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Not-so-Cleansing Recessions

Igli Bajo, Frederik H. Bennhoff, Alessandro Ferrari

Abstract

Recessions are periods in which the least productive firms in the economy exit, and as the economy recovers, they are replaced by new and more productive entrants. These cleansing effects improve the average firm productivity. At the same time, recessions induce a loss of varieties. In an economy with Homothetic Single Aggregator technology, we show that their long-run welfare effects trade off these two forces. This trade-off is governed by love-of-variety and the elasticity of substitution in aggregate production. If industry output is aggregated using the standard CES aggregator, recessions do not improve long-run GDP or welfare. If the economy features more love-of-variety than CES, the social planner optimally subsidizes economic activity both in steady state and even more so in recessions to avoid firm exit. We use the model and quasi-exogenous variation in demand to estimate love-of-variety. We find it to be significantly higher than implied by CES aggregation, suggesting that even the long-run effects of recessions are negative. Finally, we quantitatively characterize the optimal policy response both along the transition and in the steady state.

Not-so-Cleansing Recessions

Abstract

Recessions are periods in which the least productive firms in the economy exit, and as the economy recovers, they are replaced by new and more productive entrants. These cleansing effects improve the average firm productivity. At the same time, recessions induce a loss of varieties. In an economy with Homothetic Single Aggregator technology, we show that their long-run welfare effects trade off these two forces. This trade-off is governed by love-of-variety and the elasticity of substitution in aggregate production. If industry output is aggregated using the standard CES aggregator, recessions do not improve long-run GDP or welfare. If the economy features more love-of-variety than CES, the social planner optimally subsidizes economic activity both in steady state and even more so in recessions to avoid firm exit. We use the model and quasi-exogenous variation in demand to estimate love-of-variety. We find it to be significantly higher than implied by CES aggregation, suggesting that even the long-run effects of recessions are negative. Finally, we quantitatively characterize the optimal policy response both along the transition and in the steady state.

Paper Structure

This paper contains 89 sections, 28 theorems, 181 equations, 12 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Model
  4. Monopolistic Competition with HSA Demand Structure
  5. Households
  6. Production
  7. Industry Output
  8. Love-of-Variety
  9. Pricing
  10. Entry and Exit
  11. Dynamics
  12. Equilibrium
  13. Business Cycles
  14. Example 1: CES
  15. Example 2: No Incumbents
  16. ...and 74 more sections

Key Result

Lemma 1

Let $\bm{\phi}$ be a parameter vector and $m_{t-1}$ and $m_{t-1}'$ be two distributions of incumbents. Suppose, the economy given $(\bm \phi, m_{t-1})$ and the economy given $(\bm \phi, m_{t-1}^\prime)$ both attain an equilibrium with entry. Then, the aggregate price statistic and cutoff coincide in

Figures (12)

  • Figure 1: Number of Firms in Spain
  • Figure 2: Empirical CDFs (ECDFs) of log Revenue TFP (RTFP) for Entrants and Exiters. The estimation procedure for RTFP is described in Appendix \ref{['app:sabi_tfp_estim']}. In the period preceding the Global Financial Crisis (2002-2006), the entrant and exiter ECDFs overlap and cross, and we fail to reject equality of means at the 5% level. During the Global Financial Crisis (2007-2009), the entrant ECDF lies below the exiter ECDF throughout the support---consistent with first-order stochastic dominance of entrants---and we reject equality of means at the 5% level.
  • Figure 3: The figure shows the entry and exit dynamics over the business cycle. Panel (A) shows the distribution $m_1$ before the shock hits. Upon impact, the left tail of firms with productivity less than $\underline z_2$ leave, creating distribution $m_2$ (B). Finally, after fixed costs return to pre-shock levels and new firms drawn from the baseline distribution ($\mu^E$) enter, $m_3$ becomes the distribution of productivities in the market (C). The dashed light-blue line refers to $m_{t-1}$.
  • Figure 4: Evolution of $m$ through the business cycle for the market and social planner allocations, assuming that $q > q^{CES}$.
  • Figure 5: Estimated $q$ and $q^{CES}$. The figure plots the distribution of estimates of $1/(\sigma -1)$ by industry, highlighting the median, which is our preferred point estimate for $q^{CES}$. Additionally, it shows our estimate of a global $q$, with $95\%$ confidence bands.
  • ...and 7 more figures

Theorems & Definitions (64)

  • Definition 1: Equilibrium
  • Lemma 1: Invariance with Entry
  • Proposition 1: Equilibrium During the Recession
  • Theorem 1: Fundamental Trade-Off of Recessions
  • Theorem 2: Cleansing Effects of Cycles
  • Proposition 2: No internal effects iff CES
  • Proposition 3: Cleansing Effects of Business Cycles under MSLD
  • Proposition 4: Special Cases of External Effects
  • Remark 1
  • Proposition 5: Cleansing Effects of Cycles
  • ...and 54 more