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:

- 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.
- The unconditional probability of entering a crisis is 3.21% in the model and 3.47% in the data.
- The volatility of labor market tightness (job vacancies per unemployed worker) is 0.37 in the model and 0.33 in the data.
- 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:

- A representative household consists of both employed and unemployed workers.
- Unemployed workers apply for jobs at a representative firm.
- A matching function takes workers and vacancies as inputs and produces new jobs.
- Wage is determined through the credible bargaining process of Hall and Milgrom (2008).
- A three-state Markov model is fitted both to observed data and to sample data from the model’s simulated economy.
- The maximum likelihood estimate for , 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*. - The transition matrix raised to the power of 1,000 approximates the unconditional probability of the economy entering a given state.

- The maximum likelihood estimate for , or the probability that the economy switches from state
- 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.
- 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.