# 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.