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The propagation of the economic impact through supply chains: The case of a mega-city lockdown against the spread of COVID-19
Hiroyasu Inoue, Yasuyuki Todo
TL;DR
The paper examines how a COVID-19 lockdown of Tokyo could affect production elsewhere through inter-firm supply chains. It simulates shutdowns of non-essential production using a firm-level agent-based model and finds that a one-month lockdown sharply reduces Japanese production, with indirect losses exceeding direct Tokyo losses.
Problem
The study asks how a Tokyo lockdown’s economic effects would propagate through supply chains, a dimension not incorporated in earlier COVID-19 impact estimates described by the paper.
Source: §1 · p. 2Method
The authors apply a dynamic agent-based model to Japanese firm-level supply chains and simulate shutdowns of non-essential production in Tokyo for periods up to two months.
Source: §1 · p. 2, §3.2 · p. 3Results
A one-month lockdown reduces Japan’s daily production by 86.1% or 1.25 trillion yen, while indirect losses outside Tokyo are twice the direct Tokyo loss.
Source: §4.1 · p. 3, §5 · p. 5Takeaways & Limitations
The authors conclude that lockdowns of major cities should be treated as a last resort and, if unavoidable, kept as short as possible.
Source: §5 · pp. 5–6The model assumes firms cannot find new suppliers during disruptions, which may overestimate propagation, although the authors expect this overestimation to be minimal for lockdowns of at most two months.
Source: §5 · p. 6
Abstract
from arXiv · showhide
This study quantifies the economic effect of a possible lockdown of Tokyo to prevent spread of COVID-19. The negative effect of the lockdown may propagate to other regions through supply chains because of shortage of supply and demand. Applying an agent-based model to the actual supply chains of nearly 1.6 million firms in Japan, we simulate what would happen to production activities outside Tokyo when production activities that are not essential to citizens' survival in Tokyo were shut down for a certain period. We find that when Tokyo is locked down for a month, the indirect effect on other regions would be twice as large as the direct effect on Tokyo, leading to a total production loss of 27 trillion yen in Japan, or 5.3% of its annual GDP. Although the production shut down in Tokyo accounts for 21% of the total production in Japan, the lockdown would result in a reduction of the daily production in Japan by 86% in a month.
1 Introduction
The paper asks how a Tokyo lockdown could affect production beyond the city through inter-firm supply chains. It applies an agent-based model to Japan’s firm-level supply chains to quantify that effect, addressing a gap in COVID-19 impact estimates that do not incorporate complex inter-firm links.
1 Introduction
- A Tokyo lockdown could transmit economic effects to other regions through supply chains, as illustrated by Wuhan-related parts shortages that reduced Honda production in Japan.Wuhan’s lockdown affected a city central to automobile production, and the disruption reached Japanese plants through parts supplies.Source: §1 · pp. 1–2
- Prior studies mostly examined shocks from natural disasters; Inoue and Todo found earthquake-related supply-chain losses outside directly hit areas of 11 trillion yen, versus 100 billion yen in direct losses.Their findings indicate that supply-chain propagation can exceed the direct effect of a shock.Source: §1 · p. 1
- The study applies the Inoue and Todo agent-based framework to Japan’s actual supply chains to simulate production outside Tokyo when non-essential Tokyo production is shut down.Tokyo is selected as a major city and global supply-chain hub, amid policymakers’ discussion of a possible lockdown.Source: §1 · p. 2
- Earlier COVID-19 impact estimates used country-level econometric or general-equilibrium models and did not incorporate complex inter-firm linkages.The paper argues that this omission may lead to undervaluing the effects that propagate through supply chains.Source: §1 · p. 2
2 Data
The study combines firm attributes and major supplier-customer links from Tokyo Shoko Research with Japan’s input-output table. Its network data cover most Japanese firms but omit foreign links and transaction values, requiring estimation and restricting the analysis sample.
2 Data
- The Tokyo Shoko Research data contain 1,668,567 firms and 5,943,073 supply-chain links, but the analysis excludes firms without sales information and uses 966,627 firms and 3,544,343 links.Firm attributes and links are from 2016; the input-output table is from 2015, and industries are simplified from 1,460 to 187 categories.Source: §2 · p. 2
- Because transaction values are unavailable, the study estimates supplier-to-customer and consumer sales using supplier and customer sales plus the 2015 Japanese input-output table.The data also lack supply-chain links with foreign entities.Source: §2 · p. 2
- The network has power-law firm link counts, an average path length of 4.8, and a giant strongly connected component containing 46–48% of firms.The authors interpret the short paths and large component as evidence of closely connected firms and numerous supply-chain cycles.Source: §2 · p. 2
3 Method
The simulation uses a dynamic firm-level agent-based model in which supply-chain links and input varieties remain fixed. It applies specified Tokyo shutdown durations and averages five simulations with different inventory targets.
3.1 Model
- The model assumes firms use inputs from suppliers to produce output, while their input varieties and supplier-customer links remain fixed over time.Inventory targets are randomly determined from a Poisson distribution and average nine days of production.Source: §3.1 · p. 3
- Supply disruptions propagate downstream when inventories and existing substitute suppliers cannot cover shortages, and upstream when affected customers reduce demand.Firms can obtain more from already-connected suppliers with spare capacity, but cannot form new links in the model.Source: §3.1 · p. 3
3.2 Simulation Procedure
- The simulation shuts down non-essential production in Tokyo’s 23 wards for one day, one week, two weeks, one month, or two months.Essential sectors are wholesale, retail, utilities, transport, storage, communication, healthcare, and welfare; all sectors resume their pre-lockdown production level immediately afterward.Source: §3.2 · p. 3
- For each lockdown duration, the study averages five simulations using different randomly sampled firm inventory targets.The inventory targets are sampled from a Poisson distribution.Source: §3.2 · p. 3, §3.1 · p. 3
4 Result
The benchmark simulation finds that a month-long Tokyo lockdown causes large losses beyond Tokyo, with daily Japanese value added falling sharply as the lockdown continues. Alternative shutdown and demand-prioritisation assumptions produce similar month-long total losses.
4.1 Benchmark Result
- A one-month lockdown yields 27.8 trillion yen in total production losses, or 5.25% of annual GDP, with indirect losses outside Tokyo twice the direct Tokyo loss.Table 1 reports average simulation losses for shutdowns of non-essential production activities.Source: §4.1 · p. 3, Table 1 · p. 4
- After one month, Japan’s daily value added is approximately one-seventh of its pre-lockdown level, and the propagation effect grows as the lockdown continues.Figure 1 plots daily value added for different lockdown durations.Source: §4.1 · p. 4, Figure 1 · p. 4
- Firms distant from Tokyo are affected on the first lockdown day, and affected firms spread across the country within two weeks.Figure 2 visualizes the timing and geography of production reductions.Source: §4.1 · p. 4, Figure 2 · p. 5
4.2 Alternative Specifications
- Shutting down all Tokyo production raises the estimated one-month Japanese loss to 32.0 trillion yen, 15% above the 27.8 trillion yen benchmark.In this alternative, Tokyo’s daily production loss is 471 billion yen rather than 309 billion yen in the benchmark.Source: §4.2 · p. 4
- Prioritizing industrial demand over consumer demand yields a one-month Japanese production loss of 27.0 trillion yen, close to the 27.8 trillion yen benchmark.The authors conclude that this prioritization does not substantially alleviate propagation.Source: §4.2 · p. 5
5 Discussion and Conclusion
A month-long Tokyo lockdown would rapidly transmit production losses through supply chains, with losses outside Tokyo twice those in Tokyo. The authors advise treating mega-city lockdowns as a last resort and note that supplier substitution, headquarters-based location data, and the study’s Japan-only lockdown scope constrain interpretation.
5 Discussion and Conclusion
- 21.3% of Japan’s total production is in Tokyo’s non-essential sectors, yet a month-long lockdown would reduce daily Japanese production by 86.1%, or 1.25 trillion yen.After one day, value-added losses outside Tokyo are 82% of Tokyo’s loss; after one month, they are twice Tokyo’s loss, reaching firms further along supply chains.Source: §5 · p. 5
- A lockdown’s total production loss grows more than proportionally with duration, as longer shutdowns reach firms further from Tokyo along supply chains.When lockdown duration doubles, production loss becomes more than twice as large.Source: §5 · p. 5
- Measures such as limiting shutdowns or prioritising producers’ use of goods and services over consumers’ may not work well, particularly for long lockdowns.The authors caution that mitigation policies may fail when lockdown duration is long.Source: §5 · pp. 5–6
- The authors recommend mega-city lockdowns only as a last resort and, if unavoidable, keeping them as short as possible.They connect this recommendation to the large economy-wide effect of supply-chain propagation and its progressive increase with duration.Source: §5 · pp. 5–6
- The model assumes firms cannot find new suppliers after Tokyo suppliers are disrupted, though existing suppliers elsewhere can provide more.This may overestimate propagation, but the authors consider the effect potentially minimal for lockdowns of at most two months because finding new suppliers takes time.Source: §5 · p. 6
- Because the data locate headquarters rather than branches, Tokyo production may be overvalued, causing direct lockdown effects to be overestimated and propagation effects to be underestimated.The authors state that the large propagation effect found despite this possible underestimation leaves their key conclusion unchanged.Source: §5 · p. 6
- The study cannot quantify propagation from a Tokyo lockdown to foreign economies, although the authors expect international propagation during COVID-19.They reason that input substitution across countries would be difficult when all industrial countries are affected.Source: §5 · p. 6
- The simulation covers the economic effect of a major-city lockdown, not the overall economic effect of COVID-19.It excludes other regional restrictions and propagation from foreign-city lockdowns, so the total COVID-19 economic effect could be considerably larger.Source: §5 · p. 6
Appendix A Degree distribution of supply-chain network
Appendix A identifies Figure A.1 as showing the degree distribution of supply chains in Japan.
Appendix A Degree distribution of supply-chain network
- Figure A.1 presents the degree distribution of supply chains in Japan.The supplied caption identifies the figure’s subject but does not state its plotted values or pattern.Source: Figure A.1 · p. 7
Appendix B Data
Appendix B describes how firm-to-firm transaction values are estimated from reported relationships and national input-output data.
Appendix B Data
- The TSR data report at most 24 suppliers and customers per firm, but reverse-direction relationships can reveal more; headquarters coordinates are geocoded using a University of Tokyo service.The data include each firm’s headquarters address.Source: Appendix B · p. 7
- Tentative supplier sales are allocated across customers by customer sales, then adjusted using sector-pair transaction values from Japan’s 2015 input-output table.Final consumption for each sector is allocated to firms in proportion to their sales.Source: Appendix B · p. 8
Appendix C Model
Appendix C adapts Inoue and Todo’s firm-level agent-based supply-chain model, tracing how firms’ production, orders, and inventories interact. It specifies how firms set orders and production and update inventories after an economic shock.
Appendix C Model
- Initial daily production equals the sum of sales to customer firms and final consumers.The model denotes these trade volumes as A and C, respectively.Source: Appendix C · p. 8
- Firms order inputs to meet prior-day demand and gradually restore inventories toward a target measured in days of use.The inventory gap is closed over τ days; τ is set to six in the model.Source: Appendix C · p. 8
- Production capacity can fall when a shock disables production capital, while supply shortages impose additional production constraints.The model determines actual production after considering capacity and supply constraints.Source: Appendix C · p. 9
- Same-sector supplies can offset shortages, but firms cannot add new suppliers after a shock.The model assumes firms keep fixed supply chains.Source: Appendix C · p. 9
- If demand exceeds capacity, firms ration output among customers and final consumers according to their relative orders before the shock.An alternative specification prioritizes customer firms, assigning output to final consumers only after customer demand is met.Source: Appendix C · pp. 9–10
- Inventories are updated from firms’ production and procurement activities, using realized orders from customer firms and final consumers.The update sets the inventory of firm j’s product at firm i for the next day.Source: Appendix C · p. 10
Appendix D Results from Alternative Specifications
The appendix table reports value-added losses under alternative specifications of a Tokyo lockdown.
Appendix D Results from Alternative Specifications
- The table’s outcome is loss of value added under alternative specifications of a Tokyo lockdown.Source: Table D.1 · p. 10
- The comparison concerns alternative specifications of the Tokyo-lockdown scenario.Source: Table D.1 · p. 10
- The caption identifies the table as a report of losses rather than gains in value added.Source: Table D.1 · p. 10