The Influence of Complexity of Imported Products on Total Factor Productivity

School of Management Science and Information Engineering, Jilin University of Finance and Economics, Changchun 130117, China Jilin Provincial Key Laboratory on Logistic Industrial Economy and Intelligent Logistics, Jilin University of Finance and Economics, Changchun 130117, China Editorial Office of Contemporary Economic Research, Jilin University of Finance and Economics, Changchun 130117, China School of Economics and Management, Shenyang Aerospace University, Shenyang 110136, China


Introduction
In the context of globalization, the spillover effects and the research and development externalities, as channels for total factor productivity growth, brought by import trade, have been one of the major issues under discussion in international trade in the past decades. At the same time, China put forward "Belt and Road" (B&R) initiative in 2013, and it is of more practical and theoretical significance to study the impact of the trade of importing from countries along "Belt and Road" (B&R countries) on the total factor productivity of domestic industries. At present, the literature mainly focuses on the research of imported intermediate products and the types of imported products or the analysis of total factor productivity with import data at the enterprise level. However, both variety model [1] and quality ladder model [2,3] assumed that there was homogeneity between products and that the initial specialization of one product did not affect the productivity level of another product. However, Hausmann and Klinger considered that the products are highly heterogeneous [4]. ey argued that producing (exporting) some kinds of products will have a higher spillover effect than other products.
It is not difficult to find that the influence of import trade on total factor productivity is concluded differently at different levels. From the perspective of import, this paper demonstrates the impact of the import product complexity and density by China around the world on total factor productivity and the impact of the import product complexity and density by China from "B&R" countries on total factor productivity. On the basis of pertinent literature, which analyzes the role of import trade in improving total factor productivity, based on the influence of analysis of import product complexity and density on total factor productivity, the import complexity is divided into global sample and "B&R" sample, to analyze the similarities and differences of the influences of global import complexity, and "B&R" import complexity on China's total factor productivity.

Theoretical Model
Although import trade, as a technology spillover, has been recognized by many scholars, the developing countries need some suitability to improve technology level or total factor productivity through import channels. If the importing country cannot introduce technologies which are appropriate to its factor endowment structure, then, it may not achieve the productivity consistent with that of the exporting country [5]. At the same time, if it is related to more complex and advanced regional products in product space [6,7], this will promote the importing country to produce more complex products. Subsequently, producing more complex products will promote the improvement of total factor productivity in the industry, and producing a product with higher complexity will have a favorable impact on the production growth rate, because it will increase the accumulation of human capital.
is paper constructs the analysis framework of "complexity spillover regression of imported products," in each country c � 1, 2, . . .. . ., n, the size of labor force is fixed at L c level, and the average human capital level of country c is h c (for simplicity, h c is assumed to be constant across all industries). e share of human capital allocated to production in nonleisure time is λ c (λ c ∈ [0, 1]), and the share 1 − λ c is the leisure time used for the accumulation of human capital. Long-term investment in human capital is a key driving factor of economic growth. Assuming that the fixed capital is K, the complexity spillover of imported products is e α c z i , the produced products are represented by Q, then, the production function is Cobb-Douglas production equation; that is, In each country, there is a continuous industry i, which is evenly distributed in the unit interval [0, 1]: i∼U [0, 1]. Each industry feature is represented by the parameter z i (z i > 0), which represents the imported technological complexity of the industry. e complexity of the import industry also determines the location of the country's product space, while it is linked to more advanced production technologies. Higher complexity means a related division of labor, therefore involving an increase in the number of tasks in the production process. In this regard, increasingly complex tasks may lead to the benefits of specialization division, but the high complexity of imports may also reduce their initiative to produce or have an impact on domestic capital allocation. e production equation is an increasing function assigned to the current production share λ c and human capital level h c over time and also a function of the complexity z i of import industry i. e parameter α c influences the import industry complexity through the formula α c � θ c − δ c . When θ c ≥ 0, then, it shows that the complexity of import industry is consistent with the suitability of domestic resource endowment or human capital, and import complexity can be well absorbed and transformed by the domestic market. So, the import product complexity can potentially actively promote the growth of total factor productivity in the industry, such as the shared human capital, fixed costs, legal system, and market knowledge. δ c ≥ 0 expresses the possible negative effects. For example, although the import product complexity encourages domestic industries to learn and imitate, this kind of complementary production (imitation learning) may bring some risk of production failure, or import complexity does not have appropriate capacity to absorb in domestic. From the perspective of resource allocation, it is a waste, which will have a negative impact on the domestic market. In principle, α c (≺/≻)0 depends on the total effects of the import product complexity, previously analyzed, on total factor productivity.
φ c (z i ) is the complex density function of a country c, and the total output of this country c is For analysis purpose, this paper assumes that the industrial complexity z i of imports in country c obeys the general gamma distribution: z i ∼ Gamma(K c , β c ), and meanwhile, the parameters K c > 0 and β c > 0, as shown in the following: From the properties of gamma distribution, the average complexity of the country c is z c � E c (z i ) � k c β c , the variable V c (z i ) � k c β 2 c , and the skewness of the density function of its variance is 2/ �� k c , in which k c denotes to parameter shape and β c is the scale parameter of Gamma distribution. k c can be interpreted as the shape coefficient of technical parameters and industrial production characteristics. In each country, k c � k, c � 1, 2, . . ., n, and parameter β c has the effect of replacing horizontally and vertically scaled graphics, which is related to the specific distribution of complexity in each country, so every country is unique. e average import complexity of a country c is z c � k c β c .
Substituting (1) and (3) into (2), the output level of a country c can be expressed as follows: e human capital formation equation is shown as follows [8]: where μ c > 0 represents the effectiveness of the human capital training system in the country c. According to the initial level of human capital, compared with Lucas' human capital model, now, the formation of human capital includes importing average complex Z c as one of the parameters of accumulation equation. e output growth is e instantaneous output growth rate is e total factor productivity growth is According to total factor productivity (8), in the production function α c � θ c − δ c , if the α c is negative, the increased import complexity has a negative impact on total factor productivity. In other words, if θ c < δ c , the benefit of specialization plays a dominant role in the O-ring. On the contrary, it has a positive impact on total factor productivity, which will be tested by empirical analysis.

Measurement of Total Factor Productivity. Van Beveren
and Tian et al. tested the "consistency" and "robustness" of the results of different TFP measurement methods and found that if the panel data is based on the macroindustry, compared with the parametric method SFA, the nonparametric method DEA is a more suitable measurement method [9,10]. erefore, this paper used DEA-Malmquist method for calculation. e paper adopts traditional double input and single output model to calculate total factor productivity, including capital input and labor input, and the output is expressed as industrial added value. Among them, capital input is measured by capital stock. Since capital stock is different from output and labor data that may be obtained directly, it is required to make scientific estimation. According to the existing literature, the capital stock is estimated by the general perpetual inventory method [11,12].

Calculation of
en, the national adaptability and product complexity are defined: where F represents the national fitness (complexity) level, Q represents product complexity, and M cp has the same meaning as reflection method. 〈F (n) c 〉 c and 〈Q (n) p 〉 p is the average of product complexity and national fitness during each iteration. Compared with reflection method, Tacchella method has the following advantages: the calculation results of reflection method tend to converge, and the calculation results of Tacchella method are more divergent, making it easier to distinguish between national fitness and product complexity. Compared to the reflection method, Tacchella method does not undermine the relationship between national capabilities and product complexity. In reflection method, the variables K c and K p cannot be properly measured and reflect product complexity. However, in the Tacchella method, F (n) c can more accurately measure the property represented by Q (n) p [13]. If Com it p denotes the product complexity, Comim it denotes the complexity of import industry, and then, its calculation equation is as follows: where Comim it refers to the import industry complexity in t year, Com it p refers to the import product complexity in t year, Im it p refers to the total trade volume of imported products p in t year, and Im it refers to the total import trade volume of i industry in t year. According to (11), import product p is multiplied by the complexity of product p according to the weight of the total import industry volume, and then, all the product complexity values included in industry i are assigned according to the weight and summarized to obtain the industrial complexity. e paper adopts traditional double input and single output model to calculate the total factor productivity, including capital input and labor input, and the output is expressed as industrial added value. Among them, capital input is measured by capital stock. Since capital stock is different from output and labor data that may be obtained directly, it is required to make scientific estimation. According to the existing literature, the capital stock is estimated by the general perpetual inventory method [11,12]. Considering the availability of data, this paper takes the average annual number of employees in the industry to represent the labor input. Since the number of employees in the industry from 2012-2014 is no longer available in the China Statistical Yearbook, it is summarized according to the data of different industries in the China Labor Statistical Yearbook. Since 2012, the state divided "rubber and plastic product industry" into "rubber product industry" and "plastic product industry." However, considering that only three years of new industry division standards are involved in the data used in this study, the state still divides and merges the industry division

Setting of the Econometric Model.
According to the research objective, the paper set the model as two basic econometric models: ln g i,t � α 0 + β 0 L · ln g i,t + β 1 L · ln yyICom i,t + β 2 L · ln yyimmidu + cContr where ln g i,t denotes the logarithm of productivity growth rate, which is expressed as the logarithms of total factor productivity (TFP), technical change (TC), and technological efficiency (TE), respectively, i denotes 34 industries, and ln g i,t−1 denotes the productivity growth rate of one lagged stage. t refers to the year. In model equation (12), ICom is the import industry complexity and immidu is the import product density. In model equation (13), ICom i,t is the import industry complexity from countries along the "Belt and Road," and yyimmi duis the density of importing products from countries along the "Belt and Road." Contr is the control variable, including import permeability, export permeability, R&D density, enterprise scale, and capital density. η i and ε i,t reflect the individual effect of differences in various industries and other disturbance terms.

Variable Selection.
e main explanatory variables are import product complexity (ICom) and imported product density (immidu). e import product complexity was figured out using the fitness method [13] and the reflection method in robustness test [6]. Regarding the product density, the closer the distance between product and superior product is, the more easily the transformation will succeed. A higher import product density indicates it is more suitable for domestic technological absorption, thus facilitating the increase of domestic total factor productivity.
Other control variables include the following. R&D Density (rd). e R&D input behavior not only influences the total factor productivity but also affects product complexity. Taking the logarithm of the ratio of "total internal expenditure of technological development funds" and the total output value over the years as the substitution variable of R&D technology, the R&D density is expressed as ln(R&D/Y + 1). Export Permeability (imrat). e enterprise can get a greater learning effect by export, further promoting the increase of total factor productivity and technical change. Export permeability is the ratio of the export/import amount to the total output of the industry. Import Permeability (exrat). e industrial trade liberalization may have effect on total factor productivity of industry. Referring to the practice of [14], the paper used import permeability to represent the degree of industrial trade liberalization, so as to control its influence on industrial total factor. Enterprise Scale (qygm). e enterprise scale is considered one of the important factors affecting enterprise productivity. In this paper, the enterprise scale is expressed by the ratio between the constant added value of industry and the number of enterprises in the industry. Capital Density (zblab). e capital density can control its impact on total factor productivity and can eliminate the impact of national scale. Dividing the amount of capital invested in each industry by the number of people employed, we can take capital density ln (K/L + 1) and put it into equation. Table 1, equations (1)-(3) are the regression result of product complexity imported by China from all over the world, and equations (4) and (5) are the regression result of product complexity imported by China from "B&R" countries. e dependent variables of equations (1) and (4) are total factor growth index, the dependent variables of equations (2) and (5) are technology progress growth index, and the dependent variables of equations (3) and (6) are technology efficiency growth index. From the perspective of equations (1)-(3), the increase in the complexity of imported products worldwide can promote the growth of Malmquist productivity and technological progress, but the impact on technical efficiency is not significant. e import product density promotes the growth of total factor productivity but has no significant impact on technical progress and technological efficiency. Both export permeability and import permeability promote productivity and technological progress; research and development investment has a significant positive impact on the total factor and nonsignificant negative impact on technical efficiency, but it significantly promotes the growth of technological progress; enterprise scale has a negative influence on Table 1: e influence of import complexity on total factor productivity.  All over the world All over the world All over the world "B&R" "B&R" "B&R" * * * and * * * express 10%, 5%, and 1% significant levels. Table 2: e influence of import complexity on total factor productivity.  All over the world All over the world All over the world "B&R" "B&R" "B&R" (1) e import complexity of robustness is calculated by reflection method, but the explanatory variables of import complexity in the table are expressed with the same symbol. * * * and * * * express 10%, 5%, and 1% significant levels. productivity and technological progress, and its influence on technical efficiency is approximately 0; capital intensity has a significant positive impact on productivity and technological progress, while its impact on technological efficiency is negative but not so significant.

Empirical Analysis. In
From equations (4)- (6), the increase in complexity of importing products from "B&R" countries does not have a significant effect on the growth of Malmquist productivity and technological progress and has a significantly negative on the technical efficiency. Similarly, the density of imported products promotes the growth of total factor productivity but does not significantly affect technological progress and efficiency. e import permeability of China and "B&R" countries has no significant effect on the productivity, technological progress, and efficiency, while the export permeability has a significant effect on the productivity and technological progress but no significant effect on the technical efficiency. It is observed that the import product complexity and density plays a positive role to the total factor productivity.
is demonstrates that China's importing products worldwide shows a higher technical level and complexity level, and this urges China to produce more complex products, propels the increase of total factor production of the industry, and brings beneficial impact on the production growth rate. At the same time, it is conducive to domestic technology absorption and technological progress, showing good technical suitability. However, the increase in import complexity of "B&R" does not effectively promote the improvement of domestic total factor productivity, which indicates that the import trade structure of China and the "B&R" needs to be adjusted to some extent. e density of imported products is also expressed as the structure of imported products, which is manifested as insignificant technological progress and efficiency, but has a promoting effect on total factor productivity. It indicates that the import product density mainly promotes the growth of total factor productivity by increasing resource allocation efficiency from the perspective of cost.

Robustness Test.
Consider that the import complexity calculated by Tacchella et al. (2013) fitness method may have a bias on the total factor impact. In order to further verify the robustness of the model conclusion, the paper adopted the reflection method to regress the influence of import complexity on total factor productivity [13]. It can be seen from Table 2, that whether it is the entire sample or the sample of countries along " e Belt and Road," the results of the impact of import complexity on total factor productivity and the performance of the control variables are basically the same as those in Table 1. So, the conclusion of this paper can be proved to be robust.

Conclusions
is paper analyzes the effect of the import product complexity and density in promoting the growth of the total factor productivity. From the point of regression results, an increase in the complexity of China's imported products based on the samples all over the world significantly promotes the growth of the total factor productivity and technical progress, which demonstrates the technological progress is an investment used to improve people's knowledge and ability. However, the effect on promoting the technical efficiency is not obvious. e increase of import complexity based on "B&R" samples did not promote the improvement of total factor productivity and had a significant negative impact on technical effect, indicating that the structure of importing "B&R" products had no significant effect on the domestic technical progress. e import product density promotes the improvement of total factor productivity both all over the world and in "B&R" countries, and the effect is basically the same. e specific performance shows that the structure of imported products plays a certain role in promoting the cost saving and allocative efficiency.
In this paper, the analysis results show that the increase in import complexity of China from countries along the "B&R" route did not effectively promote the improvement of total factor productivity of the industry. e reason for this is that China mainly imports resources product or primary product from "B&R" countries, leading to too much of domestic resources being taken up. So, when the government expands import trade from "B&R" countries, it should pay attention to the composition of imported products, should fully respect the spontaneous market adjustment of economic resources, act as a good supporter and maker of market rules, make immediate policy adjustment to the import trade structure of "B&R," and actively encourage to expand the import of manufacturing products from "B&R" countries, such as labor-intensive consumer goods, which are the main export products of developing country and also the industry where China has gradually lost its comparative advantage. On the one hand, increasing the import of manufacturing products from "B&R" countries can promote domestic productivity, and, on the other hand, "B&R" countries can rely on China's large consumer market to drive the development of manufacturing industry in such countries and realize the common development and win-win cooperation.
Data Availability e data underlying the results presented in the study are available within the manuscript.

Conflicts of Interest
e authors declare that they have no conflicts of interest.