In examining data from the last four decades in the US (and from over 40 other countries), we discover that recessions are characterised by a huge decrease in ‘skewness’ (Salgado et al. 2020). Some firms and industries get hit far harder than others, creating a large drop in the left tail. This skewness shock is one of the most damaging characteristics of recessions as it leads to a surge in tail risks for firms and their workers.

The current COVID-19 crisis is no exception. While most firms have experienced a negative demand shock, firms in the entertainment, services, and manufacturing sector have experienced a dramatic decline in sales that is likely to persist over several months. Similar to the aggregate macro-disasters discussed in recent research (Barro 2006, Barro and Ursua 2011, Gabaix 2008), for a large fraction of firms the current crisis is a microeconomic disaster.

A simple way to measure the increase in firm-level disasters is to look at the distribution of firms’ sales growth. Figure 1 shows the distribution of sales growth for a sample of US publicly traded firms from Compustat. The solid line shows the empirical density of firms' sales growth, pooling observations from the last two recession years (2001–2002 and 2008–2009). The dashed line shows the density for the expansion years around these recessions. In this case, the periods 2003-2006, and 2010-2014. It is clear that, relative to expansion periods, the distribution of sales growth during recessions has a thicker left tail, whereas the right tail exhibits little change. This indicates an increase in dispersion that is mostly due to a widening left tail. This asymmetric change in the distribution of sales growth (from expansion to recession years) can be quantified using the ‘Kelley skewness’ (Kelley 1947), a measure that is robust to the presence of outliers. This measure is defined as the difference between the 90th-to-50th log percentiles differential (a measure of dispersion in the right tail), and the 50th-to-10th log percentiles differential (a measure of dispersion in the left tail), divided by the 90th-to-10th log percentiles differential (a measure of the total dispersion of the distribution). For a distribution with a compressed upper half and a dispersed lower half (i.e. a ‘left skew’ distribution), the Kelley skewness is negative.^{1}

**Figure 1** Distribution of sales growth

*Note*: Empirical density of the distribution of firms' log sales growth between years t and t+1 constructed from Compustat. Each density has been rescaled to have a median of zero and unit variance. The blue-dashed line shows the density of a pooled sample of expansion years (2003 to 2006 and 2010 to 2014); the red-solid line shows the density of a pooled sample of recession years (2001 and 2008). The unscaled 10th percentile of distribution during expansions (recession) is -0.22 (-0.47), the 50th is , 0.05 (-0.03), and the 90th is 0.45 (0.33).

In the case of Figure 1, the dispersion of sales growth above the median declines from 0.40 to 0.36 log points from expansion to recession years, whereas the dispersion below the median increases from 0.27 to 0.44 log points. This asymmetric change in the tails generates a decline in the Kelley skewness from 0.20 during expansion years, to –0.10 during recessions years. Hence, as we show in Figure 2, the skewness of the sales growth distribution is markedly procyclical, declining sharply during recessions. Furthermore, using US Census data on firm-level employment, Figure 2 also shows that the skewness of the employment growth distribution (across the entire non-farm US private section) is procyclical. In fact, the procyclical skewness is not only observed in the US, but also across different countries, within industries, and for other firm-level variables such as productivity shocks and stock returns (Salgado et al. 2020).

**Figure 2** Skewness of the sales growth distribution

*Note*: Kelley skewness of log employment growth and log sales growth. The blue line with squares shows the time series of the employment-weighted cross-sectional Kelley skewness of the distribution of firms' log employment growth between years t and t+1 constructed from the LBD. The black line with circles shows the time series of the cross-sectional Kelley skewness of the distribution of firms' log sales growth between years t and t+1 constructed from Compustat. Shaded areas represent the share of the year (in quarters) declared as a recession by the NBER.

The current COVID-19 crisis an even more dramatic example of this pattern. And while we do not yet have reliable information on firms’ sales, we can look at firm-level stock returns. Between 21 February 2020 (the first large decline in the stock market after the outbreak) and 20 April 2020, the Kelley skewness of the distribution of cumulative stock returns fell from 0.57 in the preceding years, to –0.42 during the two months after the initial outbreak.^{2} In short, COVID-19 has generated a huge left-tail in firm-level stock returns. This can be easily appreciated in Figure 3, which shows the cross-sectional distribution of cumulative returns for firms in the US corporate sector in the weeks following the COVID-19 outbreak (illustrated by the solid line). Relative to the distribution of returns in the years before the outbreak (illustrated by the dotted line), the left tail stretched out as most firms experienced large declines in their valuation, generating a sharp drop in the skewness of the distribution of cumulative returns. The shift in the tails of the distribution of cumulative stock returns (and the corresponding drop in skewness) was similarly large during the first eight weeks of the Great Recession, as shown in Figure 3 (illustrated by the dashed line).

**Figure 3** Cross-sectional distribution of cumulative returns

*Note*: The figure plots the density of the cumulative log stock returns for the US corporate sector. Densities adjusted to have a median of 0. The red solid line (COVID-19) is the distribution of cumulative log stock returns between 02/21 and 04/20, 2020 (40 trading days). The green line with dashes (Great Recession) is the distribution of log cumulative returns between 09/09 and 11/04, 2008; The blue lined with dots (2015 to 2019) is the distribution of 40-trading days cumulative log stock returns. Densities weighted by market capitalization. The (weighted) median of the distribution of cumulative log stock returns for the COVID-19 period is -0.18, for the Great Recession is -0.19, and for the 2015 to 2019 period is 0.02.

How important is the observed decline in skewness? While it is hard to get a causal estimate, we can evaluate the type of economic drop this would usually foreshadow. To do this, we estimate a standard vector autoregression model (VAR) using data for the US from January 1964 to December 2019 and then feed in the current skewness shock. We consider a standard set of variables including, the firm-level stock market skewness, employment, and an index of industrial production (in that order). We focus on the change in industrial production following an innovation to the skewness of stock market returns. Figure 4 shows the impact of the COVID-19 shock on industrial production. Six months after the shock, industrial production has declined by 15 percentage points below its pre-recession level, with around two percentage points of the decline accounted for by the drop in skewness.

**Figure 4** Impact of the COVID-19 shock on industrial production

*Note*: The figure plots the response of log industrial production to a combined first-moment and a skewness shock obtained from the VAR model estimated by Salgado, Guvenen, and Bloom (2020). We set the first-moment on a 2 standard deviations shock on the US stock market. The skewness shock is set to a decline of the Kelley skewness of 35-days cumulative log stock returns distribution from 0.57 (measured using data from 2015 and 2019) to -0.42 (measured using data from after the COVID-19 outbreak between February 21 and April 20, 2020). Kelley skewness calculated as (P99-P50)-(P50-P1)/(P99-P1). Dashed line show one standard deviation confidence intervals.

The total economic impact of the current COVID-19 crisis in the US (and around the world) is still unfolding but will likely exceed the 2008 Global Crisis. As we argue, the increase in the probability of microeconomic disasters for a larger fraction of firms in the economy, or (more precisely) the decrease in the skewness of the distribution of firms’ shocks, will play a significant role in the response of aggregate output and employment.

## References

Barro, R and J Ursua (2011), “Rare Macroeconomic Disasters”, NBER Working Papers 17328, National Bureau of Economic Research, Inc.

Barro, R J (2006), “Rare disasters and asset markets in the twentieth century”, *Quarterly Journal of Economics* 121 (3): 823–866.

Christiano, L J, M Eichenbaum and C L Evans (2005), “Nominal rigidities and the dynamic effects of a shock to monetary policy”, *Journal of political Economy* 113 (1): 1–45.

Gabaix, X (2008), “Variable Rare Disasters: A Tractable Theory of Ten Puzzles in Macro-finance”, *American Economic Review* 98 (2): 64–67.

Kelley, T L (1947), *Fundamentals of Statistics,* Harvard University Press.

Kim, T H and H White (2004), “On more robust estimation of skewness and kurtosis”, *Finance Research Letters* 1 (1): 56–73.

Ramey, V A (2016), “Macroeconomic shocks and their propagation”, *Handbook of Macroeconomics* 2: 71–162.

Salgado, S, F Guvenen and N Bloom (2020), “Skewed Business Cycles”, University of Minnesota, mimeo.

## Endnotes

^{1} Notice this particular measure of Kelley skewness is invariant to 20% of the distribution (the top and bottom 10%). The Kelley skewness, however, can be calculated using any symmetric pair of percentiles, such as the P99 and P1. See Kim and White for additional measures of skewness.

^{2} To capture the long left and right tails of the distribution of cumulative stock returns, we calculate the Kelley skewness as ((P99-P50) –(P50-P1))/ (P99-P1).