsjΔX+ΔbjΔsj0ΔX+13ΔbjΔsjΔX,where bjq, sjq, and Xjq, respectively, represent the impact of changes in the complete consumption coefficient, changes in industrial structure, and total output on the economic value of transportation.


## 3.1. Model Description

The basic composition of the model is(1)
Direct consumption coefficient: the direct consumption coefficient refers to the value of the unit’s total output of thejth product sector directly consumed by the ith product sector in the production process, usually recorded as aiji,j=1,2,…,n. The formula of aij is(1)aij=xijXj,wherexij represents the input amount provided by the ith sector as an intermediate product to the jth sector and Xj represents the total investment of the jth sector.(2)
Complete consumption coefficient: the complete consumption coefficient is the number of products completely consumed by thejth sector when producing a unit product. It is called the complete consumption coefficient of the jth sector for the first sector, usually denoted as bij. The complete consumption coefficient is the sum of direct consumption and all indirect consumption, and the calculation formula is(2)bij=aij+∑k=1nakjbjk.The matrix formula isB = A + BA, and the formula for solving the complete consumption matrix can be obtained:(3)B=I−A−1−I.(3)
Balance formula: the input-output table has two important balance relationships, namely, row balance and column balance. Line balance: intermediate use + final use = total output:(4)∑j=1naijxij+Yi=Xi,i=1,2,…,n,whereYi represents the final use amount provided by the ith sector andXi represents the total output of the ith sector.Its matrix is expressed asAX+Y=X.Column balance: initial investment + intermediate investment = total investment:(5)∑i=1nxij+Nj=Xj,j=1,2,…,n,where Nj represents the added value of the jth sector.


## 3.2. Model Assumptions

The basis of the input-output theory is Walras’ general equilibrium theory, which involves the following basic assumptions.


### 3.2.1. Homogeneity Assumption

Assume that each industrial sector produces only one homogeneous product. That is, the product is completely replaceable in this department but irreplaceable in other departments.


### 3.2.2. Proportionality Assumption

The input and output of the department are directly proportional, that is, there is a linear relationship between input and output.


### 3.2.3. Stability Assumption

The technology, production process, and management level are relatively stable.


## 3.2.1. Homogeneity Assumption

Assume that each industrial sector produces only one homogeneous product. That is, the product is completely replaceable in this department but irreplaceable in other departments.


## 3.2.2. Proportionality Assumption

The input and output of the department are directly proportional, that is, there is a linear relationship between input and output.


## 3.2.3. Stability Assumption

The technology, production process, and management level are relatively stable.


## 3.3. Division of Departments

This paper uses the input-output tables compiled by China from 2002 to 2017 as the basic data. To facilitate model processing and analysis, the 135 departments, 149 departments, and 41 departments in different years have been uniformly adjusted to 42 departments. The specific divisions are shown in Table2.Table 2
42 sectors of the three industries.
NumberingIndustry name1Agriculture, forestry, animal husbandry, and fishery2Coal mining and washing industry3Oil and gas extraction industry4Metal mining and dressing industry5Nonmetallic minerals and other mining and dressing industries6Food manufacturing and tobacco processing industry7Textile industry8Textile, clothing, shoes, hats, leather down, and its products’ industry9Wood processing and furniture manufacturing10Papermaking, printing and cultural, educational, and sporting goods manufacturing11Petroleum processing, coking, and nuclear fuel processing industry12Chemical industry13Nonmetallic mineral products’ industry14Metal smelting and rolling processing industry15Metal products’ industry16General and special equipment manufacturing industry17Transportation equipment manufacturing18Electrical machinery and equipment manufacturing19Communication equipment, computer, and other electronic equipment manufacturing20Instrumentation and cultural office machinery manufacturing21Crafts and other manufacturing22Scrap23Electricity and heat production and supply industry24Gas production and supply industry25Water production and supply industry26Construction industry27Transportation and storage industry28Postal industry29Information transmission, computer service, and software industry30Wholesale and retail31Accommodation and catering industry32Financial industry33Real estate34Leasing and business services35Research and rxperimental development36Comprehensive technical service industry37Water conservancy, environment, and public facilities management industry38Resident services and other services39Education40Health, social security, and social welfare industries41Culture, sports, and entertainment industry42Public administration and Social OrganizationData source: National Bureau of Statistics of China.


## 3.4. Decomposition of the Input-Output Model

According to the construction principle of the input-output table, the growth of transportation demand can be decomposed into three parts: increase in transportation demand caused by economic growth, industrial relevance and changes in production technology lead to the increase in transportation demand caused by changes in the complete consumption coefficient, and changes in transportation demand caused by the upgrading of industrial structure. Since the input-output table uses the value as the unit of measurement, the formula for calculating the economic valueQ of transportation can be expressed as(6)Q=Z∗X,where Z represents transportation intensity and X represents the total output.Taking the derivative of the above formula, we can obtain(7)∂Q=X∂Z+Z∂X.BecauseZ=Q/X=∑bjXj/X=∑bjsj, where bj represents the complete consumption coefficient of each department for transportation, Xj represents the total output of each department, and sj represents the proportion of each department’s output to the total output.The matrix of the above formula is expressed asZ = B × S, where B is the complete consumption coefficient matrix and S is the structural variable.Taking the derivative of formulas (3)–(8), we can obtain(8)∂Z=S∂B+B∂S.Putting formulas (8) and (9) into (7), we can obtain(9)∂Q=SX∂B+XB∂S+BS∂X,where SX∂B represents the changes in the transportation economy caused by changes in the complete consumption coefficient, XB∂S represents the changes in the transportation economy caused by changes in the industrial structure, and BS∂X represents the changes in the transportation economy caused by changes in the total economic scale.In the time period [0,t], the change of the economic value of transportation is(10)ΔQ=Qt−Q0=BtStXt−B0S0X0.LetBt=B0+ΔB, St=S0+ΔS, and Xt=X0+ΔX, and formula (11) can be expressed as follows:(11)ΔQ=Qt−Q0=ΔBS0X0+B0ΔSX0+B0S0ΔX+B0ΔSΔX+ΔBS0ΔX+ΔBΔSX0+ΔBΔSΔX,with Q=ZX=∑bjsjX, the demand for transportation value caused by different departments can be obtained as(12)Qj=bjsjX.Letbjt=bj0+Δbj, sjt=sj0+Δsj, and Xt=X0+ΔX; then, in the period [0, t], the changes in the economic value of transportation caused by different sectors are(13)ΔQj=Qjt−Qj0=bjtsjtXt−bj0sj0X0=Δbjsj0X0+bj0ΔsjX0+bj0sj0ΔX+bj0ΔsjΔX+Δbjsj0ΔX+ΔbjΔsjX0+ΔbjΔsjΔX.Combining the factors that cause the economic value of transportation into similar items and decomposing them according to the complete consumption coefficient change, industrial structure change, and total output change, the change in the economic value of transportation can be expressed as(14)ΔQj=bjq+sjq+Xjq,bjq=Δbjsj0ΔX+12Δbjsj0ΔX+ΔbjΔsjX0+13ΔbjΔsjΔX,sjq=bj0ΔsjX0+12bj0ΔsjΔX+ΔbjΔsjX0+13ΔbjΔsjΔX,Xjq=bj0sj0ΔX+12bj0ΔsjΔX+ΔbjΔsj0ΔX+13ΔbjΔsjΔX,where bjq, sjq, and Xjq, respectively, represent the impact of changes in the complete consumption coefficient, changes in industrial structure, and total output on the economic value of transportation.


## 4. Algorithm

### 4.1. Total Output Forecast

The total output of a department refers to the total value of all goods and services produced by the department in a certain period. To predict the total output of a department, you can first predict the added value of each department and then use the input-output model to calculate the total output of each department.According to the column balance principleAcX+N=X in the input-output table, the total output of the ith sector can be calculated as(15)Xi=1−Ac−1GDPi,i=1,2,…,n.Because gray prediction is an exponential growth prediction, its prediction interval is trumpet-shaped, and the accuracy is poor in medium and long-term predictions. Therefore, to ensure the accuracy of the prediction, this paper adopts the equal-dimensional gray number recursive dynamic prediction method. The basic principle of this method [79] is that only one value is predicted at a time, and the predicted value is used to replace the first value of the original data sequence, keeping the same dimension and predicting one by one, which speeds up the convergence of the predicted value with high accuracy. From the verification results, the 7-dimensional prediction overemphasizes the extension of the past trend, and the prediction is too high, the 5-dimensional prediction overemphasizes the extension of the recent trend, and the prediction is lower, and the 6-dimensional prediction is more appropriate.


### 4.2. Complete Consumption Coefficient Prediction

The RAS method, also known as the biproportional scaling method, was proposed by Deming and Stephan [80] in 1940. The basic principle is to first assume that the input structure of the target year and the base year are the same. Under the control of the total output and intermediate use in the target year, use a set of row control vectors and a set of column control vectors to adjust the base year accordingly. Each row element and each column element of the direct consumption coefficient matrix in the input-output table makes the total calculated direct consumption coefficient equal to each control data. The mathematical expression of the RAS method is(16)At=R^A0S^,where At is the direct consumption coefficient matrix of the target year, A0 is the direct consumption coefficient matrix of the base year, R^ is the total row multiplier matrix, and S^ is the total column multiplier matrix.The total row multiplier matrixR^=r^kr^k−1,…,r^2r^1 can reflect the degree to which intermediate products are replaced by other products. Multiply A0 by R^ left: if an intermediate product in a row in A0 is replaced by other products, all other intermediate products in this row will be replaced by other products to the same extent. The total column multiplier matrix S^=s^1s^2,…,s^l−1s^l can reflect the degree of consumption of other departments by each department in the production process. Multiply A0 by S^ right: if the intermediate input of an intermediate product in a column of A0 increases, the intermediate input of all other intermediate products in this column will increase by the same degree.


### 4.3. Economic Forecast

Assuming that the return to scale of the production function remains unchanged and according to the global economic growth model, it is estimated that China’s total GDP as(17)GDP=TFP×Kα×L1−α,where TFP represents total factor productivity, K represents capital stock, L represents the total labor force, and α represents the output elasticity of capital. According to the calculation of most scholars, α is 0.55. According to the basic laws of world economic development, when an economy enters a capital surplus, the output elasticity of capital will gradually decrease, while the output elasticity of labor will slowly rise. Therefore, this paper assumes that the elasticity of capital-output will slowly decline from 0.6 in 2016 to 0.45 in 2035 and further to 0.4 in 2050.Step 1 (predict the total labor force): the formula is(18)lnPt=α×lnPt−1,wherePt is the labor participation rate in year t, Pt−1 is the labor participation rate in the previous year in year t, and α is a constant parameter.The labor participation rate refers to the ratio of the total employed population to the total population. Statistics from the National Bureau of Statistics of China show that, between 1995 and 2015, China’s labor participation rate reached an average of about 56%, and it was quite stable. Based on this, it can be assumed that, between 2020–2050, China’s labor participation rate will also remain at around 56%. The prediction results are shown in Table3.Step 2 (predict the capital stock): the formula is(19)Kgrowth=KtKt−1−1=It−1Kt−1−6%,whereKgrowth is the growth rate of capital stock, It−1 is the amount of capital investment in the previous year, and 6% represents the annual depreciation rate of capital. Since 2010, the growth rate of China’s capital stock has been declining. The decline in capital growth may be due to the adjustment of the industrial structure. This paper predicts that, from 2021 to 2030, the average annual growth rate of capital is 7%, from 2031 to 2040, the average annual growth rate of capital is 5%, and from 2041 to 2050, the average annual growth rate of capital is 3%.Step 3 (forecast total factor productivity): the formula is(20)TFPgrowth=1.3%+CB−FP,where 1.3% is the potential growth rate of TFP, CB represents the growth rate of inertial growth in emerging developing countries, and FP represents factors that hinder productivity growth from failure. The formula for inertial growth rate is(21)CB=c∗2.33%∗lnTFPUSA,t−1TFPi,t−1,where 2.33% is a parameter of development inertia, calculated from historical data, andc is the national development speed parameter. The value is 1 for high-growth countries, 0 for declining countries, and c is between 0 and 1. Economic development itself has inertia, so this paper believes that China’s economic growth inertia CB is about 0.3.Table 3
China’s total population and employment forecast (2020–2050).
YearTotal population (unit: 100 million people)Employment rate (unit: %)Number of employees (unit: 100 million people)201513.678256.347.7063202014.050556.77.9666203014.320356.918.1497204013.864756.947.8946205012.747156.957.2595Note. The 2015 data comes from the National Bureau of Statistics of China, and the rest of the data are predicted by the author. Among them, the birth rate is assumed to be maintained at the level of 2019, and the average life expectancy is 77 years.The hindering factor FB formula is(22)FB=f∗1.8%,where f is a hindering parameter, and its nature is opposite to c. It is 1 for declining countries and 0 for high-growth countries. Since China is an emerging developing country, the value of f should be between 0 and 0.5. Since 2006, China’s total factor productivity has gradually declined. Total factor productivity is composed of human capital, R&D innovation, infrastructure, urbanization rate, and investment rate. Due to the aging of the population, the gradual improvement of infrastructure, and the decline in investment, the growth rate of TFP will continue to decline slowly in the future Trend [37]. Therefore, this paper predicts that the TFP growth rate will be 1.5% from 2021 to 2030, 1.4% from 2031 to 4040, and 1.3% from 2041 to 5050.In summary, under the baseline scenario, China’s economic development will achieve an average annual growth rate of 4.8% from 2020 to 2035 and an average annual growth rate of 3.4% from 2036 to 2050.


### 4.4. Industrial Structure Forecast

Use the gray system structure prediction method to predict the industrial structure in the input-output table. The calculation steps and methods are briefly described as follows.Step 1: list the original data. Take the intermediate input data and intermediate output data of 42 industrial sectors in the 2002–2017 input-output table as the modeling sequence.Step 2: establish a gray dynamic GM (1,1) model for the above data series. The model can reflectN related factors, and the equation of the gray state model is(23)X1=aX1+u,wherea represents the coordination coefficient between the variables.Step 3: according to the above GM model group, list the system state equation matrix:(24)X˙1X˙2⋮X˙n=a11a22⋱ann·X1X2⋮Xn+u1u2⋮un,or it is written as(25)X˙=X+U.Predict the main indicator values of each quadrant, and calculate the structure of the intermediate input and intermediate output, respectively.Step 4: use the Runge–Kutta method to solve the system state equation.Step 5: perform cumulative reduction on the solution results of the equation to obtain the fitted and predicted values of each factor in the system and analyze the results. If there is a deviation, the coefficient matrix can be adjusted, simulated, and analyzed step by step to achieve a better prediction effect.


## 4.1. Total Output Forecast

The total output of a department refers to the total value of all goods and services produced by the department in a certain period. To predict the total output of a department, you can first predict the added value of each department and then use the input-output model to calculate the total output of each department.According to the column balance principleAcX+N=X in the input-output table, the total output of the ith sector can be calculated as(15)Xi=1−Ac−1GDPi,i=1,2,…,n.Because gray prediction is an exponential growth prediction, its prediction interval is trumpet-shaped, and the accuracy is poor in medium and long-term predictions. Therefore, to ensure the accuracy of the prediction, this paper adopts the equal-dimensional gray number recursive dynamic prediction method. The basic principle of this method [79] is that only one value is predicted at a time, and the predicted value is used to replace the first value of the original data sequence, keeping the same dimension and predicting one by one, which speeds up the convergence of the predicted value with high accuracy. From the verification results, the 7-dimensional prediction overemphasizes the extension of the past trend, and the prediction is too high, the 5-dimensional prediction overemphasizes the extension of the recent trend, and the prediction is lower, and the 6-dimensional prediction is more appropriate.


## 4.2. Complete Consumption Coefficient Prediction

The RAS method, also known as the biproportional scaling method, was proposed by Deming and Stephan [80] in 1940. The basic principle is to first assume that the input structure of the target year and the base year are the same. Under the control of the total output and intermediate use in the target year, use a set of row control vectors and a set of column control vectors to adjust the base year accordingly. Each row element and each column element of the direct consumption coefficient matrix in the input-output table makes the total calculated direct consumption coefficient equal to each control data. The mathematical expression of the RAS method is(16)At=R^A0S^,where At is the direct consumption coefficient matrix of the target year, A0 is the direct consumption coefficient matrix of the base year, R^ is the total row multiplier matrix, and S^ is the total column multiplier matrix.The total row multiplier matrixR^=r^kr^k−1,…,r^2r^1 can reflect the degree to which intermediate products are replaced by other products. Multiply A0 by R^ left: if an intermediate product in a row in A0 is replaced by other products, all other intermediate products in this row will be replaced by other products to the same extent. The total column multiplier matrix S^=s^1s^2,…,s^l−1s^l can reflect the degree of consumption of other departments by each department in the production process. Multiply A0 by S^ right: if the intermediate input of an intermediate product in a column of A0 increases, the intermediate input of all other intermediate products in this column will increase by the same degree.


## 4.3. Economic Forecast

Assuming that the return to scale of the production function remains unchanged and according to the global economic growth model, it is estimated that China’s total GDP as(17)GDP=TFP×Kα×L1−α,where TFP represents total factor productivity, K represents capital stock, L represents the total labor force, and α represents the output elasticity of capital. According to the calculation of most scholars, α is 0.55. According to the basic laws of world economic development, when an economy enters a capital surplus, the output elasticity of capital will gradually decrease, while the output elasticity of labor will slowly rise. Therefore, this paper assumes that the elasticity of capital-output will slowly decline from 0.6 in 2016 to 0.45 in 2035 and further to 0.4 in 2050.Step 1 (predict the total labor force): the formula is(18)lnPt=α×lnPt−1,wherePt is the labor participation rate in year t, Pt−1 is the labor participation rate in the previous year in year t, and α is a constant parameter.The labor participation rate refers to the ratio of the total employed population to the total population. Statistics from the National Bureau of Statistics of China show that, between 1995 and 2015, China’s labor participation rate reached an average of about 56%, and it was quite stable. Based on this, it can be assumed that, between 2020–2050, China’s labor participation rate will also remain at around 56%. The prediction results are shown in Table3.Step 2 (predict the capital stock): the formula is(19)Kgrowth=KtKt−1−1=It−1Kt−1−6%,whereKgrowth is the growth rate of capital stock, It−1 is the amount of capital investment in the previous year, and 6% represents the annual depreciation rate of capital. Since 2010, the growth rate of China’s capital stock has been declining. The decline in capital growth may be due to the adjustment of the industrial structure. This paper predicts that, from 2021 to 2030, the average annual growth rate of capital is 7%, from 2031 to 2040, the average annual growth rate of capital is 5%, and from 2041 to 2050, the average annual growth rate of capital is 3%.Step 3 (forecast total factor productivity): the formula is(20)TFPgrowth=1.3%+CB−FP,where 1.3% is the potential growth rate of TFP, CB represents the growth rate of inertial growth in emerging developing countries, and FP represents factors that hinder productivity growth from failure. The formula for inertial growth rate is(21)CB=c∗2.33%∗lnTFPUSA,t−1TFPi,t−1,where 2.33% is a parameter of development inertia, calculated from historical data, andc is the national development speed parameter. The value is 1 for high-growth countries, 0 for declining countries, and c is between 0 and 1. Economic development itself has inertia, so this paper believes that China’s economic growth inertia CB is about 0.3.Table 3
China’s total population and employment forecast (2020–2050).
YearTotal population (unit: 100 million people)Employment rate (unit: %)Number of employees (unit: 100 million people)201513.678256.347.7063202014.050556.77.9666203014.320356.918.1497204013.864756.947.8946205012.747156.957.2595Note. The 2015 data comes from the National Bureau of Statistics of China, and the rest of the data are predicted by the author. Among them, the birth rate is assumed to be maintained at the level of 2019, and the average life expectancy is 77 years.The hindering factor FB formula is(22)FB=f∗1.8%,where f is a hindering parameter, and its nature is opposite to c. It is 1 for declining countries and 0 for high-growth countries. Since China is an emerging developing country, the value of f should be between 0 and 0.5. Since 2006, China’s total factor productivity has gradually declined. Total factor productivity is composed of human capital, R&D innovation, infrastructure, urbanization rate, and investment rate. Due to the aging of the population, the gradual improvement of infrastructure, and the decline in investment, the growth rate of TFP will continue to decline slowly in the future Trend [37]. Therefore, this paper predicts that the TFP growth rate will be 1.5% from 2021 to 2030, 1.4% from 2031 to 4040, and 1.3% from 2041 to 5050.In summary, under the baseline scenario, China’s economic development will achieve an average annual growth rate of 4.8% from 2020 to 2035 and an average annual growth rate of 3.4% from 2036 to 2050.


## 4.4. Industrial Structure Forecast

Use the gray system structure prediction method to predict the industrial structure in the input-output table. The calculation steps and methods are briefly described as follows.Step 1: list the original data. Take the intermediate input data and intermediate output data of 42 industrial sectors in the 2002–2017 input-output table as the modeling sequence.Step 2: establish a gray dynamic GM (1,1) model for the above data series. The model can reflectN related factors, and the equation of the gray state model is(23)X1=aX1+u,wherea represents the coordination coefficient between the variables.Step 3: according to the above GM model group, list the system state equation matrix:(24)X˙1X˙2⋮X˙n=a11a22⋱ann·X1X2⋮Xn+u1u2⋮un,or it is written as(25)X˙=X+U.Predict the main indicator values of each quadrant, and calculate the structure of the intermediate input and intermediate output, respectively.Step 4: use the Runge–Kutta method to solve the system state equation.Step 5: perform cumulative reduction on the solution results of the equation to obtain the fitted and predicted values of each factor in the system and analyze the results. If there is a deviation, the coefficient matrix can be adjusted, simulated, and analyzed step by step to achieve a better prediction effect.


## 5. Model Construction and Forecasting

### 5.1. Forecast and Analysis of the Economic Value of Transportation

Through the analysis of total output, industrial structure, and complete consumption coefficient, combined with the basic data of the input-output table from 2002 to 2017, the economic value of transportation in 2035 and 2050 can be predicted. The forecast data is shown in Tables4 and 5.Table 4
Forecast the value of each Industry’s demand for transportation in 2035.
Industry numberTotal output (unit: ten thousand yuan)Complete consumption coefficient for transportationValue of demand for transportation (unit: ten thousand yuan)Percentage (%)11694385607.671580.0954161562882.6498932.322298638845.7190850.057517175036.816530.253229301196.8363650.03959049175.657358430.134129307146.7753680.05016484079.065088760.095211843472.61720.106022453457.22009240.3263228474316.226450.1053340105785.7123924.887853635246.666950.1376117422343.6285791.698841006714.6023470.1546129998582.753921.879609580270.1159720.121474024374.91930831.0610890071738.0402420.1254111632630.3124711.6011798728493.8158420.106384897524.76209981.22124039139792.042840.1386559648454.6807458.03131880344512.127540.1396262428339.8385583.77142504229609.093180.1066266973521.4798663.83151065158416.304540.1155123006525.7929541.77161682978234.460360.1205202876346.3669292.91172429683947.140230.1271308797754.6677914.43181370308888.667530.1164159468719.3754152.29192612610892.337140.1040271783708.5527323.9020196602250.5810080.106820990293.53686990.302159787097.24149240.13227903185.386350470.1122136893612.6089030.06739218409.264253350.13231297190651.071110.0907117675194.3641561.6924159510145.2462470.090414424819.04499730.212554399953.19398410.07003806428.687051910.05265957189642.438660.1190709202296.35021910.18273161032372.825540.1779562210630.0281838.0728367581961.2185910.233385768156.94980181.23292214431048.312680.0716158565802.7622792.28303292349264.933660.0798262858124.7883143.77311035351065.409070.094998272095.28404891.41324251929683.414930.0642272915377.4388033.92332815285849.954930.0470132374469.3928681.90343206746606.760960.1609515839451.139867.4135377897718.8009840.130149152590.04491140.71361602255760.981830.1285205911785.9085072.9637364681798.1097060.108039389822.06227630.5738774785377.7757540.062448379471.92419880.69391060080189.388930.045848525487.45862290.70401375216767.211620.0961132192061.9250511.9041482313945.8819590.104950578115.61170330.73421938419823.082320.0977189436875.4900292.72Table 5
Forecast value of each Industry’s demand for transportation in 2050.
Industry numberTotal output (unit: ten thousand yuan)Complete consumption coefficient for transportationValue of demand for transportation (unit: ten thousand yuan)Percentage (%)12305058914.958580.1038161562882.6498932.322225399239.2520310.047317175036.816530.253296358702.5042360.03769049175.657358430.134130754716.2098920.02226484079.065088760.095309703690.6688920.104422453457.22009240.3264993316219.249540.1070340105785.7123924.8871169877601.058390.1415117422343.6285791.6981168227930.421330.1640129998582.753921.879898528918.2284180.119274024374.91930831.06101296795582.071950.1245111632630.3124711.60111103236675.707680.119784897524.76209981.22126082124100.939060.1380559648454.6807458.03132962043458.504940.1397262428339.8385583.77143516241093.097620.0987266973521.4798663.83151588705051.311540.1102123006525.7929541.77162334054745.426450.1144202876346.3669292.91173772776250.864540.1225308797754.6677914.43181956366422.708170.1088159468719.3754152.29194072416886.882440.0959271783708.5527323.9020273918886.8497860.098020990293.53686990.302169258710.87997720.13177903185.386350470.11221907629900.06819218409.260.132318153839140.09271176751941.69242697353350.0990144248190.212575433673.60.07053806428.690.052694434025360.115170920229610.182754714728460.17135622106308.07288113836670.222585768156.91.232943356305030.07191585658032.283056500485030.07292628581253.773116591094490.093498272095.31.413284061770690.06632729153773.923353980070010.05151323744691.903464259200470.15765158394517.41357446850820.1314491525900.713630837988550.12082059117862.96376757049950.107739389822.10.573813777738460.052148379471.90.693917884349890.039748525487.50.704024443820470.09121321920621.90418880412760.104450578115.60.734234575453220.09781894368752.72By 2035, the transportation value will be 696,538 trillion yuan. From 2017 to 2035, the average annual growth rate of the transportation value will be 7.25%. By 2050, the transportation value will be 1,121,637 billion yuan, and the average annual growth rate of transportation value will be 3.23%.


### 5.2. Regression Models

The difficulty of using the input-output model to analyze freight volume is to construct the functional relationship between value volume and freight traffic. Judging from the law of value volume and freight volume shown in the industrialization process of developed countries, the freight elasticity tends to gradually decrease, that is, the growth rate of freight volume is lower than that of value volume. The economic significance is that the tertiary industry develops faster in the middle and late stages of industrialization, while the growth rate of the primary and secondary industries that bring more freight demand has slowed, leading to a further slowdown in freight volume growth.Based on the 2002–2017, input-output table and the statistical data of freight volume from the National Bureau of Statistics of China analyze the functional relationship between transportation value and freight traffic. The statistical data over the years is shown in Table6.Table 6
2002–2017 freight demand value and freight volume statistics.
YearTransportation value (unit: ten thousand yuan)Freight volume (unit: 100 million tons)2002284916168.9148.342005569828620.4186.212007698441069227.5820101250578926324.1820121426917180410.0420151976730089417.5920172108324779480.49Data source: China National Bureau of Statistics and the author’s calculations.We started regression analysis with one explanatory variable. Firstly, analyze the correlation between freight value and freight traffic. The Pearson correlation coefficient of the two is 0.977, and the significance test probability is 0.01. The analysis shows that the correlation between the two is significant, and predictive analysis can be performed. Secondly, to predict freight traffic, it is necessary to perform a regression analysis on freight value and freight traffic. Regression analysis refers to the statistical method of quantitative analysis of the interdependence between two or more variables. According to the relationship between the independent variable and the dependent variable, it can be divided into linear regression analysis and nonlinear regression analysis. Nonlinear regression includes power function and logarithmic function.Given the characteristics of the growth rate of freight traffic, the quadratic function, cubic function, compound function, exponential function, logistic function, ands function are excluded because the predicted values of these models are too high or too low. Based on the relationship between freight value and freight volume from 2002 to 2017, this paper uses the freight value as an independent variable and freight volume as a dependent variable to construct one-variable linear, power, and logarithmic functions. The fitting effect and prediction are shown in Table 7.Table 7
The fitting effect of different models and the predicted value of freight volume comparison.
Unary linear functionPower functionLogarithmic functionFitting curveFitting equationy=0.0000001784∗x+101.547y=0.001∗0.607xy=−3176.496+168.607∗LNxR20.9770.9660.923Freight volume forecast in 20351344.17943.34644.85Freight volume forecast in 20502102.551259.68725.18Data source: China National Bureau of Statistics and the author’s calculation, unit: 100 million tons.Although the linear regression model and power regression model have higherR2, the logarithmic model also has good R2. In recent decades, the freight economic elasticity of the United States, Germany, and other major developed countries has shown a trend of “∩” shape. Considering that China is about to enter the postindustrialization period and the growth law of freight volume in developed countries, the prediction effect of the logarithmic function is better. Based on the forecast of the logarithmic function (M1), China’s freight volume in 2035 will be 64.485 billion tons and the freight volume in 2050 will be 72.518 billion tons. In 2017–2035, freight volume will achieve an average annual growth rate of 1.65% and freight volume in 2035–2050 will achieve an average annual growth rate of 0.79%. For comparison, China’s average annual growth rate of freight volume from 2000 to 2010 was 9.09%, and the average annual growth rate of freight volume from 2010 to 2020 was about 3.8%. Figure 1 shows the changes in the value of each industry’s demand for transportation.Figure 1
Statistics of changes in the value of transportation demand for various industries in China from 2002 to 2050. Data source: China National Bureau of Statistics and the author’s calculation; 1–42 represent the serial numbers of each industry.From the perspective of structural changes in the proportion of transportation demand by various industries, from 2017 to 2050, almost the proportions of the primary and secondary industries have declined, while the proportions of the tertiary industry have almost increased. This shows that, in the postindustrialization period, the development of the service industry was significantly faster than the development of other industries, which also led to a further slowdown in the growth of freight traffic.From the statistics of the past years, the ranking of the value of transportation demand by each industry is shown in Figure2.Figure 2
Statistics on the average proportion of the demand for transportation by various industries in China from 2002 to 2050. Data source: China National Bureau of Statistics and the author’s calculation.As can be seen from the above figure, apart from the transportation industry itself, the largest demand for transportation is the construction industry, chemical industry, metal smelting, and rolling processing industry in order. From the comparison of the three industries, the second industry has the largest demand for transportation, with an average demand of 67.56%, followed by the tertiary industry, with an average demand of 29.36%, and, finally, the primary industry, with an average demand of 3.08%.


### 5.3. Time Series Models

Time series regression is another reasonable method to examine the relationship between time-ordered variables. In recent decades, the freight volume per unit GDP has been declining year by year, which is closely related to the change of industrial structure. The fitting and forecasting trend line is shown in Figure3 (M2).Figure 3
Forecast chart of freight volume per unit GDP. The solid line is the actual freight, and the dotted line is the predicted freight. The ordinate is the freight volume per GDP, and the unit is 100 million tons/trillion yuan.Model 2 shows good fitting effect; according to Model 2, China’s freight volume will be 77.31 billion tons in 2035 and 87.81 billion tons in 2050.The single-equation autoregressive integrated moving average (ARIMA) time series model has also achieved good forecasting results [81, 82]. The ARIMA model is a model in which forecasted values are obtained by regressing past values of the variable itself and the current value with the error terms of the past values at different lag lengths. The proposed model structure is given in(26)Yt=C+α1GDP1+α2GDP2+βYt−1+ε,where Yt represents the freight in million tons in year t and GDP1 represents the difference between the added value of the primary industry this year and the previous year. The remaining variables and parameters are self-explanatory. The fitting results are as follows (M3):(27)Yt=−10.072+40.874GDP1+9.834GDP2+0.976Yt−1.According to Model 3, China’s freight volume will be 65.02 billion tons in 2035 and 79.18 billion tons in 2050. The errors for univariate time series models vary from about 0.06% to 7.98%, whereas the error for multivariate time series models lies between 0.13% and 7.17% at 95% confidence level. Multivariate time series model shows better prediction effect and further verifies the accuracy of the regression model.


## 5.1. Forecast and Analysis of the Economic Value of Transportation

Through the analysis of total output, industrial structure, and complete consumption coefficient, combined with the basic data of the input-output table from 2002 to 2017, the economic value of transportation in 2035 and 2050 can be predicted. The forecast data is shown in Tables4 and 5.Table 4
Forecast the value of each Industry’s demand for transportation in 2035.
Industry numberTotal output (unit: ten thousand yuan)Complete consumption coefficient for transportationValue of demand for transportation (unit: ten thousand yuan)Percentage (%)11694385607.671580.0954161562882.6498932.322298638845.7190850.057517175036.816530.253229301196.8363650.03959049175.657358430.134129307146.7753680.05016484079.065088760.095211843472.61720.106022453457.22009240.3263228474316.226450.1053340105785.7123924.887853635246.666950.1376117422343.6285791.698841006714.6023470.1546129998582.753921.879609580270.1159720.121474024374.91930831.0610890071738.0402420.1254111632630.3124711.6011798728493.8158420.106384897524.76209981.22124039139792.042840.1386559648454.6807458.03131880344512.127540.1396262428339.8385583.77142504229609.093180.1066266973521.4798663.83151065158416.304540.1155123006525.7929541.77161682978234.460360.1205202876346.3669292.91172429683947.140230.1271308797754.6677914.43181370308888.667530.1164159468719.3754152.29192612610892.337140.1040271783708.5527323.9020196602250.5810080.106820990293.53686990.302159787097.24149240.13227903185.386350470.1122136893612.6089030.06739218409.264253350.13231297190651.071110.0907117675194.3641561.6924159510145.2462470.090414424819.04499730.212554399953.19398410.07003806428.687051910.05265957189642.438660.1190709202296.35021910.18273161032372.825540.1779562210630.0281838.0728367581961.2185910.233385768156.94980181.23292214431048.312680.0716158565802.7622792.28303292349264.933660.0798262858124.7883143.77311035351065.409070.094998272095.28404891.41324251929683.414930.0642272915377.4388033.92332815285849.954930.0470132374469.3928681.90343206746606.760960.1609515839451.139867.4135377897718.8009840.130149152590.04491140.71361602255760.981830.1285205911785.9085072.9637364681798.1097060.108039389822.06227630.5738774785377.7757540.062448379471.92419880.69391060080189.388930.045848525487.45862290.70401375216767.211620.0961132192061.9250511.9041482313945.8819590.104950578115.61170330.73421938419823.082320.0977189436875.4900292.72Table 5
Forecast value of each Industry’s demand for transportation in 2050.
Industry numberTotal output (unit: ten thousand yuan)Complete consumption coefficient for transportationValue of demand for transportation (unit: ten thousand yuan)Percentage (%)12305058914.958580.1038161562882.6498932.322225399239.2520310.047317175036.816530.253296358702.5042360.03769049175.657358430.134130754716.2098920.02226484079.065088760.095309703690.6688920.104422453457.22009240.3264993316219.249540.1070340105785.7123924.8871169877601.058390.1415117422343.6285791.6981168227930.421330.1640129998582.753921.879898528918.2284180.119274024374.91930831.06101296795582.071950.1245111632630.3124711.60111103236675.707680.119784897524.76209981.22126082124100.939060.1380559648454.6807458.03132962043458.504940.1397262428339.8385583.77143516241093.097620.0987266973521.4798663.83151588705051.311540.1102123006525.7929541.77162334054745.426450.1144202876346.3669292.91173772776250.864540.1225308797754.6677914.43181956366422.708170.1088159468719.3754152.29194072416886.882440.0959271783708.5527323.9020273918886.8497860.098020990293.53686990.302169258710.87997720.13177903185.386350470.11221907629900.06819218409.260.132318153839140.09271176751941.69242697353350.0990144248190.212575433673.60.07053806428.690.052694434025360.115170920229610.182754714728460.17135622106308.07288113836670.222585768156.91.232943356305030.07191585658032.283056500485030.07292628581253.773116591094490.093498272095.31.413284061770690.06632729153773.923353980070010.05151323744691.903464259200470.15765158394517.41357446850820.1314491525900.713630837988550.12082059117862.96376757049950.107739389822.10.573813777738460.052148379471.90.693917884349890.039748525487.50.704024443820470.09121321920621.90418880412760.104450578115.60.734234575453220.09781894368752.72By 2035, the transportation value will be 696,538 trillion yuan. From 2017 to 2035, the average annual growth rate of the transportation value will be 7.25%. By 2050, the transportation value will be 1,121,637 billion yuan, and the average annual growth rate of transportation value will be 3.23%.


## 5.2. Regression Models

The difficulty of using the input-output model to analyze freight volume is to construct the functional relationship between value volume and freight traffic. Judging from the law of value volume and freight volume shown in the industrialization process of developed countries, the freight elasticity tends to gradually decrease, that is, the growth rate of freight volume is lower than that of value volume. The economic significance is that the tertiary industry develops faster in the middle and late stages of industrialization, while the growth rate of the primary and secondary industries that bring more freight demand has slowed, leading to a further slowdown in freight volume growth.Based on the 2002–2017, input-output table and the statistical data of freight volume from the National Bureau of Statistics of China analyze the functional relationship between transportation value and freight traffic. The statistical data over the years is shown in Table6.Table 6
2002–2017 freight demand value and freight volume statistics.
YearTransportation value (unit: ten thousand yuan)Freight volume (unit: 100 million tons)2002284916168.9148.342005569828620.4186.212007698441069227.5820101250578926324.1820121426917180410.0420151976730089417.5920172108324779480.49Data source: China National Bureau of Statistics and the author’s calculations.We started regression analysis with one explanatory variable. Firstly, analyze the correlation between freight value and freight traffic. The Pearson correlation coefficient of the two is 0.977, and the significance test probability is 0.01. The analysis shows that the correlation between the two is significant, and predictive analysis can be performed. Secondly, to predict freight traffic, it is necessary to perform a regression analysis on freight value and freight traffic. Regression analysis refers to the statistical method of quantitative analysis of the interdependence between two or more variables. According to the relationship between the independent variable and the dependent variable, it can be divided into linear regression analysis and nonlinear regression analysis. Nonlinear regression includes power function and logarithmic function.Given the characteristics of the growth rate of freight traffic, the quadratic function, cubic function, compound function, exponential function, logistic function, ands function are excluded because the predicted values of these models are too high or too low. Based on the relationship between freight value and freight volume from 2002 to 2017, this paper uses the freight value as an independent variable and freight volume as a dependent variable to construct one-variable linear, power, and logarithmic functions. The fitting effect and prediction are shown in Table 7.Table 7
The fitting effect of different models and the predicted value of freight volume comparison.
Unary linear functionPower functionLogarithmic functionFitting curveFitting equationy=0.0000001784∗x+101.547y=0.001∗0.607xy=−3176.496+168.607∗LNxR20.9770.9660.923Freight volume forecast in 20351344.17943.34644.85Freight volume forecast in 20502102.551259.68725.18Data source: China National Bureau of Statistics and the author’s calculation, unit: 100 million tons.Although the linear regression model and power regression model have higherR2, the logarithmic model also has good R2. In recent decades, the freight economic elasticity of the United States, Germany, and other major developed countries has shown a trend of “∩” shape. Considering that China is about to enter the postindustrialization period and the growth law of freight volume in developed countries, the prediction effect of the logarithmic function is better. Based on the forecast of the logarithmic function (M1), China’s freight volume in 2035 will be 64.485 billion tons and the freight volume in 2050 will be 72.518 billion tons. In 2017–2035, freight volume will achieve an average annual growth rate of 1.65% and freight volume in 2035–2050 will achieve an average annual growth rate of 0.79%. For comparison, China’s average annual growth rate of freight volume from 2000 to 2010 was 9.09%, and the average annual growth rate of freight volume from 2010 to 2020 was about 3.8%. Figure 1 shows the changes in the value of each industry’s demand for transportation.Figure 1
Statistics of changes in the value of transportation demand for various industries in China from 2002 to 2050. Data source: China National Bureau of Statistics and the author’s calculation; 1–42 represent the serial numbers of each industry.From the perspective of structural changes in the proportion of transportation demand by various industries, from 2017 to 2050, almost the proportions of the primary and secondary industries have declined, while the proportions of the tertiary industry have almost increased. This shows that, in the postindustrialization period, the development of the service industry was significantly faster than the development of other industries, which also led to a further slowdown in the growth of freight traffic.From the statistics of the past years, the ranking of the value of transportation demand by each industry is shown in Figure2.Figure 2
Statistics on the average proportion of the demand for transportation by various industries in China from 2002 to 2050. Data source: China National Bureau of Statistics and the author’s calculation.As can be seen from the above figure, apart from the transportation industry itself, the largest demand for transportation is the construction industry, chemical industry, metal smelting, and rolling processing industry in order. From the comparison of the three industries, the second industry has the largest demand for transportation, with an average demand of 67.56%, followed by the tertiary industry, with an average demand of 29.36%, and, finally, the primary industry, with an average demand of 3.08%.


## 5.3. Time Series Models

Time series regression is another reasonable method to examine the relationship between time-ordered variables. In recent decades, the freight volume per unit GDP has been declining year by year, which is closely related to the change of industrial structure. The fitting and forecasting trend line is shown in Figure3 (M2).Figure 3
Forecast chart of freight volume per unit GDP. The solid line is the actual freight, and the dotted line is the predicted freight. The ordinate is the freight volume per GDP, and the unit is 100 million tons/trillion yuan.Model 2 shows good fitting effect; according to Model 2, China’s freight volume will be 77.31 billion tons in 2035 and 87.81 billion tons in 2050.The single-equation autoregressive integrated moving average (ARIMA) time series model has also achieved good forecasting results [81, 82]. The ARIMA model is a model in which forecasted values are obtained by regressing past values of the variable itself and the current value with the error terms of the past values at different lag lengths. The proposed model structure is given in(26)Yt=C+α1GDP1+α2GDP2+βYt−1+ε,where Yt represents the freight in million tons in year t and GDP1 represents the difference between the added value of the primary industry this year and the previous year. The remaining variables and parameters are self-explanatory. The fitting results are as follows (M3):(27)Yt=−10.072+40.874GDP1+9.834GDP2+0.976Yt−1.According to Model 3, China’s freight volume will be 65.02 billion tons in 2035 and 79.18 billion tons in 2050. The errors for univariate time series models vary from about 0.06% to 7.98%, whereas the error for multivariate time series models lies between 0.13% and 7.17% at 95% confidence level. Multivariate time series model shows better prediction effect and further verifies the accuracy of the regression model.


## 6. Numerical Experiments and Analysis

### 6.1. Analysis of the Impact of Changes in the Economic Value of Transportation

The complete decomposition model is used to decompose the changes in the economic value of transportation, and the effects of changes in the complete consumption coefficient, changes in industrial structure, and changes in economic aggregates on the economic value of transportation are calculated, respectively. The results are shown in Table8.Table 8
Analysis of the impact of changes in the economic value of transportation in 2017–2035.
Primary industryPercentage (%)Secondary industryPercentage (%)Tertiary industryPercentage (%)2017–2035bjq64204832.3762.81526237944.419.75364246875.716.40sjq74125315.71−72.52310055653.5−11.63383447076.317.26Xjq112134478.7109.71244887295391.89147368690866.34∆Q102213995.3100266505524410022213808601002017–2050bjq103320453.657.44650215278.514.43530706763.811.65sjq143829310.4−79.96789279860.7−17.52891515068.619.58Xjq220394994.6122.524645078315103.09313152051368.77∆Q179886137.810045060137331004553742346100Data source. China National Bureau of Statistics and the author’s calculation, unit: 10,000 yuan.From 2017 to 2035, the economic value of transportation increased to 498,865 billion yuan. From the perspective of industrial structure, the secondary industry has the greatest impact on the incremental value of transportation, accounting for 53.42%, the tertiary industry also has a greater impact, accounting for 44.53%, and the primary industry has the least impact, accounting for 2.05%. From the perspective of influencing factors, the increase in total output has the greatest impact on the changes in the economic value of transportation, accounting for 80.88%, the second is the change in the complete consumption coefficient, accounting for 19.14%, and changes in the industrial structure make transportation the economic value increment decreased by 0.01%.The increase in the economic value of transportation from 2017 to 2050 was 923,964 billion yuan. From the perspective of industrial structure, the tertiary industry has the greatest impact on the incremental value of transportation, accounting for 49.28%, the secondary industry also has a greater impact, accounting for 48.77%, and the primary industry has the least impact, accounting for 1.95%. From the perspective of influencing factors, the increase in total output has the greatest impact on the changes in the economic value of transportation, accounting for 86.55%, the second is the change in the complete consumption coefficient, accounting for 13.9%, and changes in the industrial structure make transportation economic value increment decreased by 0.45%.


### 6.2. Analysis of the Impact of Changes in Economic Aggregates on Freight Volume

Because of the uncertainty of total economic growth, two scenarios of faster economic development and slower economic development are considered:(1)
Scenario of relatively rapid economic development: in this scenario, China’s economy will develop faster. It will achieve an average annual growth rate of 5% from 2021–2035 and an average annual growth rate of 3.6% from 2036–2050. Some institutions and scholars are optimistic about China’s development, as shown in Table9.(2)
Scenario of slower economic development: in the context of slower economic development, China’s economic development is slightly lower than the baseline scenario. The average annual growth rate of China’s economic development from 2021–2035 will drop to 4.6% and the average annual growth rate will drop to 3.2% from 2036–2050.Table 9
Prediction of China’s economic growth rate by some institutions and scholars.
Research institutions and scholars2021–20302031–20402041–2050Goldman Sachs5.74.43.6HSBC5.54.44.1Li Shantong, Hou Yongzhi5.44.53.4Li Jingwen5.44.94.3Xu Xianchun5.54.53.5Source: the long-term outlook for the BRICs and N-11 postcrisis; HSBC Global Economics Research Team; Li and Hou [83]; Li [84]; Xu [85]; unit: %.According to the previous assumptions for the two scenarios, the logarithmic function is used for prediction, and the calculation results and the comparison with the baseline scenario are shown in Table10.Table 10
Comparison of China freight volume forecasts under three scenarios.
ScenarioForecast for 20352017–2035 average annual growth rate of freight traffic (%)Forecast for 20502035–2050 average annual growth rate of freight traffic (%)Baseline scenario644.851.65725.180.79Slow economic development scenario639.71.60719.360.79Faster economic development scenario649.991.69739.440.86Data source: author’s calculation, forecast unit: 100 million tons.Judging from the calculation results of the three scenarios, the difference in economic growth rate has little effect on the forecast results of freight traffic. The degree of economic growth rate affecting freight volume represents the elasticity of GDP to freight traffic. The freight elasticity of the United States has gradually decreased since 1990 and is currently about 0.1-0.2. Germany’s freight elasticity has gradually decreased since 1990 and is currently around 0.2-0.3. Due to the difficulty of economic recovery in Japan, freight elasticity has been in a negative state since 1990. Judging from the experience of the United States, Germany, and other developed countries, its freight elasticity is between 0.1–0.3, which shows that the impact of economic aggregate growth on freight volume is gradually decreasing.


### 6.3. Analysis of the Impact of Industrial Structure Changes on Freight Traffic

In the late industrialization and postindustrialization period, the decline in freight volume growth was mainly caused by the upgrading of industrial structure. In this stage of industrialization, the proportion of the service industry will increase from 50% to about 70%–80%. The entire national economy is dominated by the service economy and information economy, so the growth rate of freight volume is limited.To sort out the upgrading of China’s industrial structure, its evolutionary structure over the years and the structure forecast for 2035 and 2050 are shown in Figure4.Figure 4
The evolution of China’s industrial structure based on total output from 2002 to 2050. Data source: China National Bureau of Statistics and the author’s calculation; 1–42 represent the serial numbers of each industry.From the perspective of future changes in the total output structure of the industry, the primary industry has the largest decline, from 4.88% in 2017 to 2.2% in 2050, and the secondary industry has all declined to vary degrees. Among them, the coal industry, petroleum industry, and metal mining accounted for the largest decline, with 77.9%, 45.14%, and 75.74%, respectively. The proportion of the accommodation and catering industry in the tertiary industry dropped slightly by 0.1 percentage point, and the rest increased to varying degrees. Among them, the financial industry rose the most, from 4.18% in 2017 to 8.01% in 2050.By 2050, China’s three industrial structures based on total output will account for 2.2 : 47.66 : 50.14, respectively. The structure evolution of the three industries is shown in Figure5.Figure 5
The evolution of China’s three industrial structures based on total output. Data source: China National Bureau of Statistics and the author’s calculation.To compare the impact of industrial structure on transportation, consider the change in freight volume when only changing the industrial structure with the total economic aggregate, and the complete consumption coefficient is unchanged. Assuming that the industrial structure of 2017 is maintained in 2035 and 2050 and that the demand for freight and passenger transportation from agriculture and industry is 8 : 2 and the demand for freight and passenger transportation from the service industry is 2 : 8, then the forecast value of freight volume in 2035 and 2050 is shown in Table11.Table 11
Comparison of the predicted value of freight volume with the baseline predicted value when the industrial structure remains unchanged.
Forecast for 2035Forecast for 2050Baseline forecastPredicted value when the industrial structure is unchangedBaseline forecastPredicted value when the industrial structure is unchangedPrimary industry25.8547.325.5756.75Secondary industry510.88574.58553.92686.03Tertiary industry107.8583.83145.6999.99Total freight volume644.58705.72725.18842.77Data source: China’s National Bureau of Statistics and the author’s calculation, freight volume unit: 100 million tons.When the industrial structure of 2017 is maintained, the predicted value of freight volume in 2035 and 2050 is 9.49% and 16.22% higher than the baseline value, respectively. This shows that the upgrading of the industrial structure has slowed down the growth rate of freight traffic. In the forecast of freight traffic, the importance of industrial structure exceeds that of economic aggregate.


### 6.4. Analysis of the Impact of Changes in the Complete Consumption Coefficient on Freight Traffic

The impact of technological progress on transportation is mainly reflected in three aspects: industrial upgrading has led to a decline in the proportion of traditional industrial added value such as coal, petroleum, and steel and an increase in the proportion of high-end industries such as computers, precision instruments, and equipment manufacturing. The improvement of technology makes the industry’s consumption rate of coal, oil, natural gas, and other energy sources gradually drop; the transportation capacity and service level are improved. Reflected in the input-output table, it is mainly reflected in the change of the complete consumption coefficient.The complete consumption factor is affected by two factors. One is the direct consumption coefficient, which represents the relationship between the demand of the industry and another industry and reflects the degree of energy consumption; the second is the indirect consumption coefficient, which represents the direct and indirect demand relationship between the industry and other industries and reflects the depth and breadth of the industrial chain. Figure6 shows the direct consumption of transportation by various industries.Figure 6
Statistics of direct consumption coefficients over the years and forecast values in 2035 and 2050. Data source: China’s National Bureau of Statistics and the author’s calculation; 1–42 are the industry numbers.From the perspective of the direct consumption coefficient, the largest direct consumption of transportation is the transportation, postal, and nonmetallic mining and processing industries. Because the direct consumption coefficient cannot reflect the industry’s complete demand for transportation, it is necessary to calculate the complete consumption coefficient. The complete consumption coefficient is shown in Figure7.Figure 7
Statistics of complete consumption coefficient over the years and forecast values in 2035 and 2050. Data source: China’s National Bureau of Statistics and the author’s calculation; 1–42 are the industry numbers.From the perspective of the full consumption coefficient, the postal, transportation, and construction industries have the greatest demand for transportation. From the perspective of the changes in the complete consumption coefficient and the direct consumption coefficient, except for petroleum, coking products, and nuclear fuel processing industries, the coefficient of variation of the complete consumption coefficient of other industries exceeds that of the direct consumption coefficient. This indicates that the industry chain will further deepen from now on, which also leads to a further increase in the complete consumption coefficient.Assuming that the full consumption coefficient of 2017 is maintained in 2035 and 2050, the forecast value of freight volume in 2035 and 2050 is shown in Table12.Table 12
Comparison of the predicted value of freight volume with the baseline predicted value when the complete consumption coefficient remains unchanged.
Forecast for 2035Forecast for 2050Baseline forecastPredicted value when the complete consumption coefficient does not changeBaseline forecastPredicted value when the complete consumption coefficient does not changePrimary industry25.8518.1425.5713.3Secondary industry510.88317.02553.92459.76Tertiary industry107.8545.25145.69116.55Total freight volume644.58380.41725.18589.6Data source: China’s National Bureau of Statistics and the author’s calculation.When the complete consumption coefficient remains unchanged, the predicted value of freight volume in 2035 and 2050 will decrease by 40.98% and 18.7%, respectively. This shows that the change in the complete consumption coefficient is the main reason for the change in freight traffic.


## 6.1. Analysis of the Impact of Changes in the Economic Value of Transportation

The complete decomposition model is used to decompose the changes in the economic value of transportation, and the effects of changes in the complete consumption coefficient, changes in industrial structure, and changes in economic aggregates on the economic value of transportation are calculated, respectively. The results are shown in Table8.Table 8
Analysis of the impact of changes in the economic value of transportation in 2017–2035.
Primary industryPercentage (%)Secondary industryPercentage (%)Tertiary industryPercentage (%)2017–2035bjq64204832.3762.81526237944.419.75364246875.716.40sjq74125315.71−72.52310055653.5−11.63383447076.317.26Xjq112134478.7109.71244887295391.89147368690866.34∆Q102213995.3100266505524410022213808601002017–2050bjq103320453.657.44650215278.514.43530706763.811.65sjq143829310.4−79.96789279860.7−17.52891515068.619.58Xjq220394994.6122.524645078315103.09313152051368.77∆Q179886137.810045060137331004553742346100Data source. China National Bureau of Statistics and the author’s calculation, unit: 10,000 yuan.From 2017 to 2035, the economic value of transportation increased to 498,865 billion yuan. From the perspective of industrial structure, the secondary industry has the greatest impact on the incremental value of transportation, accounting for 53.42%, the tertiary industry also has a greater impact, accounting for 44.53%, and the primary industry has the least impact, accounting for 2.05%. From the perspective of influencing factors, the increase in total output has the greatest impact on the changes in the economic value of transportation, accounting for 80.88%, the second is the change in the complete consumption coefficient, accounting for 19.14%, and changes in the industrial structure make transportation the economic value increment decreased by 0.01%.The increase in the economic value of transportation from 2017 to 2050 was 923,964 billion yuan. From the perspective of industrial structure, the tertiary industry has the greatest impact on the incremental value of transportation, accounting for 49.28%, the secondary industry also has a greater impact, accounting for 48.77%, and the primary industry has the least impact, accounting for 1.95%. From the perspective of influencing factors, the increase in total output has the greatest impact on the changes in the economic value of transportation, accounting for 86.55%, the second is the change in the complete consumption coefficient, accounting for 13.9%, and changes in the industrial structure make transportation economic value increment decreased by 0.45%.


## 6.2. Analysis of the Impact of Changes in Economic Aggregates on Freight Volume

Because of the uncertainty of total economic growth, two scenarios of faster economic development and slower economic development are considered:(1)
Scenario of relatively rapid economic development: in this scenario, China’s economy will develop faster. It will achieve an average annual growth rate of 5% from 2021–2035 and an average annual growth rate of 3.6% from 2036–2050. Some institutions and scholars are optimistic about China’s development, as shown in Table9.(2)
Scenario of slower economic development: in the context of slower economic development, China’s economic development is slightly lower than the baseline scenario. The average annual growth rate of China’s economic development from 2021–2035 will drop to 4.6% and the average annual growth rate will drop to 3.2% from 2036–2050.Table 9
Prediction of China’s economic growth rate by some institutions and scholars.
Research institutions and scholars2021–20302031–20402041–2050Goldman Sachs5.74.43.6HSBC5.54.44.1Li Shantong, Hou Yongzhi5.44.53.4Li Jingwen5.44.94.3Xu Xianchun5.54.53.5Source: the long-term outlook for the BRICs and N-11 postcrisis; HSBC Global Economics Research Team; Li and Hou [83]; Li [84]; Xu [85]; unit: %.According to the previous assumptions for the two scenarios, the logarithmic function is used for prediction, and the calculation results and the comparison with the baseline scenario are shown in Table10.Table 10
Comparison of China freight volume forecasts under three scenarios.
ScenarioForecast for 20352017–2035 average annual growth rate of freight traffic (%)Forecast for 20502035–2050 average annual growth rate of freight traffic (%)Baseline scenario644.851.65725.180.79Slow economic development scenario639.71.60719.360.79Faster economic development scenario649.991.69739.440.86Data source: author’s calculation, forecast unit: 100 million tons.Judging from the calculation results of the three scenarios, the difference in economic growth rate has little effect on the forecast results of freight traffic. The degree of economic growth rate affecting freight volume represents the elasticity of GDP to freight traffic. The freight elasticity of the United States has gradually decreased since 1990 and is currently about 0.1-0.2. Germany’s freight elasticity has gradually decreased since 1990 and is currently around 0.2-0.3. Due to the difficulty of economic recovery in Japan, freight elasticity has been in a negative state since 1990. Judging from the experience of the United States, Germany, and other developed countries, its freight elasticity is between 0.1–0.3, which shows that the impact of economic aggregate growth on freight volume is gradually decreasing.


## 6.3. Analysis of the Impact of Industrial Structure Changes on Freight Traffic

In the late industrialization and postindustrialization period, the decline in freight volume growth was mainly caused by the upgrading of industrial structure. In this stage of industrialization, the proportion of the service industry will increase from 50% to about 70%–80%. The entire national economy is dominated by the service economy and information economy, so the growth rate of freight volume is limited.To sort out the upgrading of China’s industrial structure, its evolutionary structure over the years and the structure forecast for 2035 and 2050 are shown in Figure4.Figure 4
The evolution of China’s industrial structure based on total output from 2002 to 2050. Data source: China National Bureau of Statistics and the author’s calculation; 1–42 represent the serial numbers of each industry.From the perspective of future changes in the total output structure of the industry, the primary industry has the largest decline, from 4.88% in 2017 to 2.2% in 2050, and the secondary industry has all declined to vary degrees. Among them, the coal industry, petroleum industry, and metal mining accounted for the largest decline, with 77.9%, 45.14%, and 75.74%, respectively. The proportion of the accommodation and catering industry in the tertiary industry dropped slightly by 0.1 percentage point, and the rest increased to varying degrees. Among them, the financial industry rose the most, from 4.18% in 2017 to 8.01% in 2050.By 2050, China’s three industrial structures based on total output will account for 2.2 : 47.66 : 50.14, respectively. The structure evolution of the three industries is shown in Figure5.Figure 5
The evolution of China’s three industrial structures based on total output. Data source: China National Bureau of Statistics and the author’s calculation.To compare the impact of industrial structure on transportation, consider the change in freight volume when only changing the industrial structure with the total economic aggregate, and the complete consumption coefficient is unchanged. Assuming that the industrial structure of 2017 is maintained in 2035 and 2050 and that the demand for freight and passenger transportation from agriculture and industry is 8 : 2 and the demand for freight and passenger transportation from the service industry is 2 : 8, then the forecast value of freight volume in 2035 and 2050 is shown in Table11.Table 11
Comparison of the predicted value of freight volume with the baseline predicted value when the industrial structure remains unchanged.
Forecast for 2035Forecast for 2050Baseline forecastPredicted value when the industrial structure is unchangedBaseline forecastPredicted value when the industrial structure is unchangedPrimary industry25.8547.325.5756.75Secondary industry510.88574.58553.92686.03Tertiary industry107.8583.83145.6999.99Total freight volume644.58705.72725.18842.77Data source: China’s National Bureau of Statistics and the author’s calculation, freight volume unit: 100 million tons.When the industrial structure of 2017 is maintained, the predicted value of freight volume in 2035 and 2050 is 9.49% and 16.22% higher than the baseline value, respectively. This shows that the upgrading of the industrial structure has slowed down the growth rate of freight traffic. In the forecast of freight traffic, the importance of industrial structure exceeds that of economic aggregate.


## 6.4. Analysis of the Impact of Changes in the Complete Consumption Coefficient on Freight Traffic

The impact of technological progress on transportation is mainly reflected in three aspects: industrial upgrading has led to a decline in the proportion of traditional industrial added value such as coal, petroleum, and steel and an increase in the proportion of high-end industries such as computers, precision instruments, and equipment manufacturing. The improvement of technology makes the industry’s consumption rate of coal, oil, natural gas, and other energy sources gradually drop; the transportation capacity and service level are improved. Reflected in the input-output table, it is mainly reflected in the change of the complete consumption coefficient.The complete consumption factor is affected by two factors. One is the direct consumption coefficient, which represents the relationship between the demand of the industry and another industry and reflects the degree of energy consumption; the second is the indirect consumption coefficient, which represents the direct and indirect demand relationship between the industry and other industries and reflects the depth and breadth of the industrial chain. Figure6 shows the direct consumption of transportation by various industries.Figure 6
Statistics of direct consumption coefficients over the years and forecast values in 2035 and 2050. Data source: China’s National Bureau of Statistics and the author’s calculation; 1–42 are the industry numbers.From the perspective of the direct consumption coefficient, the largest direct consumption of transportation is the transportation, postal, and nonmetallic mining and processing industries. Because the direct consumption coefficient cannot reflect the industry’s complete demand for transportation, it is necessary to calculate the complete consumption coefficient. The complete consumption coefficient is shown in Figure7.Figure 7
Statistics of complete consumption coefficient over the years and forecast values in 2035 and 2050. Data source: China’s National Bureau of Statistics and the author’s calculation; 1–42 are the industry numbers.From the perspective of the full consumption coefficient, the postal, transportation, and construction industries have the greatest demand for transportation. From the perspective of the changes in the complete consumption coefficient and the direct consumption coefficient, except for petroleum, coking products, and nuclear fuel processing industries, the coefficient of variation of the complete consumption coefficient of other industries exceeds that of the direct consumption coefficient. This indicates that the industry chain will further deepen from now on, which also leads to a further increase in the complete consumption coefficient.Assuming that the full consumption coefficient of 2017 is maintained in 2035 and 2050, the forecast value of freight volume in 2035 and 2050 is shown in Table12.Table 12
Comparison of the predicted value of freight volume with the baseline predicted value when the complete consumption coefficient remains unchanged.
Forecast for 2035Forecast for 2050Baseline forecastPredicted value when the complete consumption coefficient does not changeBaseline forecastPredicted value when the complete consumption coefficient does not changePrimary industry25.8518.1425.5713.3Secondary industry510.88317.02553.92459.76Tertiary industry107.8545.25145.69116.55Total freight volume644.58380.41725.18589.6Data source: China’s National Bureau of Statistics and the author’s calculation.When the complete consumption coefficient remains unchanged, the predicted value of freight volume in 2035 and 2050 will decrease by 40.98% and 18.7%, respectively. This shows that the change in the complete consumption coefficient is the main reason for the change in freight traffic.


## 7. Conclusion

This paper constructs a freight value and freight volume analysis model based on the input-output method and predicts the development trend of China’s freight volume and uses a complete decomposition model to analyze the factors affecting freight value and freight volume. The study reached the following conclusions:(1)
The growth rate of China’s freight volume will gradually decline, with an average annual growth rate of 1.65% from 2017 to 2035 and an average annual growth rate of 0.79% from 2035 to 2050. Research shows that China freight volume in 2035 is 64.458 billion tons and 72.518 billion tons in 2050.(2)
From the perspective of industrial structure, the tertiary industry has the greatest impact on the incremental value of transportation, accounting for 49.28%, the secondary industry also has a greater impact, accounting for 48.77%, and the primary industry has the least impact, accounting for 1.95%. From the perspective of influencing factors, the increase in total output has the greatest impact on the changes in the economic value of transportation, accounting for 86.55%, the second is the change in the complete consumption coefficient, accounting for 13.9%, and changes in the industrial structure make transportation economic value decreased by 0.45%.(3)
When the industrial structure of 2017 is maintained, the predicted value of freight volume in 2035 and 2050 is 9.49% and 16.22% higher than the baseline value, respectively. This shows that the upgrading of the industrial structure has slowed down the growth rate of freight traffic. When the complete consumption coefficient remains unchanged, the predicted freight volume in 2035 and 2050 will decrease by 40.98% and 18.7%, respectively. This shows that the change in the complete consumption coefficient is the main reason for the change in freight traffic. The change in economic aggregate has a limited impact on freight traffic, and the upgrading of industrial structure will cause a decline in freight traffic. The increase in the full consumption coefficient indicates that the integration between industries is improving, which means that the accuracy of freight forecasting through industry division will decrease.As this paper is compared with the previous models, the main differences of this paper are as follows: (1) this paper further subdivides the industry, dividing the industry sector into 42 sectors, which is more refined than the previous three industry divisions and can better reflect the relationship between different industries and freight demand; (2) in the past, factor analysis often used methods such as multiple regression and cluster analysis, which could not reflect the importance and relevance of factors. This paper uses a complete decomposition model to analyze the influencing factors of freight volume, which can effectively analyze the relationship between the influencing factors; (3) this paper combines gray forecasting and input-output analysis, which can analyze the factors of future freight demand changes, which is more practical and referential than the previous analysis of the current status of influencing factors.Due to the lack of freight data of related industries, this paper predicts the freight volume from the overall freight value and industry GDP, and the accuracy of the forecast needs to be tested. Future research can further analyze the influence relationship between different industries based on this model, use feature analysis to further optimize the industrial structure, and use this model in conjunction with the OD tables for transportation planning research. Further statistics on the freight volume data of related industries and the use of the fusion of multiple models to make predictions can improve the accuracy of freight volume forecasts, which is the direction of future research.



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*Source: 5581742-2021-03-31.xml*