Hysteresis and Duration Dependence of Financial Crises in the US:   Evidence from 1871-2016
  This study analyses the duration dependence of events that trigger volatility persistence in stock markets. Such events, in our context, are monthly spells of contiguous price decline or negative returns for the S&P500 stock market index over the last 145 years. Factors known to affect the duration of these spells are the magnitude or intensity of the price decline, long-term interest rates and economic recessions, among others. The result of interest is the conditional probability of ending a spell of consecutive months over which stock market returns remain negative. In this study, we rely on continuous time survival models in order to investigate this question. Several specifications were attempted, some of which under the proportional hazards assumption and others under the accelerated failure time assumption. The best fit of the various models endeavored was obtained for the log-normal distribution. This distribution yields a non-monotonic hazard function that increases up to a maximum and then decreases. The peak is achieved 2-3 months after the spells onset with a hazard of around 0.9 or higher; this hazard then decays asymptotically to zero. Spells duration increase during recessions, when interest rate rises and when price declines are more intense. The main conclusion is that short spells of negative returns appear to be mainly frictional while long spells become structural and trigger hysteresis effects after an initial period of adjustment. Although in line with our expectations, these results may be of some importance for policy-makers. 
Rui Menezes and Sonia Bentes
q-fin.ST