The Persistent Effects of Entry and Exit

We develop a model with endogenous entry and exit in an economy subject to aggregate total factor productivity shocks that are non-stationary. Firms exhibit a life-cycle consistent with data and our model economy reproduces both their size and age distribution. In this setting, persistent shocks to aggregate total factor productivity growth rates endogenously drive long term reductions in business formation. The economic consequences of this persistent decline in entry grows over time. In our model, individual firms vary in both the permanent and transitory components of their total factor productivity and in their capital stock. Capital adjustment is subject to one period time-to-build and involves both convex and nonconvex costs. Our dynamic stochastic general equilibrium model involves an aggregate state that includes a distribution of firms over total factor productivity and capital. Changes in this distribution, following aggregate shocks to the common component of TFP, drive persistent fluctuations in aggregate economic activity. We show that equilibrium movements in firms' stochastic discount factors, following persistent shocks to TFP growth, imply long-run declines in the value of entry. The resulting fall in the number of firms propagates a reduction in economic activity. This slows down the recovery. We apply our model to understanding the last decade of economic activity in the U.S. This period began with a large recession followed by a period of slow economic growth. At the same time there was a persistent reduction in the new business formation. Our dynamic stochastic general equilibrium analysis is consistent with relatively small reductions in the level of total factor productivity, as seen in the last recession, and large reductions in GDP and Business Fixed Investment. Moreover, the recovery from such a large recession is slowed by a persistent reduction in firm entry.