Figure 1: Illustration of L-Shaped and U-Shaped
Recoveries
Figure 1 presents a schematic illustration contrasting L-shaped and U-shaped recoveries from recessions. The figure uses simple line graphs to visualize the concepts: both lines begin with an economic decline, representing a recession, but diverge in their aftermath. The U-shaped line shows a strong rebound, eventually converging to the pre-recession trend indicated by a black dotted line. In contrast, the L-shaped line never returns to this trend, depicting a persistent shortfall in output—this is the empirical signature of hysteresis. The shaded area denotes the recession period, visually reinforcing the distinction between transitory and lasting economic damage.
Figure 2: Nonfarm Payroll Employment Growth at the National Level and
in Virginia
Figure 2 shows actual employment growth data over time, with Panel A for the national level and Panel B for Virginia. Each panel displays quarterly employment growth in red, overlaid with a blue dashed line that tracks the long-run trend (calculated as a 40-quarter moving average). At the national level, sharp employment declines are evident during major recessions such as the early 1980s, the Great Recession, and the COVID-19 pandemic. Virginia’s panel illustrates similar patterns but includes local fluctuations, such as less pronounced declines or different rebound speeds. This comparison underscores regional variation in the depth and pace of labor market recoveries.
Figure 3: National Level Recession Probabilities
Figure 3 plots estimated probabilities of experiencing L-shaped and U-shaped recessions at the national level, with Panel A based on payroll employment and Panel B based on GDP growth. The red lines represent L-shaped probabilities, and the blue lines represent U-shaped ones. Overall, the payroll-based estimates correspond well with NBER recession dates, but differ from GDP-based ones in key periods—most notably, the Great Recession is identified as L-shaped in employment but U-shaped in GDP. The COVID-19 recession is classified as U-shaped in both, although the second wave is interpreted differently: payroll data suggests a new U-shaped episode, while GDP data sees continued expansion. This divergence illustrates that employment measures may better capture persistent labor market weaknesses.
Figure 4: Probabilities of L- and U- Shape Recessions across States
over Time
Figure 4 presents two heatmaps (Panels A and B) that display, across all U.S. states, the quarterly probabilities of experiencing L-shaped and U-shaped recessions from 1960 to 2020. Each row is a state, and each column is a time period, with darker colors indicating higher probabilities. Panel A (L-shaped) reveals that since the 1990s, L-shaped recessions have become more prevalent, while Panel B (U-shaped) shows a marked decline in such recoveries. Some states display isolated recessionary episodes independent of national cycles—for example, Louisiana in 2005 and North Dakota in 2015. The COVID-19 recession, however, stands out as broadly U-shaped across nearly all states, reflecting a rapid bounceback from an unusually deep shock.
Figure 5: L-shaped and U-shaped Recession Probabilities: New York and
Wisconsin
Figure 5 compares two specific states—New York and Wisconsin—in their recession dynamics. Panel A plots the probabilities of L- and U-shaped recessions for New York, and Panel B does the same for Wisconsin. The red line represents the L-shaped probability and the blue line the U-shaped one, while shaded areas denote NBER recession periods. These panels show strong heterogeneity: Wisconsin experienced pronounced L-shaped recessions in the 1980s, likely due to its manufacturing base, whereas New York saw a persistent L-shaped recession in the early 1990s. Both states exhibited U-shaped recessions during the COVID-19 period, but their post-pandemic dynamics diverged, reflecting differing industry structures and labor market responses.
Figure 6: Effects of expansionary demand policies on the relative risk
of L-shaped recession over U-shaped recession
Figure 6 shows the response of the relative probability of an L-shaped recession compared to a U-shaped recession following a one-unit expansionary monetary policy shock. Negative values indicate that such a policy significantly reduces the likelihood of an L-shaped recession relative to a U-shaped one, thereby mitigating hysteresis, while positive values suggest the opposite. In the top panels, Panel A presents estimates under greater downward nominal wage rigidity, and Panel B under lower rigidity. In the regime of greater downward nominal wage rigidity, expansionary monetary policy significantly reduces the relative probability of an L-shaped recession about four quarters after the shock, with persistent effects. In contrast, these hysteresis-mitigating effects are weaker and shorter-lived under weaker downward nominal wage rigidity, with a statistically significant impact only in the fourth quarter following the shock. This result confirms the long-run effectiveness of monetary policy in mitigating hysteresis and highlights that these effects are stronger when nominal wages are more downwardly rigid. Panels C and D examine the effects of expansionary tax shocks in mitigating hysteresis. Tax cuts exhibit sizable hysteresis-reducing effects, as indicated by their statistically significant and negative pass-through to the relative probability of an L-shaped recession. Specifically, they lower the likelihood of an L-shaped recession relative to a U-shaped one when nominal wages are more downwardly rigid during a recession (Panel C). In contrast, the effect is smaller and shorter-lived under weaker downward nominal wage rigidity (Panel D). These findings suggest that tax cuts are more effective at mitigating hysteresis in environments with greater downward nominal wage rigidity. The bottom panels report how the gender employment gap interacts with the effectiveness of tax cuts in mitigating hysteresis. Unlike monetary policy shocks, the gender employment gap does not produce discernible differences in the transmission of tax cuts.
Figure 7: The role of DNWR in amplifying the hysteresis
effect
Figure 7 shows the impulse response functions to a contractionary demand shock under two scenarios: with the downward nominal wage rigidity constraint (red solid line) and without it (blue dashed line). This picture presents the effects of downward nominal wage rigidity by comparing the impulse responses to a contractionary demand shock under scenarios with and without the rigidity constraint (no policy indicated with the blue dashed line; with policy indicated with the solid red line). The size of the demand shock is calibrated to match the estimated national-level value of μ2 for an L-shaped recession (hysteresis). Employment on impact declines by 1.20 percent without downward nominal wage rigidity and by 1.92 percent with downward nominal wage rigidity. The impulse responses of employment and output show that hysteresis effects are highly persistent and that downward nominal wage rigidity amplifies the impact of the shock, leading to declines in employment and output that are approximately 60 percent larger, consistent with stronger hysteresis effects. Unemployment rises under downward nominal wage rigidity because higher real wages increase labor supply, which suppresses labor demand. In the New Keynesian Phillips curve, inflation is driven by output and real wage gaps. The upward pressure on real wages outweighs the recessionary effect on output, producing a smaller decline in inflation. Consequently, the larger output contraction and smaller inflation decline largely offset each other in the monetary policy rule, so the nominal interest rate behaves similarly with or without downward nominal wage rigidity. This leads to a substantially larger decline in the real interest rate under this rigidity.
Figure 8: Hysteresis and expansionary monetary policy under
DNWR
Figure 8 displays the impulse response functions to a contractionary demand shock in the presence of downward nominal wage rigidity, comparing the case with expansionary monetary accommodation (blue dashed line) to the case without it (red solid line). We show a counterfactual analysis of an expansionary monetary policy implemented alongside hysteresis driven by a contractionary demand shock under downward nominal wage rigidity. This expansionary policy is modeled as a 50 basis points per annum (εm = −0.125% at a quarterly rate), occurring simultaneously with the onset of the contractionary demand shock. This figure shows that this intervention substantially mitigates the shock’s adverse effects. In particular, it nearly offsets the rise in real wages induced by the price decline, preventing sharp contractions in employment and output that would otherwise generate persistent hysteresis. Consequently, hysteresis in employment and output is largely eliminated, underscoring the importance of timely and forceful monetary accommodation when downward nominal wage rigidity limits labor market adjustment.
Figure 9: The Amplification of Expansionary Monetary Policy Effects by
DNWR
Figure 9 displays the effects of an expansionary monetary policy implemented during hysteresis, obtained by taking the difference between the impulse responses to a contractionary demand shock with and without the monetary policy shock, under two scenarios: with the downward nominal wage rigidity constraint (red solid line) and without it (blue dashed line). This figure shows the difference in impulse responses to a contractionary demand shock with and without an accompanying expansionary monetary policy, comparing outcomes under downward nominal wage rigidity and without the constraint. The shocks are calibrated as in Figures 7 and 8. When downward nominal wage rigidity binds, nominal wages cannot fall, causing real wages to rise, depressing labor demand, and amplifying the recession. Expansionary monetary policy mitigates this effect by raising the price level, lowering real wages, and restoring labor market equilibrium. Consequently, as shown in this figure, the same monetary expansion under downward nominal wage rigidity substantially cushions the downturn in employment and output and lowers unemployment relative to the case without it. Overall, downward nominal wage rigidity makes monetary policy roughly 1.6 times more effective in stabilizing output, employment, and unemployment.
Figure B1: Nonfarm Payroll Employment growth by state (1)
Figures B1–B2 display employment growth by state. Each panel shows quarterly employment growth for the indicated state in red, overlaid with a blue dashed line that tracks the long-run trend (calculated as a 40-quarter moving average). At the national level (panel A), sharp employment declines are evident during major recessions such as the early 1980s, the Great Recession, and the COVID-19 pandemic. Each state panel illustrates similar patterns but also includes local fluctuations, such as less pronounced declines or different rebound speeds. This comparison underscores regional variation in the depth and pace of labor market recoveries.
Figure B2: Nonfarm Payroll Employment growth by state (2)
Figures B1–B2 display employment growth by state. Each panel shows quarterly employment growth for the indicated state in red, overlaid with a blue dashed line that tracks the long-run trend (calculated as a 40-quarter moving average). At the national level (panel A), sharp employment declines are evident during major recessions such as the early 1980s, the Great Recession, and the COVID-19 pandemic. Each state panel illustrates similar patterns but also includes local fluctuations, such as less pronounced declines or different rebound speeds. This comparison underscores regional variation in the depth and pace of labor market recoveries.
Figure C3: Estimated recession probabilities by state (1)
Figures C3–C4 display the recession probabilities by state. The red line represents the L-shaped probability and the blue line the U-shaped one, while shaded areas denote NBER recession periods. These panels show similarities, yet notable heterogeneity, in the recession experiences across states.
Figure C4: Estimated recession probabilities by state (2)
Figures C3–C4 display the recession probabilities by state. The red line represents the L-shaped probability and the blue line the U-shaped one, while shaded areas denote NBER recession periods. These panels show similarities, yet notable heterogeneity, in the recession experiences across states.