Temporary Layoffs, Loss-of-Recall, and Cyclical Unemployment Dynamics

Q1. What distinguishes temporary-layoff unemployment from jobless unemployment in the data, and why does the distinction matter for cyclical dynamics?

Temporary-layoff unemployment (TL) is the state in which a CPS respondent indicates an expectation of recall — either a specific return date or a stated expectation of recall within six months — while jobless unemployment (JL) is unemployment without such an expectation; the two states have starkly different reemployment probabilities, with TL workers returning to employment at substantially higher rates than JL workers, making the composition of total unemployment — not just its level — a key determinant of unemployment persistence. In the Markov transition matrix estimated from CPS data 1979-2019 (Table 2), TL is a transient state: workers on TL transition to employment at a far higher rate than workers in JL, reflecting the attached recall relationship. The stock of TL unemployment is consequently small — averaging roughly one-eighth of total unemployment — even though TL separations account for roughly one-third of all separations from employment to unemployment. The distinction matters for aggregate dynamics because a recessionary increase in TL generates both a direct, relatively transient component (elevated TL stock) and an indirect, more persistent component (heightened loss-of-recall feeding into JL stock). Standard two-state unemployment models that lump TL and JL together miss the indirect channel entirely, understating both the volatility and persistence of total unemployment in the presence of countercyclical loss-of-recall.

Q2. What is the recursive accumulation method for estimating JL-from-TL, and what does it reveal about the indirect contribution of temporary layoffs?

The paper proposes a novel method to estimate the time series stock of jobless unemployed workers whose most recent employment exit was through temporary-layoff unemployment — the JL-from-TL stock — by propagating forward through the Markov transition matrix each cohort of workers who enter TL from employment, tracking the fraction that survive in any unemployment state without returning to employment, and summing across all past cohorts. Formally, if $x_{t-m,t}$ denotes the distribution of workers at time $t$ whose last exit from employment was to TL at time $t-m$, then $x_{t-m,t} = \tilde{P}t x{t-m,t-1}$ where $\tilde{P}t$ is a modified transition matrix, and the JL-from-TL stock is $u^{JL,TL}t = \sum{j=0}^{T} e’{JL} x_{t-j-1,t}$. The method requires only the Markov transition matrix — no individual-level panel data — and extends the Shimer (2012) / Elsby-Hobijn-Sahin (2015) variance decomposition approach to level decompositions. Applied to CPS data, the JL-from-TL stock has a standard deviation 16 times that of GDP (versus 2 times for TL itself) and a correlation of 0.93 with total unemployment — substantially higher than the 0.83 correlation of the vacancy-unemployment ratio with total unemployment. The large relative volatility reflects that the JL-from-TL stock compounds both the volatility of TL separations and the cyclical variation in the TL-to-JL transition probability (loss-of-recall); both components are countercyclical, so they co-amplify in recessions.

Q3. How does the paper’s structural model generate endogenous temporary versus permanent layoffs and a procyclical recall probability?

Temporary layoffs and permanent exits arise endogenously from two cost shocks in the model: an employee-specific cost shock (ϑ) and a firm-specific overhead shock (γ), with thresholds ϑ and γ determined by firm optimization; workers whose idiosyncratic cost exceeds ϑ* are placed on temporary layoff (retaining recall rights), while firms whose overhead shock exceeds γ* exit, converting their TL workers to jobless unemployment.** The framework is a modified DMP model with staggered Nash wage bargaining (following Gertler-Trigari 2009), where firms can expand their workforce either by recalling workers from TL unemployment or by hiring new workers from JL unemployment, with separate quadratic adjustment costs for each margin ($\kappa$ for new hires, $\kappa_r$ for recalls). The recall elasticity exceeds the new-hire elasticity, consistent with the lower cost of re-integrating previously attached workers. Recall hiring (xr) and new hiring (x) are both driven by the discounted value of a worker to the firm, J(w,s), but respond with different sensitivities governed by their respective adjustment cost parameters. The TL-to-JL (loss-of-recall) flow is endogenous and driven by firm exit: when the overhead shock γ exceeds γ*(w,s), the firm exits and its TL workers lose their recall option, converting to JL unemployment. Because γ* rises in bad times (higher firm insolvency), loss-of-recall is countercyclical, matching the data pattern. An exogenous loss-of-recall probability $(1-\rho_r)$ is also included to capture TL-to-JL flows that occur even when the firm survives (e.g., firm restructuring or expiration of recall expectations), and this parameter is calibrated to long-run flow moments.

Q4. What does the calibrated model reveal about the amplification role of loss-of-recall, and how is this quantified?

A counterfactual exercise that sets the TL-to-JL transition probability to zero (shutting off loss-of-recall) shows that total unemployment peaks earlier and at a lower level following a recessionary TFP shock, and that unemployment displays markedly less persistence — revealing loss-of-recall as an important amplification mechanism by which a recessionary increase in temporary layoffs can generate persistently higher total unemployment. The model is calibrated to monthly frequency with 16 parameters: 9 assigned externally (β=0.991^{1/3}, δ=0.025^{3}, α=1/3, standard AR(1) TFP parameters, matching function elasticity σ=0.5, bargaining power η=0.5, λ=8/9 targeting quarterly wage adjustment frequency), and 7 calibrated to long-run flow moments and business cycle volatility moments (Table 8-9). The calibrated model captures the cyclical volatility of aggregate labor market stocks and flows, and the impulse response to a negative 1% TFP shock shows a hump-shaped increase in total unemployment with TL unemployment recovering within roughly two years (due to lower recall costs) while JL unemployment recovers more slowly (due to lower job-finding rates). The countercyclical overshooting of employment-to-JL transition probabilities during the subsequent expansion reflects the procyclicality of the reservation wage — workers are less willing to accept pay cuts in good times, triggering exits from employment at the margin. The overall result is that loss-of-recall accounts for a quantitatively significant share of unemployment persistence in recessions, particularly in the later part of the sample.

Q5. How is the model adapted for the pandemic recession, and what are the specific mechanisms through which PPP reduced jobless unemployment?

The pandemic application introduces two temporary shock processes: (i) a “virus shock” that exogenously raises the TL rate above the threshold determined by ϑ (capturing mandatory closures and social distancing-induced reductions in effective labor demand), and (ii) a productivity shock from social-distancing requirements; PPP is modeled as a policy that subsidizes firms’ wage bills conditionally on maintaining worker-firm attachments, reducing firms’ incentive to exit and thereby directly dampening the endogenous TL-to-JL (loss-of-recall) flow.* With these modifications the model captures the key features of pandemic labor market dynamics: the extraordinary March-April 2020 TL spike, the rapid initial recall, and the subsequent slow recovery of employment. In the PPP counterfactual (no PPP), cumulative TL-to-JL flows over the pandemic period would have been approximately double their actual levels — the model generates a 47.4% ratio of actual-to-counterfactual cumulative TL-to-JL flows, indicating PPP prevented roughly 53% of the loss-of-recall that would have otherwise occurred. At peak (six months after the shock), employment under the no-PPP counterfactual is 8.8% below pre-pandemic levels versus 6.8% with PPP — a 2 percentage point gap. Jobless unemployment peaks at 7.0% without PPP versus 5.9% with PPP. Consistent with estimates from Hubbard and Strain (2020), the estimated average monthly PPP employment gain is approximately 2.0% over the first six months, with gains of 1.57% through February 2021 before convergence toward zero.

Q6. What does the evidence on reemployment probabilities of workers who transition from TL to JL establish, and why is it important for identifying loss-of-recall?

Workers in jobless unemployment who were in temporary-layoff unemployment in the previous period have reemployment probabilities virtually indistinguishable from those of the full population of jobless unemployed (Table 3), which — because JL workers have far lower reemployment probabilities than TL workers — establishes that the TL-to-JL transition is a true loss-of-recall event: the worker has genuinely lost the recall relationship and now faces the same search frictions as other permanently separated workers. This finding is important for the paper’s empirical strategy because it validates the interpretation of CPS-recorded TL-to-JL transitions as genuine loss-of-recall rather than mismeasurement or recategorization without substantive change in the worker’s employment prospects. The result also implies that TL-to-JL transitions create true duration dependence in reemployment probabilities among workers initially on TL: workers who spend longer in TL unemployment are more likely to lose recall, so the average reemployment probability of the TL cohort declines with duration. This duration dependence is consistent with the model’s mechanism — exit probability rises over time as firms facing prolonged overhead cost shocks eventually breach the exit threshold — and provides a micro-level validation of the endogenous loss-of-recall channel.

Key Concepts

temporary-layoff (TL) unemployment : the labor market state in which an unemployed worker retains an expectation of recall to the prior employer (either a specific return date or an indication of recall within six months, per CPS classification); characterized by substantially higher reemployment probabilities than jobless unemployment, accounting for roughly one-third of separations from employment but only one-eighth of the total unemployment stock due to the transient nature of TL spells.

loss-of-recall : the conversion of a temporary layoff into a permanent separation — the event by which a worker initially on TL status transitions to jobless unemployment because the prior employer exits or cannot recall; the paper’s central amplification mechanism, shown to be countercyclical (higher in recessions), to account for 8.5–11.0% of unemployment increases in pre-pandemic recessions, and to be substantially dampened by PPP during the pandemic.

JL-from-TL stock : the accumulated stock of workers currently in jobless unemployment whose most recent exit from employment was through temporary layoff — constructed via the paper’s novel recursive accumulation method; has a standard deviation 16 times GDP and 2 times total unemployment, correlates 0.93 with total unemployment, and constitutes a leading slack indicator that captures the indirect destabilizing contribution of temporary layoffs to unemployment dynamics.

recall hiring versus new-hire margin : the model’s two channels through which firms can expand their workforce — recalling workers from their own TL pool (lower adjustment cost, higher recall elasticity) versus hiring new workers from the pool of jobless unemployed (higher cost); both margins respond positively to the discounted firm value J(w,s) but with different sensitivities calibrated to match the differential volatility of TL-to-E and JL-to-E transition probabilities in the CPS.

staggered Nash wage bargaining : the model’s wage rigidity mechanism (following Gertler-Trigari 2009), in which firms and workers negotiate base wages with probability (1-λ) each period; the calibrated λ=8/9 targets a wage adjustment frequency of roughly one per quarter, consistent with Taylor (1999) and Gottschalk (2005) evidence; wage rigidity — combined with the allowance for temporary pay cuts to prevent exit — is quantitatively important for replicating the observed volatility of labor market flows and stocks.