Volatility convergence among private and public firms: predictions from an industry dynamics model

This paper develops a model that is capable of replicating these empirical findings. It extends Hopenhayn (1993) industry dynamics framework by introducing firm ownership status (private or public) and allowing private firms to go public at a cost. The key assumption is that privately held firms face (exogenous) borrowing constraints, which are relaxed if the firm becomes public. As in the original Hopenhayn’s model, firms receive productivity shocks, which follow an exogenously given stochastic process, and the flows of entry and exit are determined endogenously. In the equilibrium, firms with higher productivity levels choose to become public and, if productivity is negatively related to volatility, publicly owned firms are on average less volatile than the privately held ones. I then show that a decline in the cost of going public can explain the volatility convergence of public and private firms documented by Davis et al. (2006). The volatility of the public firms rises because less productive (and more volatile) firms join the pool of publicly owned firms when the cost of going public falls. The effect on the volatility of private firms is twofold. On one hand, the most productive (and the least volatile) of the private firms decide to go public. This increases the mean volatility of the private firms. On the other hand, since at the moment of going public the firms’ borrowing constraints are relaxed, the aggregate demand for labor rises. This drives up the wage rate and forces the least productive (and the most volatile) firms to exit from the industry. Since most of these firms are private, this reduce the mean volatility of the private firms. Thus a decline in the cost of going public has two opposite effects on the volatility of the private firms. I then calibrate the model to the US data and investigate numerically whichever of the two effects dominates.