# Production Chains

David K. Levine (2012 Review of Economic Dynamics)

Summary

• 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.

Takeaways

1. With specialization, correlation of shocks in production chains leads to higher expected output, higher welfare, longer production chains, and greater sensitivity to shocks.
1. This greater sensitivity is the “price we pay” for the higher productivity.
2. 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.

# Unemployment Crises

Petrosky-Nadeau, Nicolas, and Lu Zhang, “Unemployment Crises,” NBER Working Paper No. 19207 (July 2013).

Purpose: to explain unemployment crises in the U.S. through a search and matching model with hiring costs and credible wage bargaining.

Results:

1. In a three-state Markov chain, the persistence of a crisis state (defined as unemployment over 20%) is 84.18% in the model versus 82.35% for the period April 1929 to December 2012.
2. The unconditional probability of entering a crisis is 3.21% in the model and 3.47% in the data.
3. The volatility of labor market tightness (job vacancies per unemployed worker) is 0.37 in the model and 0.33 in the data.
4. The welfare costs of business cycle fluctuations is 1.2% of consumption, which is a far larger than the negligible costs estimated by Lucas (1987).

Data: consists of monthly unemployment and estimates of vacancies, from multiple sources, beginning as early as 1919 and continuing through December 2012.

Model:

1. A representative household consists of both employed and unemployed workers.
2. Unemployed workers apply for jobs at a representative firm.
3. A matching function takes workers and vacancies as inputs and produces new jobs.
4. Wage is determined through the credible bargaining process of Hall and Milgrom (2008).
5. A three-state Markov model is fitted both to observed data and to sample data from the model’s simulated economy.
1. The maximum likelihood estimate for $\lambda_{jk}$, or the probability that the economy switches from state k to state j (it is possible that k=j), is calculated as the number of times the economy makes such a switch divided by the number of periods in which the economy is in state k.
2. The transition matrix raised to the power of 1,000 approximates the unconditional probability of the economy entering a given state.
6. The model consists of five functional equations: 1 for the firm’s decision to post a vacancy, 1 for the value of the worker’s unemployment activities, and three for the credible wage bargaining process.
1. Simulation the economy for 1 million periods (months), draw 50,000 samples of 1,005 months each (to match the duration of the period April 1929 to December 2012) and compare sample moments to actual moments.

# Endogenous Disasters and Asset Prices

Petrosky-Nadeau, Nicolas, Lu Zhang, Lars-Alexander Kuehn, “Endogenous Disasters and Asset Prices,” Charles A. Dice Center Working Paper No. 2012-1 (October 1, 2013).

Purpose: This model produces a realistic equity premium and stock return variance, and endogenously leads to rare economic disasters, at the confluence of small corporate profits, large job flows, and frictions in the matching process that connects unemployed workers with job vacancies.

Model:

1. A representative household, with both employed and unemployed members, chooses its optimal consumption and asset allocation (holdings of shares in a representative firm and of a risk-free bond).
2. A representative firm posts job vacancies, and unemployed workers apply for them.
1. vacancies are costly for the firm.
3. The labor market is a matching function that produces jobs using vacancies and unemployed workers as inputs.
1. Matching frictions are composed of fixed and variable hiring costs.
2. The wage rate is determined by a Nash bargaining process.

Results:

1. The model generates an equity premium of 5.70%, versus 5.07% in the data (adjusted for financial leverage).
2. Annual stock market volatility in the model is 10.83%, versus 12.94% in the data.
3. The model’s interest rate volatility is 1.34%, versus the observed 1.87%.
4. The equity premium is countercyclical, both in the model and in the data.
5. The ratio of vacancies to unemployed workers forecasts (with a negative slope) excess returns; this is confirmed in the data.
6. Rare disasters are endogenous.
1. The average peak-to-trough magnitude of a disaster is roughly 20%, both modeled and observed.
2. The probability of a consumption disaster is 3.08% in the model and 3.63% in the data.
3. The probability of a GDP disaster is 4.66% in the model and 3.69% in the data.
7. Comparative statics
1. The value of workers’ activities in unemployment are assumed to have a high value, which makes wages inelastic. When output falls in hard times, wages fall less, and so the cyclical nature of profits and dividends is magnified. This raises the equity premium and makes the stock market more volatile compared to other models.
2. Job flows are assumed to be about 5%, consistent with previous literature (5% of the workforce quits each month), so frictions in the matching process contribute to macroeconomic risk.
3. Matching frictions (especially fixed hiring costs) cause marginal hiring costs to fall slowly in a recession and to rise quickly in an expansion.
1. In a recession, there are many unemployed workers and few vacancies. An additional vacancy has only a slight impact on the likelihood of an existing vacancy being filled, so hiring costs fall slowly.  As workers continue to attrite  at a 5% rate, hiring may not keep up and the economy may fall off a cliff.
2. In an expansion, there are few unemployed workers and many vacancies.  An additional vacancy in an expansion has a large (negative) impact on the likelihood of a vacancy being filled, so marginal hiring costs rise quickly, hampering the expansion.