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.