Supply Chain Disruptions, the Structure of Production Networks, and the Impact of Globalization

TL;DR

This paper develops a parsimonious multi-sector model of international production to study how supply chain disruptions propagate through production networks and how the effects differ across time horizons. It introduces a Shock Propagation Algorithm to characterize short-run, out-of-equilibrium disruptions, contrasted with long-run equilibrium adjustments governed by an adaptation of Hulten's Theorem. The analysis shows that short-run disruptions can be disproportionately large because they depend on downstream value across the network, and that greater supply-chain complexity increases the probability and potential size of disruptions, while globalization-driven specialization changes the distribution and magnitude of these effects. The framework further defines disruption centrality and a formal notion of power to quantify how a disruption in one country’s technologies can affect another country, including strategic responses and the disruption frontier. Collectively, the results offer theoretical benchmarks for assessing fragility in global value chains and provide a foundation for evaluating policy tools such as sanctions, quotas, and trade-shock countermeasures under different network structures.

Abstract

We introduce a parsimonious multi-sector model of international production and use it to study the impact of a disruption in the production of some goods propagates to other goods and consumers, and how that impact depends on the goods' positions in, and overall structure of, the production network. We show that the short-run impact of a disruption can be dramatically larger than the long-run impact. The short-run disruption depends on the value of all of the final goods whose supply chains involve a disrupted good, while by contrast the long-run disruption depends only on the cost of the disrupted goods. We use the model to show how increased complexity of supply chains leads to increased fragility in terms of the probability and expected short-run size of a disruption. We also show how decreased transportation costs can lead to increased specialization in production, lowering the chances for disruption but increasing the impact conditional upon disruption. We use the model to characterize the power that a country has over others via diversions of its production as well as quotas on imports and exports.

Figures (20)

• Figure 1: An example of an economy with three technologies and 10 units of labor, outputting 1 unit of a final good.
• Figure 2: Long-run production of good 2 according to a Cobb-Douglas function of labor and good 1: $y_2=L^{\alpha}x_1^{1-\alpha}$, can be approximated by setting $T_n$ to be the intersection of $\{(-l,-x_1,1):l^{\alpha}x_1^{1-\alpha}=1\}$ with some grid.
• Figure 3: An example of the short-run impact of the shock to a technology, and the contrast to the long run. A 10 percent disruption of the production propagates through the network to the final good. Even though labor is not disrupted, it cannot produce the outputs without the corresponding inputs and so final good disruption is disrupted to the full extent of the input disruption. The disruption is 5 times larger than the corresponding long-run impact. In the long run, labor reallocates to even out the production needed as inputs downstream.
• Figure 4: Long run: In both cases have supply networks that have two copies of technologies similar to those in the example from Figure \ref{['fig:flow_network']}. Each final good needs one resource and one intermediate good, but which combination of inputs are needed downstream differs between the networks. In the long run the details of the network structure do not matter if the amount spent on the shocked technology is the same. In both cases the labor endowment is 20, the initial prices are $p=\left(\frac{1}{10},\frac{1}{10},\frac{4}{5},1\right)$ and $GDP=\sum_f p_f c_f=2$. Thus, from Hulten's Theorem, the marginal impact is $\frac{p_{R1} y_{R1}}{\text{GDP}}= \frac{1}{10}$ and then extrapolating for a $10\%$ shock, the long-run impact is $1/100$th of GDP. We do see, however, that the new long-run equilibrium flows differ across the two variations, but the GDP impact is similar.
• Figure 5: Short run: the details of the network structure matter even with identical initial prices and technological structures. Here the impact is either 5 or 10 times more than the long-run impact (which was 1/100th), and here it depends on the network structure.

Theorems & Definitions (5)

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