How production networks amplify economic growth James McNerney1, Charles Savoie2, Francesco Caravelli3, J. Doyne Farmer2;4 Technological improvement is the most important cause of long- 1 5.0 term economic growth, but the factors that drive it are still Met Tpt Elc China not fully understood. In standard growth models technology ChmRub Ait Cok Mnf is treated in the aggregate, and a main goal has been to un- 4.5 TexLth Mch Cst derstand how growth depends on factors such as knowledge Omn Wtt Pst 2 4.0 Wod Pup Ele production. But an economy can also be viewed as a net- Fod Min Fin Obs Hth work, in which producers purchase goods, convert them to new RtlHtl Otr Est goods, and sell them to households or other producers.3 Here 3.5 Whl Pub Ldt Ocm we develop a simple theory that shows how the network prop- erties of an economy can amplify the effects of technological 3.0 Output multiplier Edu improvements as they propagate along chains of production. Agr A key property of an industry is its output multiplier, which 2.5 can be understood as the average number of production steps required to make a good. The model predicts that the out- 2.0 United States put multiplier of an industry predicts future changes in prices, 3.5 Fod Cok Chm Tpt and that the average output multiplier of a country predicts Lth Est Agr Rub Wod Elc Wtt future economic growth. We test these predictions using data Tex Met 3.0 Mnf from the World Input Output Database and find results in Pup Mch Omn good agreement with the model. The results show how purely Min Ele Htl Ait structural properties of an economy, that have nothing to do 2.5 Fin Cst Sal with innovation or human creativity, can exert an important Ldt Ocm influence on long-term growth. Pst Hth Output multiplier Rtl Economic output is made by a complex network of industries that 2.0 Edu Otr buy goods from one another, convert them to new goods, and sell them Whl Obs Pub to households or other industries. Studies have examined a number of characteristics of production networks that hold across diverse economies, 1.5 including their link weight and industry size distributions,4{8 community Agriculture Manufacturing Services structure,7 and path-length properties.9 Economies typically have a Figure 1: Output multipliers in the Chinese and U.S. economies. heterogeneous network structure with a few highly central industries that The output multiplier of each industry is plotted against a standard are strong suppliers to the rest of the network,6, 8, 10 a feature that has industry classification. Node size corresponds to an industry's gross been incorporated into models where short-term fluctuations of economic output. Three-letter industry codes are given in Extended Data Table 1. output are generated by shocks to individual industries.8, 11{15 Here, we focus on how the structure of production networks affects long-term economic growth. Over the long term, changing industry productivities i's expenditures, Eq. (1) gives a measure of the trophic level of an significantly alter prices and production flows in the network. Multiple industry. In economics, L is also called i's total backward linkage17 or economic processes contribute to productivity change,16 but long-term i downstreamness.20 Letting A denote the matrix with elements a and improvements are thought to result primarily from improvements to ij L the vector with elements L , rearranging Eq. (1) gives the vector of technology,16 which is widely understood to be the principle driver of i output multipliers as L = (I − AT )−11, where 1 is a vector of 1s. growth.1 However, the processes of technological change and growth remain imperfectly understood. The output multiplier can also be understood in terms of network path 20{22 As technology evolves, the network structure of production plays a key lengths. Regarding the elements aji as transition probabilities in 23 role in amplifying changes to prices and production flows in an economy. a Markov chain, Li gives the average length of all production chains 17 ending at industry i, following each path backward through inputs until A key property of an industry i is its output multiplier Li, which can be defined recursively as it reaches households. (See Supplementary Information.) As a result, two factors influence the output multiplier of a producer: the fraction X of its expenditures that go directly to purchasing labor, and the output Li = Lj aji + 1; (1) multipliers of the goods that it buys. Higher labor expenditures make j it more likely that a dollar spent will go directly to the household node, where aji is the fraction of good j in producer i's expenditures. realizing the shortest possible path length of 1, and lowering the output To build intuition for this quantity, we make an ecosystem analogy. A multiplier. Similarly, dollars spent on goods from producers with high species in a food web can be represented as a node in a network, with output multipliers will take more steps to reach the household node than links to the species it eats. A species' place in the food web is often dollars spent on goods with low output multipliers. characterized by its trophic level { informally, its position along a food The output multipliers of an economy collectively help characterize chain.18 Photosynthesizers, which use sunlight as a resource, have trophic the economy's network structure. Two examples are shown in Fig. 1. level 1 by convention, while species that consume only photosynthesizers Using data from the World Input Output Database (WIOD),24 we plot have trophic level 2, and so on. Food webs typically have complex the output multipliers of China and the United States. (The WIOD structures where each node obtains inputs from multiple trophic levels, provides money flows between producers, aggregated into 35 industries so that trophic levels are usually not integers. Letting aji represent the in 40 countries, representing about 86% of global GDP.) The output energy fraction of prey j in species i's diet, Eq. (1) states that the trophic multipliers of industries in China are higher than those of the U.S. for two level Li of species i is one greater than the average trophic levels of the reasons. First, China is heavily concentrated in manufacturing industries species it consumes.19 such as Electrical and Optical Equipment (Elc) or Basic Metals and Similarly, an economy can be regarded as a network in which an Fabricated Metals (Met), which tend to have high output multipliers industry producing a good is a node, with links to the input goods because they have many steps of production.25 In contrast, the U.S. is it uses for production. (For simplicity, we lump together goods and heavily concentrated in industries such as Public Administration and services, calling them both \goods" for brevity, and assume each industry Defense and Compulsory Social Security (Pub) or Renting of Machinery produces only one good.) Household factors of production such as labor & Equipment and Other Business Activities (Obs), which tend to have are the base resource, so that producers that pay only households occupy shallow production chains. The second reason is that China's labor share trophic position 1. With aji as the fraction of good j in producer of gross expenditures is lower. The difference in the output multiplier 1 a Output GDP change Price change agriculture is more labor-intensive, giving it a lower output multiplier multiplier (% yr-1) (% yr-1) relative to other industries. Price a γ γ γa Output multipliers have long been used for predicting the impacts of a 2 a b <latexit sha1_base64="pBGmPKRIyEzMVGWZKzXVhUOJnDs=">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</latexit> γa γb GDP ` ´ ´ a change in final demand, such as a government stimulus.26 Additional final demand for a good requires the industry producing it to buy more H H inputs, increasing its production and setting off a chain reaction that Households increases the gross output of the economy. Intuitively, this amplification b Price b γb 1 <latexit sha1_base64="HlJ0B9dhyeVHdm66O9ndmNhesSE=">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</latexit> γb factor is greater when production chains are longer. ´ Industries Improvement rate Here we go further and propose that production chains play a key role in long-term, technology-driven growth. Let φ denote the amount of (% yr-1) ij b 15 good j needed