Savagar, Anthony, and Huw Dixon (2017). “Firm Entry, Excess Capacity and Aggregate Productivity”

Supplementary Appendix and Code

Slow firm entry over the business cycle causes measured TFP to vary endogenously because incumbent firms bear shocks. Our main theorem states that imperfect competition and dynamic firm entry are necessary and sufficient conditions for these endogenous productivity fluctuations. The result focuses on the short-run absence of entry and incumbents’ output response given this quasi-fixity. Quantitatively we show the endogeneous productivity effect is as large as a traditional capital utilization effect.

I present a theory of firm entry and exit in the business cycle that links short-run productivity overshooting to long-run persistence, a dynamic observed in contemporary

‘productivity puzzles’. The theory emphasizes two mechanisms: (1) slow firm entry/exit and (2) firm pricing that reflects the number of competitors in the market. Given these mechanisms, economic contraction causes a short-run exacerbated fall in productivity (overshooting) because the negative shock is absorbed by incumbents due to slow exit responses. This weakens incumbents’ returns to scale, thus worsening productivity. However, the productivity overshooting recedes over time as firms exit whichdynamically reallocatesresources among incumbents, reviving the remainders returns to scale and thus productivity. This process of exit consolidating the market is not purely beneficial for productivity because the remaining firms face fewer competitors and thus charge higher markups which damages productivity. Therefore despite some reversion from the initial fall, there is a long-run persistent negative effect on productivity due to higher markups responding to the fall in number of firms. To analyze the trade-off between productivity improving dynamic reallocation and productivity degrading endogenous markups, I develop a continuous time, analytically tractable DGE model. The main mechanisms are dynamic entry so firms are slow to respond causing initial overshooting, and endogenous markups so pricing behaviour depends on the number of competitors firms face.

We reduce a four-dimensional economic system with entry to a two-dimensional stable manifold. Whence we derive analytical solutions for the model within a neighborhood of the hyperbolic fixed point. Analytical solutions show that imperfect competition reduces the set of complex dynamics, and raises eigenvalues which hastens convergence to steady state. The intuition is that imperfect competition raises profits, so an entrant reduces industry profits more thus arbitrage quickens.