David K. Levine (2012 Review of Economic Dynamics)
- In economies with greater specialization of agents, production chains are necessarily longer.
- If shocks to (failures of) agents are randomly distributed, the longer chains have a greater probability of failure.
- If shocks are correlated, the existence of chains where no agents fail is more likely, and so chains will be longer; however, these longer chains are more sensitive to changes in the probability of the failure of any single agent.
- Shocks that are concentrated within production chains can be less costly than shocks that hit multiple chains, even if their first-order impacts are identical.
- Consider an economy with two production chains, composed of equal sized firms. Let a shock be an instance where a firm fails, causing its production chain to shut down. A shock that hits two firms in production chain 1 (and shuts it down) is less costly than a shock that hits one firm in each chain (shutting down both chains).
- In an economy with 3 chains, a shocks that hits two chains can be transferred so that it affects only chain if the chains’ inputs are substitutes (see Table 1)
- There are three auto manufacturing chains, using three specialized firms each that produce tires, pistons, and other parts.
- Shock A hits all three firms in the production chain for Jaguars. This chain shuts down, but the chains producing BMWs and Toyotas still operate.
- Shock B hits the tire producer for Jaguar, the piston producer for BMW, and the other parts producer for Toyota. However, if these parts can be substituted across firms, then Jaguar’s piston and other parts producers can be reassigned to the BMW and Toyota chains so that, as with shock A, only one chain shuts down.
- Shock C hits all three tire producers. All three chains shut down.
- The author models the correlation of shocks as the probability r≥0 that a firm is in a chain where all firms are failures. Given that a firm is not in such a chain, it fails with independent probability p.
- With specialization, correlation of shocks in production chains leads to higher expected output, higher welfare, longer production chains, and greater sensitivity to shocks.
- This greater sensitivity is the “price we pay” for the higher productivity.
- Correlation of shocks within production chains is less costly than correlation of shocks across chains, especially when inputs in one process can be substitutes for inputs in another.