Recognizing the risks posed by ongoing, frequent interruptions to supply chains, governments are increasingly interested in how–or if–policy can encourage firms to promote supply chain resilience.

In a new working paper that pays special attention to vertical supply chains, Princeton University’s Gene Grossman and Alejandro Sabal and Harvard University’s Elhanan Helpman develop a detailed model of these complex supply chains and help identify key areas for policy intervention.

The model reveals that without policy intervention, vertical supply chains can be inefficient in several key ways. Achieving the optimal allocations for a supply chain in their model–in terms of input purchases, network formation, and resilience–ultimately requires subsidies to firm-to-firm transactions. 

The complexity of vertical supply chains

The paper focuses on a type of vertical supply chain—flagged as vulnerable by the 2022 Economic Report to the President from the Council of Economic Advisers—where inputs travel “downstream” until they are transformed into a final product. 

These types of supply chains, where lead firms don’t own or control most of their suppliers, are often long, overwhelmingly complex, and highly vulnerable to disruptions or market failures. For example, General Motors relies on 856 direct suppliers and more than 18,000 suppliers to those direct suppliers. For Apple, those numbers are 638 and more than 7,400, respectively.[i]

While it’s typical for firms to invest time in building relationships with back-up suppliers or training their staff to be agile in the face of supply chain disruptions, these investments require up-front spending. A key contribution of the research is demonstrating that, without policy intervention, firms may not be adequately incentivized to build supply chain resilience on their own.

A model that captures real-world features

Another major contribution of the paper is the design of a complex and rich model that identifies several features of vertical supply chains policymakers should pay attention to, including: 

• Features of specific supply chain tiers. In the model, lead firms in tier “S” purchase inputs from tier “S-1,” which in turn fulfills orders by procuring inputs from tier “S-2.” The vertical chain ends with tier 0, where firms produce inputs from labor alone and sell them to firms in tier 1.
• Network thickness. Each firm can form relationships with any fraction of the firms in the tier immediately above. Though thicker supply networks can be more resilient, they are also costlier to build. 
• Arms-length transactions. The supply chains in the model don’t make use of off-the-shelf products. Rather, each supplier negotiates the terms of a deal with each of its potential customers for products that are made-to-order. Transactions can take place only between firms that have formed a prior relationship.
• Bargaining. The model allows cooperative bargaining among isolated pairs of firms (as opposed to grand bargaining between all firms, which would be impractical). When the firms in a tier bargain with their suppliers upstream, the negotiations take place simultaneously. Across tiers, bargaining takes place sequentially, beginning with final producers who procure their inputs from firms in tier S-1, then these firms procure inputs from firms in tier S-2, and so on, until finally firms in tier 1 procure inputs from those in tier 0.
• Risk of disruption. Every firm in the economy faces a non-zero probability of a catastrophic disruption. If a firm suffers such a disturbance, it will be unable to produce in the period captured by the model. Firms are given the opportunity to invest in moderating their risk.

Inefficiencies in the absence of government policy

The model uncovers several sources of inefficiency when firms prepare for supply chain disruptions based only on their own incentives. 

In terms of inputs, firms in adjacent tiers of the supply chain will not choose the socially-optimal volume of input sales. Instead, they will negotiate a contract that calls for more limited sales, in anticipation that the supplier will face a marked-up cost of its own inputs when it subsequently bargains with its own suppliers. 

In terms of resilience, firms throughout the supply chain will not, on their own, choose the socially-optimal investments to avoid their own supply chain disruptions. Finally, the authors find that firms’ incentives to form thick supply networks–as a hedge against disruptions to their suppliers–are not aligned with social incentives. Perhaps surprisingly, private incentives to invest in resilience and thick networks might sometimes be too great, as well as too little.

Policies to create “first-best” vertical supply chain environments

With these inefficiencies in mind, the authors use their model to identify policies that would achieve the “first-best” scenario in terms of firm-to-firm input transactions, resilience, and network formation in a given supply chain.

To create this “first-best” supply chain environment, the model suggests policymakers need to employ three policy tools: 

1. Subsidies or taxes on transactions between firms in adjacent tiers to ensure the ideal sizes of tier-to-tier transactions.
2. Subsidies or taxes to promote or discourage investments in agility. 
3. Subsidies or taxes on investments in supplier relationships to counteract the distorting effects of negotiated markup.

However, political constraints–for example if subsidies on firm-to-firm transactions are seen as handouts to the corporate sector–might make it impossible for policymakers to use all three of these tools together, therefore making it impossible to achieve the “first-best” supply chain environment. As such, the authors consider a “second-best” environment in which the government can subsidize investments in resilience and network formation, but cannot subsidize firm-to-firm transactions along the supply chain.

When policy can target specific tiers in a supply chain, thereby taking into account markups and input shares in all transactions downstream from a targeted tier, the result is subsidies that are constant for each tier with similar bargaining weights and production parameters. In contrast, the “second best” policies result in larger subsidies for producers further upstream. 

By applying new sources of data to the authors’ model, researchers can study policy interventions to promote supply chain resilience in a variety of contexts. To learn more, download the full paper.