The Nature of Countercyclical Income Risk

The paper poses two questions: “how does the distribution of idiosyncratic earnings shocks change over the business cycle?” and “are there any observable characteristics of a worker that can help us predict his fortunes during a business cycle episode?” To answer both at once, the authors decompose each individual’s earnings growth into “a component that can be predicted based on the observable characteristics of individuals (prior to the episode)” – the between-group component – “and a separate residual component that represents purely idiosyncratic shocks that hit individuals that are ex ante very similar” – the within-group component – using a factor-structure specification in which a function f(V) lets the conditional mean of earnings growth vary systematically with the business cycle across groups defined by age, pre-episode average earnings, and pre-episode earnings growth, while separately allowing the variance of both permanent and transitory idiosyncratic shocks to vary with the cycle and across groups.

The paper’s main dataset is “a 10 percent random sample of U.S. males who had a Social Security number between the ages of 25 and 60 from 1978 to 2010,” drawn from the SSA’s confidential Master Earnings File, yielding “about 4.5 million individuals in each year for a total of 165 million individual-year observations.” The authors emphasize three advantages over typical survey data: earnings are uncapped (no top-coding), which “allow[s] us to study individuals with very high earnings”; the large sample size supports flexible nonparametric methods with precise estimates even for extreme percentiles; and the records-based nature of the data means “very little measurement error,” in contrast to survey datasets like the PSID.

“Contrary to past research, we do not find the variance of idiosyncratic earnings shocks to be countercyclical” – the paper reports that both one-year (“transitory”) and five-year (“persistent”) shock standard deviations show little business-cycle variation, with the 2001-02 recession the only partial exception. This directly contradicts Storesletten, Telmer, and Yaren (2004), who “estimated the variance of AR(1) innovations to be three times higher during recessions” using PSID data; the authors suggest this earlier finding may reflect that smaller PSID samples could not separately identify countercyclical variance from countercyclical skewness, and note their result is “more consistent with Mankiw (1986), who showed that one can resolve the equity premium puzzle if idiosyncratic shocks have countercyclical left-skewness.”

The paper finds it is “the left-skewness of shocks that is strongly countercyclical”: during recessions “the upper end of the shock distribution collapses – large upward earnings movements become less likely – whereas the bottom end expands – large drops in earnings become more likely.” This is documented percentile by percentile: comparing expansion to recession, “P99 falls by about 30 log points… P95 falls by 20, P90 falls by 15, P75 falls by 6, and P50 falls by 5 log points,” so “the entire upper half of the shock distribution gets squeezed toward the median,” while below the median “P50 falls by 5 log points, whereas P25 falls by 9, and P10 falls by 20 log points” – the bottom half of the distribution expanding symmetrically as the top half contracts. The authors note the P90-minus-median and median-minus-P10 gaps for five-year earnings changes move in tight opposition over the cycle (correlation of -0.67), which is why overall dispersion (the P90-P10 gap) “changes little over the business cycle” even as the shape of the distribution shifts dramatically.

The paper argues that relative to the earlier countercyclical-variance literature, “which results in some individuals receiving larger positive shocks during recessions,” its own findings are “even more pessimistic: uncertainty increases in recessions without an increasing chance of upward movements.” Under a symmetric countercyclical-variance model, a recession’s added risk would be two-sided – some lucky workers end up better off than they otherwise would have. The paper’s left-skewness finding implies instead that the extra risk recessions bring is almost entirely on the downside: the probability of large earnings gains falls rather than rises, even as the probability of large losses grows.

The paper finds that “average earnings loss during this recession was almost a linear (upward-sloping) function of pre-recession average earnings all the way up to the 95th percentile” – for the Great Recession specifically, workers at the 10th percentile of pre-recession average earnings lost about 25 log points versus only 8 log points for those at the 90th percentile, a 17-log-point gap – but “this good fortune of high-income workers did not extend to the very top: those in the top 1 percent… experienced an average loss that was 21 percent worse than that of workers in the 90th percentile,” with the group’s own earnings falling about 27 log points versus 12.5 log points for the next-highest (95th-99th percentile) group. The authors are explicit that this top-1%-reversal pattern is not a fixture of all recessions: in the 1980-83 downturn, by contrast, “there is no steep fall in earnings for the top 1 percent… in fact, these individuals experienced the highest earnings growth of all income groups during this recession,” and the authors identify the 2000-02 recession – otherwise mild for most workers – as “the worst episode for the top 1 percent,” whose average earnings loss exceeded that of 90th-percentile workers by almost 30 log points.

Using the panel structure to track the same individuals over time (rather than synthetic cohorts from repeated cross sections, as in earlier work by Piketty and Saez (2003) and Parker and Vissing-Jørgensen (2010)), the paper finds “the very high persistence of these fluctuations”: “individuals who were in the 99.9th percentile as of 1999 experienced a 5-year average earnings loss between 2000 and 2005 that exceeded 50 log points,” with “similarly large persistent losses… found for the top income earners during the 5-year periods covering the Great Recession (2005-10) as well as the 1990-95 period.”

The authors draw an explicit parallel to Lilien (1982), who argued that countercyclical dispersion in employment growth across sectors was evidence that sectoral reallocation shocks drove unemployment fluctuations, and to Abraham and Katz’s (1986) rebuttal showing that a common factor structure – different sectors loading differently onto the same aggregate shock – could generate the identical dispersion pattern without any sectoral-shift mechanism at all. The paper states that, “in a similar vein, our results show that the well-documented countercyclicality of earnings inequality does not have to stem from the countercyclical variance of idiosyncratic shocks, but rather is due to a factor structure that expands inequality during recessions and contracts during expansions” – i.e., the apparent rise in earnings inequality during recessions is substantially a systematic, predictable (between-group) phenomenon rather than a symptom of individuals facing more variable idiosyncratic risk.

The paper’s own summary verdict is that “recessions are best viewed as a small negative shock to the median and a large negative shock to the skewness of the idiosyncratic earnings shock distribution, with little change in the variance.” The authors argue this has direct implications for how macroeconomists should model business-cycle earnings risk: “the traditional approach to modeling recession risk consists of a (negative) aggregate shock and a positive shock to the variance of idiosyncratic shocks,” and the paper’s results “suggest that this simple view is seriously inadequate,” redirecting attention “to the countercyclical variation in the third moment (skewness) of idiosyncratic shocks as central to understanding how the fortunes of ex ante similar individuals fare during recessions.”

The paper explains its deliberately nonparametric approach (presenting results via percentiles and simple statistics rather than fitting a parametric stochastic earnings process) by noting that “earnings growth rates exhibit significant deviations from normality, in the form of very strong left-skewness and substantial leptokurtosis,” so that a parametric model flexible enough to capture these features – let alone their business-cycle variation – “would have to be very complicated, which would take away from the clarity afforded by the current approach.” The authors also note their baseline sample is restricted to men “motivated by the fact that this group had a relatively stable employment rate and labor supply during this period,” since the dataset lacks hours information that would be needed to separate earnings changes from labor-supply changes for women, whose participation rose substantially over the sample period.