# Supply Chain Network Reconstruction

Measuring the risk of supply chain disruptions

Released
7/09/2022
##### Abstract

This concept paper, first proposed to the Australian Bureau of Statistics (ABS) Methodological Advisory Committee in October 2018, explores the feasibility of reconstructing the Australian network of domestic supply chains through entropy maximisation. This 'network approach' captures the flow (magnitude and direction) of goods and services through the economy. If feasibility can be established, the reconstructed network would fill a critical information gap in contemporary governance. Based on existing data and a partial observation of the underlying network, the reconstructed network could model the propagation of shocks throughout the economy. Notably, the network could address nascent concerns around supply chain disruption and systemic risk.

## Introduction

The disruptive events of the COVID-19 pandemic, trade restrictions and emerging risks from single-source imports have demonstrated the vulnerabilities of modern integrated economies. Emerging literature has demonstrated the potential to 1) reconstruct business supply chains, and 2) model the impact of shocks. Therefore, the ABS is investigating the prospect of reconstructing supply chain networks to measure systemic risks and strategic vulnerabilities. As a comprehensive map of the economy, a reconstructed network would fill critical data gaps and provide new statistical tools in policymaking, macro-economics, and supply chain research.

Existing ABS statistics paint a detailed picture of business specific characteristics, but only broad brushstrokes of economic movement. The ABS business longitudinal analysis data environment, for example, includes firm-level characteristics but does not include the relationships and flows between businesses. In terms of economic movement, the ABS national accounts provide information on the flow of goods and services through input-output tables (ABS, 2021) and supply-use tables (ABS, 2020). However, these statistics are aggregated by industry and product classifications. In contrast, the reconstructed network could harmonise these datasets and reveal the flow of goods and services at the firm level.

## Network Reconstruction

Network reconstruction methods are designed to estimate a complete network based on a partial observation of the underlying network. This can include individual nodes or connections, as well as global observations. For example, the number of connections for each node or simply the distribution of connections per node. We refer here to a directed network where the nodes are individual businesses, and the network connections indicate the supply or receipt of goods and services between two businesses.

Given the missing information, it is usually not possible to perfectly reconstruct the network. Instead, the aim is to generate an ensemble $$\mathbb{G}$$ of all possible networks that satisfy the observed data. Specifically, to generate a probability matrix $$\small{P=[{p_{ij}]}_{i,j=1}^N}$$ that encodes the distribution of all possible networks. Here, each $$p_{ij}$$ describes the probability $$\small{0<p_{ij}<1}$$ of a connection between $$i$$ and $$j$$. A Bernoulli trial of each $$p_{ij}$$ results in a graph $$\small G\in\mathbb{G}$$ described by an adjacency matrix $$\small{A=[{a_{ij}]}_{i,j=1}^N}$$ where each element $$a_{ij}=1$$ if a link exists, otherwise $$a_{ij}=0$$. After reconstructing a graph $$\small G\in\mathbb{G}$$, we then need to ascertain the weight $$w_{ij}$$ or value of goods and services being traded between businesses. Therefore, we construct a weighted adjacency matrix $$\small{W=[{w_{ij}]}_{i,j=1}^N}$$ to describe the weight and direction of goods and services from node $$i$$ to node $$j$$.

### Maximum Entropy Network Reconstruction

For the reconstruction to be statistically defensible, it should minimise bias with respect to all available information. Maximising entropy ensures that the link probabilities are 'maximally random' and therefore captures the uncertainty inherent in the estimate. Moreover, this approach reproduces the values of the information constraints on average, ensuring the outcome is unbiased. In this regard, entropy maximisation can be considered as a more general (non-parametric) form of Bayes’ theorem.

To maximise entropy, first consider that the reconstructed network contains information $$\small{I\left(G\right)=-\text{ln}P\left(G\right)}$$ about the underlying network (Cover & Thomas, 2006; Squartini et al., 2018). Where a reconstructed network $$\small{G}$$ is unlikely $$\small{P\left(G\right)\simeq0}$$, the information presents an almost infinite amount of 'surprise' (Cover & Thomas, 2006; Squartini et al., 2018). Where the reconstructed network is certain $$\small{P\left(G\right)=1}$$, no new information about the underlying network is presented. Iterating over the ensemble of all possible networks results in the Shannon entropy equation:

$$S=\left\langle I\right\rangle=\sum_{G\in\mathbb{G}} P\left(G\right)I\left(G\right)=\sum_{G\in\mathbb{G}}{-P\left(G\right)\text{ln} P\left(G\right)}$$

(Squartini et al., 2018)

From here, the aim is to maximise entropy subject to $$m$$ constraints $$C_m$$, each representing known information of the network. In general the constraints take the form:

$$\sum_{G\in\mathbb{G}}{P\left(G\right)C_m(G)=\left\langle C_m\right\rangle}$$

where the first constraint acts as a normalising condition,  $$\sum_{G\in\mathbb{G}}{P\left(G\right)=1}$$.

Here $$C_m(G)$$ is the value of the $$m^{th}$$ constraint for graph $$G$$ and $$\small \langle C_m \rangle$$ is the observed (or expected) value for constraint $$m$$. Constraining entropy by the expected value ensures the subsequent distribution preserves our observation in expectation (on average). Therefore, the Lagrangian maximising entropy with respect to our $$m$$ constraints follows:

$$\displaystyle \mathcal{L}\left[P\right]=S-\lambda_0\left[\sum_{G\in\mathbb{G}}{P\left(G\right)-1}\right]-\sum_{m=1}^{M}{\lambda_m\left[\sum_{G\in\mathbb{G}}{P\left(G\right)C_m(G)-\left\langle C_m\right\rangle}\right]}$$

Solving the partial derivatives results in the exponential random graph model distribution:

$$\sum_{G\in\mathbb{G}}{P\left(G\right)} =\displaystyle \frac{e^{-\sum_{m=1}^M \lambda_m \cdot C_m(G)}} {\sum_{G\in\mathbb{G}} \exp (-\sum_{m=1}^M \lambda_m \cdot C_m(G))} = \frac{e^{-H(G)}}{Z}$$

(Squartini et al., 2018)

In statistical mechanics terms, the Hamiltonian $$\small{H\left(G\right)=\sum_{m=1}^{M}{\lambda_mC_m\left(G\right)}}$$ describes the total energy of the system, and the partition function $$\small{Z=\sum_{G\in\mathbb{G}} \exp\left(-\sum_{m=1}^{M}{\lambda_mC_m\left(G\right)}\right)}$$ acts as a normalising constant (Squartini et al., 2018).

If the degree or number of connections $$k$$ for each node is known, then one of the constraints becomes $$\sum_{G\in\mathbb{G}}\sum_{i}{P\left(G\right)k_i\left(G\right)=\left\langle k\right\rangle}\$$where $$k_i\left(G\right)$$ is the degree of node $$i$$ for graph $$G$$. Given the degree $$k_i=\sum_{j} a_{ij}$$ is the number of connections for each node and the network is directed, each node has an in-degree $$k_i^{in}$$ and an out-degree $$k_i^{out}$$. So, the Hamiltonian takes the form:

$$H\left(G\right)=\sum_{i}\sum_{j\neq i}{\lambda_i^{out}a_{ij}+\lambda_j^{in}a_{ji}}\ =\sum_{i}\sum_{j\neq i}{\lambda_i^{out}k_i^{out}+\lambda_j^{in}k_j^{in}}$$

(Squartini et al., 2018)

Now that we have defined the Hamiltonian at the node-level, we can also define the probability distribution at the node-level. Consider that the probability $$p_{ij}$$ of a connection between $$i$$ and $$j$$ is equal to the expected value of a connection existing $$\small \left\langle a_{ij} \right\rangle$$ (Rachkov, Pjipers, & Garlashceilli, 2021). Therefore, the network can be split into pairs of directed links:

$$\displaystyle{p_{ij}=\frac{e^{-\sum_{i}{\lambda_i^{\text{out}}k_i^{\text{out}}}}e^{-\lambda_j^{\text{in}}k_j^{\text{in}}}}{1+e^{-\sum_{i}{\lambda_i^{\text{out}}k_i^{\text{out}}}}e^{-\lambda_j^{\text{in}}k_j^{\text{in}}}}}$$

For simplicity, we use the convention that $$x_j^{in}=e^{-\lambda_j^{in}k_j^{in}}$$ and $$x_i^{out}=e^{-\sum_{i}{\lambda_i^{out}k_i^{out}}}$$. Therefore:

$$\displaystyle{p_{ij}=\frac{x_i^{\text{out}}x_j^{\text{in}}}{1+x_i^{\text{out}}x_j^{\text{in}}}}$$

Recall that each $$p_{ij}$$ is an element in a probability matrix $$P$$ that encodes the probability of selecting a realisation $$G$$ of all possible graphs $$\mathbb{G}$$:

$$P=\left[\begin{matrix}p_{ij}^\ &\cdots&p_{iN}^\ \\\vdots&\ddots&\vdots\\p_{Nj}^\ &\cdots&p_{NN}^\ \\\end{matrix}\right]$$

### Fitness-Induced Exponential Random Graph

The degree, or number of connections per node, is usually unknown given the confidentiality of financial flows. However, Caldarelli et al. (2002) show that the link probability can be derived from a node's 'fitness', as opposed to any topological property. Here, fitness denotes a node's influence in the network, meaning high fitness nodes attract more connections. This method has been demonstrated to hold in international trade networks (Almog, Squartini, & Garlaschelli, 2015; Garlaschelli & Loffredo, 2008), interbank networks (De Masi et al., 2006; Garlaschelli & Loffredo, 2004; Bollobas et al., 2003), and financial securities networks (Cimini et al., 2015; Garlaschelli et al., 2005). Therefore, a 'fitness ansatz' $$\small{z}$$ correlated with the Lagrangian multipliers is used to approximate the nodes' degrees.

The theory of node fitness has also been observed in highly detailed domestic trade networks in Japan (Bernard, Moxnes and Saito, 2015) and Belgium (e.g. Bernard, Dhyne, Magerman, Manova and Moxnes, 2018; Dhyne and Duprez, 2017). These examples show that:

1. Larger firms generally have more trade connections.
2. Larger firms tend to transact with other large firms.
3. Firms tend to transact with geographically closer firms.

Additionally, the presence of the power law in many aspects such as the connection distribution (Bernard et al., 2018; Bernard, Moxnes and Saito, 2015), distance distribution (Bernard, Moxnes and Saito, 2015; Dhyne and Duprez, 2017) and weight distribution (Bernard et al., 2018) affirm the structural properties of the network.

Unlike the degrees, the weight of incoming and outgoing flows (total sales and purchases) for each businesses is generally known (e.g. from publicly disclosed balance sheets or taxation data). This aggregated weight or strength is defined for each node as $$\small{\hat{s}_i^{out}=\sum_{j=1}^{N} w_{ij}}$$ for the out-strength, and  $$\small{\hat{s}_j^{in}=\sum_{i=1}^{N} w_{ij}}$$ for the in-strength. For businesses, this can be considered as the total value of purchases (out-strength) and sales (in-strength) to other businesses. Therefore the link probability can be defined as:

$$\displaystyle{p_{ij}=\frac{x_i^{\text{out}}x_j^{\text{in}}}{1+x_i^{\text{out}}x_j^{\text{in}}}\approx\frac{zs_i^{\text{out}}s_j^{\text{in}}}{1+zs_i^{\text{out}}s_j^{\text{in}}}}$$

Notice that under this formulation the sum of incoming and outgoing probabilities for each node is equal to the expected in-degree $$\small{\sum_{j} p_{ij}=\langle k_i^{\text{out}} \rangle}$$ and out-degree $$\small{\sum_{i} p_{ij}=\langle k_j^{\text{in}} \rangle}$$. That is, the row-sum and column-sum of the $$\small{P}$$ matrix describe the expected number of links for each node. It follows too, that the probability matrix sums to the expected number of links $$\small{\langle L \rangle}$$ in the network:

$$\displaystyle{\sum_{i}\sum_{j\neq i} p_{ij}=\langle L \rangle}$$

This implies that if the total number of links (or even a sample of links) in the network is known, then $$z$$ can be calculated and shown to meet the expected value of the Lagrangian multipliers (Squartini et al., 2018). Furthermore, the reconstruction takes on a more intuitive process, wherein the expected number of links for each firm is simply the total number of links in the market, apportioned by each firm’s market share.

Finally, Squartini et al. (2018) demonstrate the validity of incorporating a gravity model, which employs a distance function $$\small{f(d_{ij})}$$ to penalise connections between geographically distant nodes, thereby accounting for logistics costs observed in the Japanese and Belgium trade networks (Bernard, Moxnes and Saito, 2015; Dhyne and Duprez, 2017):

$$\displaystyle p_{ij}=\frac{z\hat{s}_i^{out}\hat{s}_j^{in}e^{f(d_{ij})}}{1+z\hat{s}_i^{out}\hat{s}_j^{in}e^{f(d_{ij})}}$$

### Production Network Reconstruction

The Dutch Central Bureau of Statistics (CBS) has demonstrated the potential for applying network reconstruction to an entire economic network (Rachkov, Pijpers, & Garlaschelli, 2021; Hooijmaaijers & Buiten, 2019). Drawing from the work of Squartini et al. (2018), the CBS adapts the maximum entropy framework to the system of national accounts. Specifically, Rachkov, Pijpers, & Garlaschelli (2021) make use of supply-use tables to determine commodity flows and input-output tables to determine industry flows:

$$\displaystyle p_{ij}^{[\alpha]}=\frac{(z^{[\alpha]}\hat{s}_i^{out,[\alpha]}\hat{s}_j^{in,[\alpha]}I_{ij})d_{ij}} {1+(z^{[\alpha]}\hat{s}_i^{out,[\alpha]}\hat{s}_j^{in,[\alpha]}I_{ij})d_{ij}}$$

where:

• the link probabilities of each commodity group $$\alpha$$ are estimated independently;
• the out-strength $$\small{\textstyle \hat{s}_j^{out,[\alpha]}}$$ represents the volume of goods and services of commodity group $$\textstyle \alpha$$ that firm $$\textstyle j$$ supplies;
• the in-strength $$\small{\textstyle \hat{s}_i^{in,[\alpha]}}$$ represents the volume of goods and services of commodity group $$\alpha$$ that firm $$i$$ purchases;
•  $$\small c_i$$ refers to the industry classification of business $$i$$;

• $$\small I_{ij}$$ is a binary indicator that takes the value $$\small 1$$ where industry $$\textstyle c_i$$ trades with industry $$\textstyle c_j$$, and $$0$$ otherwise; and
• $$\small d_{ij}$$ is the sum of the absolute difference in location (i.e., longitude and latitude coordinates) between two businesses.

Note that the in-strength and out-strength are defined for each product market (or commodity group) as:

$$\hat{s}_j^{in,[\alpha]} =\frac{\mathrm{Net \ turnover \ of \ firm \ }j} {\mathrm{Total\ net \ turnover \ of \ industry \ }c} \small{D_{c_j}^{in,[\alpha]}}$$       and          $$\hat{s}_i^{out,[\alpha]} =\frac{\mathrm{Net \ turnover \ of \ firm \ }i} {\mathrm{Total\ net \ turnover \ of \ industry\ }c} \small{D_{c_i}^{out,[\alpha]}}$$

where:

•  $$\small D_{c_j}^{in,[\alpha]}$$ represents the value of commodity group $$\alpha$$ used in industry $$c$$; and
• $$\small D_{c_i}^{out,[\alpha]}$$  represents the value of commodity group $$\alpha$$ supplied by industry $$c$$.

### Weight Reconstruction

The simplest method for generating weights follows the maximum entropy approach. Maximising the Shannon entropy $$\small S=\sum_{i=1}^{N}\sum_{j=1}^{N} w_{ij}\text{ ln }w_{ij}$$ leads to $$\small w_{ij}^{ME}=\frac{s_i^{out}s_j^{in}}{W}\$$$$\forall i,j$$ where $$\small W=\sum_{j=1}^{N}s_j^{in}\equiv\sum_{i=1}^{N}s_i^{out}$$ is the total network weight. Here, the weights are conditional on the existence of a link. That is, each weight matrix is conditional on the graph (adjacency matrix) drawn from the probability matrix $$\small P$$. The marginal weights and marginal degrees are met on average (Squartini et al., 2018).

An alternative approach described by Parisi, Squartini, & Garlaschelli (2020) takes the probability matrix $$\small P$$ as prior information and maximises the Shannon entropy, constrained by the observed strength. The conditional entropy maximisation produces a distribution of weighted connections described by the tensor of coefficients $$\beta_{ij}$$ that can be sampled:

$$\displaystyle\beta_{ij}=\frac{p_{ij}}{w_{ij}^{ME}}\ \ \ \ \ \forall i\neq j$$

(Parisi, Squartini, & Garlaschelli, 2020)

Despite the size of the tensor, the method is computationally feasible given that each parameter can be calculated independently, enabling parallelisation (Parisi, Squartini, & Garlaschelli, 2020).

## Reconstruction Feasibility

The following section considers how the Dutch approach to network reconstruction can be applied in the Australian context with particular attention to potential data sources. Broadly speaking, the reconstruction can be considered as a constrained optimisation problem with national accounts input-output and supply-use tables forming global constraints, and individual tax records forming local unit-level constraints. If available, a sample of business connections would then be used to calibrate the optimisation. The calibration step verifies the assumption of the fitness ansatz by ensuring the expected degree of the sample meets the expected degree of the reconstruction. Given the datasets used to form constraints are commonly available to statistical offices (including the ABS), the only novel data component is the sample of links between businesses.

The primary units of analysis are businesses with a registered Australian Business Number (i.e., with an annual turnover greater than AU\$75,000.) As such, the frame has almost complete coverage of Australian businesses and transaction value. Business activity statement (BAS) data provided by the Australian Tax Office (ATO) break down sales and purchases made with a goods and services tax (GST) for each business. Given the GST on imports is reported separately and the GST on exports is generally exempt (ATO source), the scope can be easily reduced to domestic sales and purchases. Despite some missingness from GST-exempt products (namely agricultural), we can therefore determine the value of domestic sales and purchases for each business. For agriculture, sales volume can be calculated from total sales (from BAS data), less the value of exports as reported on customs declarations. This value can also be calculated for other industries to account for any other GST exceptions.

The ABS and CBS conform to the conceptually equivalent national accounting standards (system of national accounts) and similar categorisation of products and industries (the CBS reports 98 products across 81 industries, and the ABS reports 114 products across 67 industries). Therefore, the method's main data requirements are already satisfied.

Observations of the degree (or degree distribution) are required to calibrate and validate the reconstruction. Although bank transaction data would be ideal, practical limitations mean that this source would require significant investment to ensure it is usable for statistical purposes. Similarly, consignment data from freight transportation or package tracking information may prove to be viable, but currently faces similar practical limitations (aside from the obvious absence of digital goods and services). Instead, the ABS is considering manageable and scalable alternatives.

The introduction of single-touch payroll reporting has proliferated the use of common accounting software for businesses with more than 19 employees (Australian Tax Office, 2020). As a result, there has been a concurrent uptake in e-invoicing (i.e., using accounting software to send digital invoices). As such, a small number of accounting software companies provide business accounting software services (including e-invoices) to the majority of businesses. Although the coverage is skewed towards small businesses, the data covers pairs of trading businesses (buyers and suppliers). Therefore, large businesses will be present as suppliers to small businesses.

E-invoicing is a key feature of the Government’s modern digital economy strategy (Prime Minister of Australia, 2021; Department of Treasury, 2020). Although on hold due to the COVID-19 pandemic, it is reasonable to expect that e-invoicing will eventually be rolled out nation-wide (Prime Minister & Cabinet, 2021). Therefore, in the long term, e-invoicing data with near complete coverage could be suitable for statistical purposes.

Survey Data

Existing surveys could be amended to include information on trading relationships. To preserve privacy and reduce administrative burden, these questions would only need to capture aggregate relational data (Breza et al., 2020). For example, additional questions could include: 'How many businesses in industry $$c$$ do you supply commodity $$\alpha$$ to?', and 'What is the total value?' Therefore, in principle, existing surveys can be tailored to inform reconstruction without identifying individual businesses.

## Applications

The following sections describe the potential applications of the reconstructed network, specifically: in the context of government policymaking, macro-economic modelling, and supply chain research. The proposed method should be viewed as a two-stage model wherein the first stage requires reconstructing the network, and the second involves analysing or modelling potential shocks in the network. This additional step combines two, often separate, fields of research, as most network modelling is conducted on fully sampled (as opposed to reconstructed) networks. Given the abundance of information and implied dependence networks convey, it is reasonable to expect that networks could provide greater insight than existing data assets.

### Policymaking

Social and economic systems are driven by complex interactions between numerous interdependent agents, like households and businesses. The growing abundance of information available to policymakers makes it possible to embrace the complexity of these systems and better understand complex issues, i.e., wicked problems (Roberts, 2000).

The traditional approach to complex issues is to simplify the problem: reduce the number of factors, operate in distinct silos, aggregate data, assume linearity, and so on (Cairney & Geyer, 2017; Eppel & Rhodes, 2018; OECD, 2017). The complexity approach on the other hand, recognises that macroscopic phenomena (e.g. climate change, inequality, GDP, etc.) cannot be modelled as linear or independent processes (Cairney & Geyer, 2017; Eppel & Rhodes, 2018; OECD, 2017). Instead, outcomes result from complex interdependent interactions between micro-level agents (Cairney & Geyer, 2017; Eppel & Rhodes, 2018; OECD, 2017). Therefore, by reconstructing the complex network of micro-level relationships between businesses, policymakers can develop a greater understanding of broader economic outcomes.

In practical terms, the reconstructed network can quantify the effects of business relationships on business behaviour and performance. Given that the reconstructed network defines business suppliers and clients, it also implies competitors. Therefore, analysts can calculate the peer effects of neighbouring businesses (for details on peer effect, see: Lee, 2007; Di Falco, Doku, & Mahajan, 2020). For example, how a business is affected by supply shortages among neighbouring firms.

More complex modelling, discussed in the Macro-economic Modelling section below, can simulate dynamic changes in the network. The analytical potential is, for the time being, largely limited to tax data. However, linking additional data (e.g. from other administrative sources) makes it possible to study business dynamics in a variety of fields. For example:

• Macro-economic agencies (e.g. Department of Treasury) can study how economic forces (e.g. prices, interest rates, productivity, etc.) reverberate, dampen, or amplify across the economy.
• Micro-economic agencies (e.g. Australian Competition & Consumer Commission) can analyse the effects of business relationships on firm performance and market efficiency.
• Financial agencies (e.g. Australian Prudential Regulation Authority) can study the risk of financial crises and the impact of a market crash.
• Environmental agencies (e.g. Australian Climate Service) can use the network to understand energy use in production or the flow-on impacts of a natural disaster.

### Macro-economic Modelling

The policymaking examples above rely on sound macro-economic models. However, one of the main shortcomings of economic models is their reliance on highly aggregated statistics (Hendry & Muellbauer, 2018; Pagan, 2019). Fortunately, the abundance and granularity of information in the reconstructed network can be used to fine-tune a variety of models (Mitic, 2020).

Economic shocks can be triggered by a single business and are transmitted along business-level connections (Gabaix, 2011; Acemoglu et al., 2012). Therefore, the reconstructed network is necessary for policymakers to model how economic shocks propagate throughout the economy. For example, COVID-19 impacts, financial instability, supply chain disruption, or policy implementation.

The severity of economic shocks is not only determined by the starting point, but by the structure of the network (Starnini, Boguñá, & Serrano, 2019; Acemoglu, Akcigit, & Kerr, 2016). Squartini et al. (2013) for example, show that the changes in the network structure can be used as an 'early warning signal' of financial collapse. Additionally, Freixas, Laeven & Peydró (2015) explain that regulation designed to improve the stability of individual businesses can inadvertently harm the structure of the economy as a whole. Therefore, policymakers need to consider network structure as well as the most central (highly connected) nodes.

A vector auto-regression (VAR) model can be used as a parsimonious, data-driven approach to extend existing flows into the future while keeping the network structure fixed (Kumar at al., 2021; Kumar, Bansal, & Chakrabarti, 2020; Acemoglu, Akcigit, & Kerr, 2016). Hence, the model can provide detailed insights into short-term effects, such as disruptions in highly efficient just-in-time supply chains.

Although complex, an agent-based model (ABM) is well suited to complex networks because it simulates the interactions of each agent in the network (Ghorbani et al., 2014; Haldane & Turrell, 2019). Unlike traditional macro-economic models, ABMs are not restricted by assumptions around general equilibrium, perfect competition, or rationality (Mercure et al., 2016; Haldane & Turrell, 2019). Accordingly, there is considerable interest in incorporating ABMs as a standard tool for macro-economic modelling (Blanchard, 2018; Hendry & Muellbauer, 2018; Mercure et al., 2016; Haldane & Turrell, 2019). Within ABMs, actors can exhibit ‘realistic’ heterogeneous behaviour, interact with one another, and form new connections (Ghorbani et al., 2014; Mercure et al., 2016; Haldane & Turrell, 2019). Due to this flexibility, ABMs are an effective tool for policy experimentation as they can simulate how networks change over time (Ghorbani et al., 2014; Haldane & Turrell, 2019). To that end, ABMs are not limited by past observations when simulating future events and assessing risk (Hoffmann, 2017).

A pressing concern for policymakers is understanding how supply chains can adapt to disruptions. Given the level of detail available, the reconstructed network can be used to estimate the elasticity and substitution of products along the supply chain. This not only applies to VARs and ABMs but to existing and widely used economic models. For example, ABMs (Inoue & Todo, 2019) and general equilibrium models (Flaaen, & Pandalai-Nayar, 2019; Kashiwagi, Todo, & Matous, 2018; Carvalho et al., 2016) have been used to model the effect of product substitution among firms after a natural disaster. Therefore, policymakers can apply existing economic frameworks to study the capacity of supply chains to absorb or adapt to exogenous shocks.

### Supply Chain Resilience

As a trade-dependent nation, Australia is particularly exposed to international supply chain disruptions. Customs records (import and export declarations) are effective at identifying the primary source of import risk. However, these records fail to capture downstream dependencies in the domestic economy.

The Productivity Commission's report on supply chain vulnerabilities underscores the current data gap in downstream (domestic) supply chains (Productivity Commission, 2021). The reconstructed network offers a potential solution to fill this gap as it can reveal supply chains that are masked in industry-level statistics. The construction of the reconstructed network is based on 114 classifications of goods and services (from the national accounts). In comparison, customs records include detailed descriptions of goods (up to 5,722 for exports and 7,688 for imports (ABS, 2018)). Integrating customs records into the reconstructed network can improve the specificity of products, however the full path can only be implied. Therefore, additional data may be necessary to capture specific product supply chains.

The global pandemic and geopolitical disruptions have highlighted underlying vulnerabilities and triggered a whole-of-government response to supply chain resilience:

• The Department of Prime Minister and Cabinet (2021) Office of Supply Chain Resilience is coordinating the whole of government response.
• The Productivity Commission has developed a framework to identify supply chain risk as the intersection of essential, critical and vulnerable goods and services (Productivity Commission, 2021).
• The Department of Industry, Science, Energy and Resources (2021) is working with Australian industries to identify vulnerabilities and boost resilience in critical products.
• The Department of the Treasury is analysing and mitigating the impact of supply chain disruption, particularly centred around imports.
• The Department of Infrastructure, Transport, Cities and Regional Development (2021a; 2021b), in conjunction with the Commonwealth Scientific and Industrial Research Organisation (2021), is working to quantify and alleviate supply chain risk in physical infrastructure (roads, rail, etc).
• The Department of Home Affairs (2021a; 2021b; 2021c) is investigating and mitigating vulnerabilities in cyber supply chains and critical government infrastructure.
• The Department of Defence (2021) is continuing to review and limit supply chain risk to defensive capability.
• The Australian Trade and Investment Commission, alongside the Department of Foreign Affairs and Trade (2021a; 2021b), is supporting Australian exporters, trade relations, and supply chain adaptability.

The ongoing work on supply chains among government agencies has yielded a considerable amount of high-quality information. Quantitative findings can be easily integrated with the proposed reconstructed network and shared across organisations. But critically, expert and industry-specific information can be used to interpret the reconstructed network and guide policymaking.

Adjacent ABS work on real-time shipping can further increase the value and timeliness of the reconstructed network (MD News, 2021). The ABS, alongside the United Nations, is working to improve trade statistics using real-time ship positions from automated identification system (AIS) transponders. AIS data make it possible to identity port congestion and anticipate supply chain disruption (Verschuur, Koks, & Hall, 2020; Cerdeiro et al., 2020). Therefore, the reconstructed network can integrate physical supply chain vulnerabilities alongside production vulnerabilities.

To summarise, the reconstructed network, alongside techniques described in the Macro-economic Modelling section above, can help quantify and anticipate supply chain disruption and structural risk in the economy.

## Conclusion

Network reconstruction presents new opportunities to quantify complex economic and social systems. More research is needed on how to apply the reconstructed network in practice. However, the growing body of work in network science suggests that network reconstruction has considerable potential to address emerging issues in policymaking, macro-economic modelling, and supply chain vulnerabilities.

Harry Raymond & Daniel Elazar

Australian Bureau of Statistics, Methodology Division, Canberra

### References

Acemoglu D., Akcigit U., Kerr W. (2016). Networks and the macroeconomy: An empirical exploration NBER Macroecon. Annual, 30 (1), pp. 273-335

Acemoglu, D., Carvalho, V. M., Ozdaglar, A., & Tahbaz‐Salehi, A. (2012). The network origins of aggregate fluctuations. Econometrica, 80(5), 1977-2016. https://doi.org/10.3982/ECTA9623

Almog, A., Squartini, T., & Garlaschelli, D. (2015). A GDP-driven model for the binary and weighted structure of the international trade network. New Journal of Physics, 17(1), 13009. https://doi.org/10.1088/1367-2630/17/1/013009

Anand, K., van Lelyveld, I., Banai, Á., Friedrich, S., Garratt, R., Hałaj, G., Fique, J., Hansen, I., Jaramillo, S. M., Lee, H., Molina-Borboa, J. L., Nobili, S., Rajan, S., Salakhova, D., Silva, T. C., Silvestri, L., & de Souza, Sergio Rubens Stancato. (2018). The missing links: A global study on uncovering financial network structures from partial data. Journal of Financial Stability, 35, 107-119. https://doi.org/10.1016/j.jfs.2017.05.012

Australian Bureau of Statistics (2020). Australian National Accounts: Supply Use Tables, retrieved September 9, 2020 https://www.abs.gov.au/statistics/economy/national-accounts/australian-national-accounts-supply-use-tables/latest-release

Australian Bureau of Statistics (2021). Australian National Accounts: Input-Output Tables, retrieved September 9, 2020 https://www.abs.gov.au/statistics/economy/national-accounts/australian-national-accounts-input-output-tables/2018-19

Australian Tax Office, (2020). Single Touch Payroll, retrieved September 1, 2020, https://www.ato.gov.au/business/single-touch-payroll/

Bernard, A. B., Dhyne, E., Magerman, G. C. G., Moxnes, A., & Manova, K. (2019). The origins of firm heterogeneity: A production network approach, National Bureau of Economic Research. https://doi.org/10.3386/w25441

Bernard, A. B., Moxnes, A., & Saito, Y. U. (2019). Production networks, geography, and firm performance. The Journal of Political Economy, 127(2), 639-688. https://doi.org/10.1086/700764

Boehm C. E., Flaaen A., Pandalai-Nayar A. (2019). Input Linkages and the Transmission of Shocks: Firm-Level Evidence from the 2011 Tōhoku Earthquake. The Review of Economics and Statistics; 101 (1): 60–75.

Breza, E., Chandrasekhar, A. G., McCormick, T. H., & Pan, M. (2020). Using aggregated relational data to feasibly identify network structure without network data. The American Economic Review, 110(8), 2454-2484. https://doi.org/10.1257/aer.20170861

Buldyrev, S. V., Parshani, R., Paul, G., Stanley, H. E., and Havlin, S. (2010). Catastrophic cascade of failures in interdependent networks. Nature, 464(7291), 1025.

Cairney, P. & Geyer:, R. (2017). "A Critical Discussion of Complexity Theory how does Complexity Thinking improve our Understanding of Politics and Policymaking?" Complexity, Governance & Networks, Vol. 3, No 2, p. 1-11  doi: http://dx.doi.org/10.20377/cgn-56

Caldarelli, G., Capocci, A., De Los Rios, P., & Muñoz, M. A. (2002). Scale-free networks from varying vertex intrinsic fitness. Physical Review Letters, 89(25), 258702-258702. https://doi.org/10.1103/PhysRevLett.89.258702

Carvalho V. M., Nirei M., Saito Y. U., & Tahbaz-Salehi, A. (2016). "Supply Chain Disruptions: Evidence from the Great East Japan Earthquake", Discussion papers 287, Policy Research Institute, Ministry of Finance Japan.

Cerdeiro, D. A, Komaromi, A., Liu, Y., Saeed, M. (2020). World Seaborne Trade in Real Time: A Proof of Concept for Building AIS-based Nowcasts from Scratch, IMF Working Papers, International Monetary Fund

Cimini, G. Squartini, T., Garlaschelli, D., Gabrielli, A. (2015). Systemic risk analysis on reconstructed economic and financial networks, Sci. Rep. 5 15758. http://dx.doi.org/10.1038/srep15758.

Commonwealth Scientific and Industrial Research Organisation (2021). ‘Unlocking infrastructure investment and regulatory options for more efficient transport of agriculture and broader freight’, Transport logistics-TraNSIT, retrieved September 9, 2020, https://www.csiro.au/en/research/technology-space/it/transport-logistics-transit

Cover, T. M., Thomas, J. A. (2006). Elements of Information Theory, Wiley-Interscience

De Masi, G., Iori, G., & Caldarelli, G. (2006). Fitness model for the italian interbank money market. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 74(6 Pt 2), 066112-066112. https://doi.org/10.1103/PhysRevE.74.066112

Department of Defence (2021). Global Supply Chain Program, retrieved September 9, 2020, https://www1.defence.gov.au/business-industry/industry-programs/global-supply-chain

Department of Foreign Affairs and Trade (2021a). Joint Statement on the Supply Chain Resilience Initiative by Australian, Indian and Japanese Trade Ministers, retrieved September 9, 2020, https://www.dfat.gov.au/news/media-release/joint-statement-supply-chain-resilience-initiative-australian-indian-and-japanese-trade-ministers

Department of Foreign Affairs and Trade (2021b). ‘Pivot: Diversifying Australia’s Trade and Investment Profile’, Australian government response joint standing committee trade investment growth report retrieved September 9, 2020, https://www.dfat.gov.au/sites/default/files/government-response-joint-standing-committee-trade-investment-growth-report.pdf

Department of Home Affairs (2021a). Critical Technology Supply Chain Principles, Discussion Paper, retrieved September 9, 2020, https://www.homeaffairs.gov.au/reports-and-pubs/files/critical-technology-supply-chain-principles-discussion-paper.pdf

Department of Home Affairs (2021b). Protecting Critical Infrastructure and Systems of National Significance, Consultation Paper, retrieved September 9, 2020, https://www.homeaffairs.gov.au/reports-and-pubs/files/protecting-critical-infrastructure-systems-consultation-paper.pdf

Department of Home Affairs (2021c). Australia’s Cyber Security Strategy 2020, retrieved September 9, 2020, https://www.homeaffairs.gov.au/cyber-security-subsite/files/cyber-security-strategy-2020.pdf

Department of Industry, Science, Energy and Resources (2021). Make it Happen: The Australian Government’s Modern Manufacturing Strategy, retrieved September 9, 2020, https://www.industry.gov.au/data-and-publications/make-it-happen-the-australian-governments-modern-manufacturing-strategy

Department of Infrastructure, Transport, Cities and Regional Development (2021a). The National Freight Data Hub, retrieved September 9, 2020, https://www.infrastructure.gov.au/transport/freight/national-freight-data-hub/index.aspx

Department of Infrastructure, Transport, Cities and Regional Development (2021b). National Freight and Supply Chain Strategy, National Action Plan, retrieved September 9, 2020, https://www.freightaustralia.gov.au/sites/default/files/documents/national-action-plan-august-2019.pdf

Department of Treasury (2020). Options for mandatory e-Invoicing adoption by businesses, retrieved September 1, 2020, from https://treasury.gov.au/consultation/c2020-122716

Dhyne, E., & Duprez, C. (2017). It's a small, small world. A guided tour of the Belgian production network. International Productivity Monitor, (32), 84-96.

Dr Amineh Ghorbani A, Dr Francien DechesneB , Dr Virginia DignumC, Prof. Dr. Catholijn Jonker (2014). Enhancing ABM into an Inevitable Tool for Policy Analysis

Eppel, E.A. & Rhodes, M.L. (2018). "Complexity theory and public management: a ‘becoming’ field", Public management review, vol. 20, no. 7, pp. 949-959.

Freixas X, Laeven L, Peydró J (2015). “Chapter 8 – system risk and microprudential regulation” Systemic risk, crises, and macroprudential regulation. MIT Press, Boston

Furtado, B. A., Fuentes, M. A., & Tessone, C. J. (2019). Policy modeling and applications: State-of-the-art and perspectives. Complexity (New York, N.Y.), 2019, 1-11. https://doi.org/10.1155/2019/5041681

Gabaix X. (2011). The granular origins of aggregate fluctuations, Econometrica, 79 (3), pp. 733-772

Garlaschelli, D., & Loffredo, M. I. (2004). Fitness-dependent topological properties of the world trade web. Physical Review Letters, 93(18), https://doi.org/10.1103/PhysRevLett.93.188701

Garlaschelli, D., Battiston, S., Castri, M., Servedio, V. D. P., & Caldarelli, G. (2005). The scale-free topology of market investments. Physica A, 350(2), 491-499. https://doi.org/10.1016/j.physa.2004.11.040

Ghorbani, A, Dechesne, F, Dignum, V & Jonker, CM (2014). 'Enhancing ABM into an inevitable tool for policy analysis', Journal of Policy and Complex Systems, vol. 1, no. 1, pp. 61-76.

Haldane, A. G., & Turrell, A. E. (2019). Drawing on different disciplines: Macroeconomic agent-based models. Journal of Evolutionary Economics, 29(1), 39-66. doi:http://dx.doi.org.virtual.anu.edu.au/10.1007/s00191-018-0557-5

Hoffmann, C. H. (2017). Towards understanding dynamic complexity in financial systems Structure‐based explanatory modelling of risks. Systems Research and Behavioral Science, 34(6), 728-745. https://doi.org/10.1002/sres.2414

Hooijmaaijers, S., & Buiten, G., (2019). A methodology for estimating the Dutch interfirm trade network, including a breakdown by commodity, Centraal Bureau van Statistiek

Inoue, H., Todo, Y. (2019). Firm-level propagation of shocks through supply-chain networks. Nat Sustain 2, 841–847

Kashiwagi, Y., Todo, Y., & Matous, P. (2018). Propagation of economic shocks through global supply chains—Evidence from Hurricane Sandy. Review of International Economics. https://doi.org/10.1111/roie.12541

Kumar, A., Chakrabarti, A. S., Chakraborti, A., & Nandi, T. (2021). Distress propagation on production networks: Coarse-graining and modularity of linkages. Physics A, 568, 125714. https://doi.org/10.1016/j.physa.2020.125714

Kumar, S., Bansal, A., & Chakrabarti, A. S. (2020). Ripples on financial networks. The European Journal of Finance, 1-22. https://doi.org/10.1080/1351847X.2020.1835686

Lebacher, M., Cook, S., Klein, N., and Kauermann, G., (2019). In search of lost edges: a case study on reconstructing financial networks arXiv:1909.01274

LeBaron, B., & Tesfatsion, L. (2008). Modeling macroeconomies as open-ended dynamic systems of interacting agents. The American Economic Review, 98(2), 246-250. https://doi.org/10.1257/aer.98.2.246

Mazzarisi, P., and Lillo, F., (2017). Methods for Reconstructing Interbank Networks from Limited Information: A Comparison. 10.1007/978-3-319-47705-3_15.

Mercure, J., Pollitt, H., Bassi, A. M., Viñuales, J. E., & Edwards, N. R. (2016). Modelling complex systems of heterogeneous agents to better design sustainability transitions policy. Global Environmental Change, 37, 102-115. https://doi.org/10.1016/j.gloenvcha.2016.02.003

Mitic, P. (2020). Systemic shock propagation in a complex system. Soft Comput 24, 13667–13685 https://doi.org/10.1007/s00500-019-04466-6

Organisation for Economic Cooperation and Development (2017). Debate the Issues: Complexity and policy making, OECD Insights, OECD Publishing, Paris, http://dx.doi.org/10.1787/9789264271531-en.

Pagan, A. (2019). Australian Macro-Econometric Models and Their Construction – A short History Centre for Applied Microeconomic Analyses Working Paper, Australian National University

Parisi, F., Squartini, T., & Garlaschelli, D. (2020). A faster horse on a safer trail: Generalized inference for the efficient reconstruction of weighted networks. New Journal of Physics, 22(5), 53053. https://doi.org/10.1088/1367-2630/ab74a7

Prime Minister & Cabinet (2021). Tracking progress to 2030, Australia’s Digital Economy retrieved from https://digitaleconomy.pmc.gov.au/strategy/tracking-progress

Prime Minister of Australia (2021). A modern digital economy to secure Australia’s future, Media release, retrieved September 1, 2020, https://www.pm.gov.au/media/modern-digital-economy-secure-australias-future

Productivity Commission (2021). Vulnerable Supply Chains, Productivity Commission Study Report, retrieved from https://www.pc.gov.au/inquiries/completed/supply-chains/report/supply-chains.pdf

Rachkov, A., Pijpers, F.P., Garlaschelli, D. (2021). Potential Biases in Network Reconstruction Methods Not Maximizing Entropy, Discussion Paper, Centraal Bureau van Statistiek https://www.cbs.nl/en-gb/background/2021/09/potential-biases-in-network-reconstruction-methods

Ramadiah, A., Caccioli, F., & Fricke, D. (2020). Reconstructing and stress testing credit networks. Journal of Economic Dynamics & Control, 111, 103817. https://doi.org/10.1016/j.jedc.2019.103817

Roberts, N.C. (2000). "Wicked Problems and Network Approaches to Resolution", International Public Management Review, International Public Management Network https://journals.sfu.ca/ipmr/index.php/ipmr/article/view/175

Squartini, T., Almog, A., Caldarelli, G., Van Lelyveld, I., Garlaschelli, D., & Cimini, G. (2017). Enhanced capital-asset pricing model for the reconstruction of bipartite financial networks. Physical Review. E, 96(3), 032315-032315. https://doi.org/10.1103/PhysRevE.96.032315

Squartini, T., Caldarelli, G., Cimini, G., Gabrielli, A., & Garlaschelli, D. (2018). Reconstruction methods for networks: The case of economic and financial systems. Physics Reports, 757, 1-47. https://doi.org/10.1016/j.physrep.2018.06.008

Squartini, T., Van Lelyveld, I., & Garlaschelli, D. (2013). Early-warning signals of topological collapse in interbank networks. Scientific Reports (Nature Publisher Group), 3, 3357.

Starnini M., Boguñá M., Serrano M.Á. (2019). The interconnected wealth of nations: Shock propagation on global trade-investment multiplex networks, Sci. Rep., 9 (1), pp. 1-10

Verschuur, J., Koks, E. E., & Hall, J. W. (2020). Port disruptions due to natural disasters: Insights into port and logistics resilience. Transportation Research. Part D, Transport and Environment, 85, 102393. https://doi.org/10.1016/j.trd.2020.102393