Finance and Economics Discussion Series: Accessible versions of figures for 2026-058

Beyond the Unemployment Rate: A Structural Labor Market Indicator

Accessible version of figures

Figure 1: Cross-Correlations with Output: Data vs. Model
(a) GDP
(b) c
(c) I
(d) w
(e) u
(f) LFPR
(g) v
(h) \(\pi\)
(i) i
(j) ww
(k) spread
Notes: Cross-correlations computed from HP-filtered series (\(\lambda = 10^5\)). Solid gray lines: data; solid black lines: model average over 1,000 simulations using the baseline (constant pre-2013) Taylor rule. Dash-lines: minimum and maximum over the simulations that use a time-varying Taylor rule. Horizontal axis shows leads (positive) and lags (negative) in quarters. Each panel shows correlations between the indicated variable at time \(t\) and output at \(t+j\).

This figure consists of 11 subplots (panels a through k) showing cross-correlation functions:

(a) GDP: Line chart showing cross-correlations of GDP with itself at various leads and lags from -8 to +8 quarters. The solid gray line (data) and solid black line (model) both show perfect correlation (1.0) at lag zero, declining symmetrically to approximately 0.2 at both -8 and +8 quarters. Dashed lines indicate minimum and maximum bounds from simulations with time-varying Taylor rule.

(b) Consumption (c): Line chart displaying cross-correlations between consumption and output. Both data (gray) and model (black) lines show strong positive correlation peaking near 0.9 at lag zero, declining to approximately 0.2-0.3 at extreme lags of ±8 quarters. The pattern is relatively symmetric around zero.

(c) Investment (I): Line chart showing cross-correlations between investment and output. Both series show strong positive correlation peaking around 0.8-0.9 near lag zero, with slight leading behavior (correlation rises before lag zero). Correlations decline to near zero at extreme lags.

(d) Real Wage (w): Line chart depicting cross-correlations between real wages and output. Both data and model show weak to moderate positive correlation (0.2-0.4) across all lags, with relatively flat profiles. Model slightly understates the correlation magnitude compared to data.

(e) Unemployment Rate (u): Line chart showing cross-correlations between unemployment and output. Both series display strong negative correlation throughout, with correlations ranging from approximately -0.8 to -1.0 across all leads and lags. The relationship is nearly symmetric around lag zero.

(f) Labor Force Participation Rate (LFPR): Line chart displaying cross-correlations between LFPR and output. Both data and model show moderate positive correlation (0.4-0.6) that is relatively stable across leads and lags, with slight increases at positive lags.

(g) Vacancies (v): Line chart showing cross-correlations between vacancies and output. Both series display strong positive correlation (0.6-0.8) with slight leading behavior—correlation peaks 1-2 quarters before output. Pattern shows mild procyclical and leading indicator properties.

(h) Inflation (π): Line chart depicting cross-correlations between inflation and output. Both data and model show weak correlations ranging from -0.2 to +0.4 across all lags. The pattern is more variable and less systematic than other series, with model capturing the weak relationship.

(i) Nominal Interest Rate (i): Line chart showing cross-correlations between the nominal interest rate and output. Both series show moderate to strong positive correlation (0.4-0.8), with correlations declining at longer lags. Model tracks data closely throughout.

(j) Workweek (ww): Line chart displaying cross-correlations between average workweek hours and output. Both data and model show strong positive correlation (0.6-0.9) near lag zero, declining symmetrically to near zero at extreme lags of ±8 quarters.

(k) Credit Spread: Line chart showing cross-correlations between credit spreads and output. Both series display negative correlation (-0.4 to -0.6) near lag zero, indicating countercyclical behavior. The relationship weakens at longer leads and lags, approaching zero at ±8 quarters.

General Note: All subplots include shaded regions representing NBER recession dates. Solid gray lines represent actual data, solid black lines represent model averages, and dashed lines show minimum and maximum ranges from time-varying Taylor rule simulations.

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Figure 2: Model-Implied Gaps vs. External Estimates
Notes: “Model” refers to our model’s gaps, defined as deviations from flexible-price equilibrium, using the time-varying monetary policy rule. Federal Reserve estimates are based on the December 2020 Tealbook projections, which extend through 2023:Q4, and were retrieved via the Federal Reserve Bank of Philadelphia real-time database. CBO estimates are from the Congressional Budget Office. Shaded regions represent NBER recessions.

This figure contains two panels comparing model-based gaps with external estimates:

(Top Panel) Output Gap: Time series line chart from 1990 to 2025 showing three measures of the output gap. The y-axis ranges from -25 to +5 percentage points. The model-based gap (black solid line) shows deep negative values during recessions: approximately -8% in 1991, -10% in 2001, -20% during the 2008-2009 financial crisis, and -23% during the 2020 COVID-19 recession. The Congressional Budget Office (CBO) estimate (shown in one color) and Federal Reserve estimate (shown in another color) generally track the model but with smaller magnitudes, particularly during the 2020 recession. In recent years (2024-2025), the model shows a small negative gap around -2%, while CBO estimates show a small positive gap. Gray shaded regions indicate NBER-dated recessions.

(Bottom Panel) Unemployment Rate Gap: Time series line chart from 1990 to 2025 showing three measures of the unemployment rate gap. The y-axis ranges from -2 to +8 percentage points. The model-based unemployment gap shows large positive spikes during recessions: approximately +2 percentage points in 1991, +2.5 in 2001, +6 in 2009, and +7 in 2020. Between recessions, the gap fluctuates around zero. The CBO and Federal Reserve estimates show similar patterns but with differences in magnitude, especially during the COVID-19 recession where the model indicates greater labor market slack. Recent values (2024-2025) show all three measures converging near zero. Gray shaded regions indicate NBER-dated recessions.

Note: The Federal Reserve estimates extend only through 2023:Q4 based on December 2020 Tealbook projections retrieved via the Federal Reserve Bank of Philadelphia real-time database.

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Figure 3: Model-Based Labor Market Gaps and SLMI
(a) Model-Based Gaps
(b) SLMI
Notes: Red and gray lines in panel 3b represent the SLMI and all model-based gaps presented in panel 3a, respectively. Shaded regions represent NBER recessions.

This figure consists of two panels:

(a) Model-Based Gaps: Time series line chart from 1990 to 2025 showing nine overlaid labor market gap measures. The y-axis ranges from -40 to +10. Multiple colored lines represent gaps in: employment (E), unemployment level (U), unemployment rate (u), labor force participation rate (LFPR), total hours worked (H), workweek hours (ww), vacancies (v), labor market tightness (θ), and real wages (w). All gaps move together broadly, showing large negative values (slack) during recessions and positive values (tightness) during expansions. The 2008-2009 recession shows gaps reaching -30 to -35, while the 2020 COVID recession shows the most extreme values approaching -40. The gaps exhibit high correlation but differ in magnitude and timing at business cycle turning points. Gray shaded regions indicate NBER-dated recessions.

(b) SLMI: Time series line chart from 1990 to 2025 with the same y-axis scale (-40 to +10) as panel (a). The red line represents the Structural Labor Market Indicator (SLMI), which synthesizes the nine individual gaps shown in panel (a) using principal component analysis. Gray lines in the background show all nine individual gaps from panel (a) for comparison. The SLMI tracks within the envelope of individual indicators, capturing their common cyclical movement. It shows deep slack during the 1991 recession (approximately -8), the 2001 recession (approximately -5), the 2008-2009 financial crisis (approximately -20), and the 2020 COVID recession (approximately -35). The SLMI generally lies in the middle of the range spanned by individual indicators, representing their weighted average. Gray shaded regions indicate NBER-dated recessions.

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Figure 4: Historical Decomposition SLMI
(a) Shock Decomposition
(b) Data Decomposition
Notes: Panel 4a presents the historical shock decomposition of the SLMI, showing the contribution of each structural shock to the deviation of the SLMI from its steady state over the sample period. Panel 4b presents the data decomposition, indicating the contribution of each observable variable used in the model’s estimation to the SLMI dynamics. Both decompositions sum to the total SLMI value shown by the solid black line.

This figure contains two complementary decomposition panels:

(a) Shock Decomposition: Stacked area chart from 1990 to 2025 showing contributions of various structural shocks to the SLMI. The y-axis ranges from -30 to +20. Different colored areas represent: risk premium shocks (RP), government spending shocks (Gov), investment efficiency shocks, monetary policy shocks, productivity shocks, markup shocks, wage markup shocks, labor supply shocks affecting LFPR, labor supply shocks affecting hours, effective lower bound (ELB) effects, and initial conditions. The black solid line shows the total SLMI. Risk premium shocks (largest area) dominate during the 2008-2009 crisis, contributing approximately -15 to -20 percentage points of slack. Investment efficiency shocks contribute substantially during the 2001 recession and 2010s recovery. Monetary policy shocks show visible contributions before 2013 but become negligible afterward (post time-varying Taylor rule implementation). The 2020 COVID recession shows large negative contributions from multiple shocks simultaneously. Recent years show risk premium and investment shocks as primary drivers of modest slack.

(b) Data Decomposition: Stacked area chart from 1990 to 2025 showing contributions of observable variables to the SLMI. The y-axis ranges from -25 to +10. Different colored areas represent contributions from: GDP growth, consumption growth (C), investment growth (I), real compensation per hour (RCPRHW), PCE inflation, CPI inflation, federal funds rate (FFR), unemployment rate (u), labor force participation rate (LFPR), average hours worked, vacancies, credit spreads, ELB effects, and initial conditions. The black solid line shows the total SLMI. The unemployment rate and LFPR are consistently the largest contributors throughout the sample, reflecting their direct measurement of labor market quantities. GDP growth shows important contributions, particularly in 2020-2021 (indicating slack) and 2024-2026 (indicating modest tightness). Inflation measures (PCE and CPI) contribute notably during 2021-2023, validating tightness signals. Credit spreads show substantial contributions during financial stress episodes. The decomposition illustrates that all variables contribute meaningfully in different periods, validating the multi-variable structural approach.

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Figure 5: The Role of Non-Labor Market Data
(a) SLMI: Full Data vs. Labor Market Data Only
(b) Data Decomposition: Non-Labor Data
Notes: Panel 5a presents the SLMI constructed using all available data (solid black line) and using only labor market variables (solid red line). Panel 5b presents the data decomposition of non-labor market variables to the gap between the two indicators in Panel 5a.

This figure contains two panels analyzing non-labor market data contributions:

(a) SLMI: Full Data vs. Labor Market Data Only: Time series line chart from 1990 to 2025 comparing two versions of the SLMI. The y-axis ranges from -25 to +5. The solid black line shows the SLMI constructed using all available data (labor market variables plus GDP, consumption, investment, inflation, interest rates, and spreads). The solid red line shows the SLMI constructed using only labor market observables (unemployment rate, LFPR, workweek hours, and vacancies). Both indicators track closely over most of the sample but diverge notably during specific episodes. During the 2020-2021 pandemic recovery, the labor-market-only indicator (red) shows less slack than the full-data indicator (black), with the gap reaching approximately 3-4 percentage points. In recent years (2024-2026), the labor-only indicator suggests tighter conditions than the full SLMI, with a gap of approximately 2 percentage points. The largest divergences occur at business cycle turning points, particularly during recoveries. Gray shaded regions indicate NBER-dated recessions.

(b) Data Decomposition: Non-Labor Data: Stacked area chart from 1990 to 2025 decomposing the gap between the full-data and labor-market-only SLMIs into contributions from non-labor market variables. The y-axis ranges from -4 to +5 percentage points. Different colored areas represent contributions from: GDP growth (blue), consumption growth (C), investment growth (I), real compensation per hour (RCPRHW), PCE inflation (red), CPI inflation (maroon), federal funds rate (FFR, gray), and credit spreads (light green). GDP growth emerges as a major contributor, particularly in 2020-2021 where it adds approximately -3 to -4 percentage points of slack beyond what labor data alone suggests. Inflation (PCE and CPI) contributes positively (indicating tightness) during 2021-2023, with PCE adding up to 2 percentage points and CPI adding approximately 1 percentage point. Credit spreads show countercyclical contributions, positive during the 2008-2009 crisis (suggesting conditions were tighter than labor data indicated) and negative during the 2020 recession (reinforcing slack signals). The federal funds rate contributes throughout the sample with varying signs. The decomposition demonstrates that non-labor market data account for approximately 19% of SLMI variance and often provide offsetting signals to labor market data, offering complementary rather than redundant information.

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Figure 6: SLMI and Alternative Labor Market Gaps
Notes: \(HP(10^5)\): first principal component of the labor market data when filtered with the HP filter and a smoothing parameter equal to \(10^5\). \(HP(1,600)\): first principal component of the labor market data when filtered with the HP filter and a smoothing parameter equal to \(1,600\). Shaded regions represent NBER recessions.

This figure is a single-panel time series comparison chart from 1990 to 2025:

The y-axis ranges from -20 to +5. Multiple lines represent different labor market slack measures:

All measures show general agreement on recession periods with deep negative values: 1991 recession (approximately -5 to -7), 2001 recession (approximately -3 to -5), 2008-2009 crisis (approximately -12 to -18), and 2020 COVID recession (approximately -15 to -20). However, important differences emerge in timing and magnitude:

The SLMI (black solid line) tends to signal deterioration earlier at recession onset, particularly before the 2001 and 2008 recessions, where it turns negative 1-2 quarters before alternative measures. During expansions, the SLMI recovers more gradually, lagging the filtered-data measures in the mid-1990s and 2010s. The unemployment rate gap (gray) correlates highly with the SLMI but shows some divergence, notably in 2021 when the SLMI indicated tightness earlier. The purely statistical measures (HP-filtered and Hamilton-filtered) show more similarity to each other than to the structural SLMI, especially during turning points. The LMCI tracks closely with HP-filtered measures. In recent years (2024-2026), all measures converge toward zero, though with modest dispersion of approximately 2-3 percentage points. Gray shaded regions indicate NBER-dated recessions.

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Figure 7: SLMI 68% Credible Intervals
Notes: Shaded region represents the 68 percent credible interval. The blue line corresponds to the median SLMI.

This figure is a time series chart from 1990 to 2025 with uncertainty bands:

The y-axis ranges from -25 to +5. The chart displays:

The credible intervals vary in width across the sample period. They are relatively narrow (approximately ±2 percentage points) during the early 1990s and late 1990s. The intervals widen considerably during the 2010-2015 post-Great Recession recovery period, reaching widths of approximately ±4 to ±5 percentage points and often straddling zero, indicating substantial model uncertainty about whether labor markets had returned to equilibrium. The intervals narrow again during the mid-to-late 2010s. During the 2020 COVID recession, the intervals widen to approximately ±3 percentage points. In recent years (2024-2026), the credible intervals have narrowed substantially to approximately ±1 to ±2 percentage points, reflecting increased confidence in slack estimates.

The distribution exhibits modest downward skew, with the lower bound of the credible interval extending further from the median than the upper bound during most periods, particularly during recoveries. This asymmetry indicates heavier tails toward greater labor market tightness. The median SLMI tracks the point estimate closely, showing deep slack during recessions: approximately -8 in 1991, -5 in 2001, -20 in 2009, and -20 in 2020. The uncertainty quantification reveals that parameter uncertainty about labor market slack is especially elevated during recoveries when policymakers face genuine ambiguity about normalization timing. Gray shaded regions indicate NBER-dated recessions.

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Figure 8:
Notes: Shaded regions represent NBER recessions.

This figure is a time series comparison chart from 1990 to 2025:

The y-axis ranges from -20 to +5. Two lines are plotted:

The two series are highly correlated throughout the sample, confirming that the SLMI provides reliable real-time signals without the benefit of future data revisions. Both indicators track closely during recessions: 1991 recession (approximately -8), 2001 recession (approximately -5), 2008-2009 financial crisis (approximately -18 to -20), and 2020 COVID recession (approximately -18).

However, a systematic difference emerges: since approximately 2015, the one-sided indicator (red) has been visibly higher than the two-sided indicator (black), with gaps of 1-3 percentage points. This suggests the real-time indicator tends to understate slack (or overstate tightness) relative to the full-sample estimate. Despite this level difference, the one-sided SLMI preserves the key cyclical properties, including earlier warning signals at recession onset compared to alternative indicators. The one-sided version shows slightly more volatility at high frequencies, reflecting the absence of future data smoothing.

In recent years (2024-2026), both indicators show values near or slightly below zero, indicating roughly balanced labor market conditions, with the one-sided measure approximately 1-2 percentage points higher. The close tracking between the two versions validates the SLMI's implementability for practical real-time policy analysis. Gray shaded regions indicate NBER-dated recessions.

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Figure A.1: Time-Varying Taylor Rule Parameters
(a) \(\rho_i\)
(b) \(\kappa_\pi\)
(c) \(\kappa_y\)
Notes: Shaded areas represent NBER recession dates.

This figure contains three subplots showing monetary policy rule coefficients from 2013 to 2026:

(a) Interest Rate Smoothing Parameter (ρ_i): Line chart showing the inertia parameter in the Taylor rule. The y-axis ranges from 0.8 to 0.95. The coefficient exhibits minor variations over time, starting around 0.90 in 2013, declining slightly to approximately 0.87-0.88 during 2015-2017, rising back to approximately 0.90 during 2018-2019, showing a brief dip during the 2020 recession to about 0.85, then recovering to approximately 0.90 by 2021 and remaining relatively stable through 2026. The overall range of variation is modest (approximately 0.85 to 0.92), indicating that interest rate smoothing behavior has been relatively stable over this period. Gray shaded region indicates the 2020 NBER recession.

(b) Inflation Response Coefficient (κ_π): Line chart showing the coefficient on inflation deviations from target. The y-axis ranges from 0.5 to 4.0. This coefficient displays substantial variation over the sample period. It starts around 1.5 in 2013, rises gradually to approximately 2.5 by 2015, increases further to approximately 3.0-3.5 during 2016-2019 (pre-COVID), drops sharply during the 2020 recession to approximately 2.0, partially recovers to about 2.5-3.0 during 2021-2022, then declines steadily from 2022 through 2026, ending near 1.0. This pattern suggests monetary policy became more responsive to inflation during the mid-to-late 2010s but has become substantially less responsive in recent years (2024-2026). The large variation (range of approximately 1.0 to 3.5) indicates meaningful changes in systematic monetary policy responses to inflation. Gray shaded region indicates the 2020 NBER recession.

(c) Output Gap Response Coefficient (κ_y): Line chart showing the coefficient on the output gap. The y-axis ranges from 0.2245 to 0.2275, a very narrow range. The coefficient shows remarkable stability throughout the entire sample period, fluctuating only between approximately 0.2250 and 0.2270. There is no clear trend or systematic pattern, and even the 2020 recession shows minimal impact. The coefficient ends the sample period in 2026 at approximately 0.2260, nearly identical to its 2013 starting value. This stability contrasts sharply with the variability observed in the inflation coefficient, indicating that while the Federal Reserve's response to inflation has changed substantially, its response to the output gap has remained virtually constant. Gray shaded region indicates the 2020 NBER recession.

General Note: These time-varying coefficients are estimated from Federal Open Market Committee Summary of Economic Projections (SEP) data using the methodology of González-Astudillo and Tanvir (2026). Prior to 2013, the model uses constant coefficients estimated over the pre-2013 period.

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Figure A.2:
Notes: Y-axis represents number of quarters that the ELB is expected to bind. Shaded regions represent NBER recessions.

This figure is a time series chart from 2009 to 2022:

The y-axis represents the number of quarters that the effective lower bound (ELB) on interest rates is expected to bind, ranging from 0 to 16 quarters. The chart shows two distinct ELB episodes:

First Episode (2009-2015): The series begins in early 2009 at approximately 10 quarters, indicating expectations that the federal funds rate would remain at the ELB for about 2.5 years. Expected duration rises to approximately 12-14 quarters during 2009-2010, peaks near 15-16 quarters in early 2011 (expecting nearly 4 years at the ELB), remains elevated around 12-14 quarters through 2012-2013, then declines steadily from 2014 through 2015, reaching zero by late 2015 when the Fed began raising rates. This episode reflects the prolonged zero lower bound period following the Global Financial Crisis.

Second Episode (2020-2022): Expected ELB duration jumps suddenly in March 2020 (COVID-19 pandemic onset) to approximately 8-10 quarters, indicating expectations of about 2-2.5 years at the ELB. The expected duration declines relatively quickly compared to the first episode, falling to approximately 6 quarters by late 2020, 4 quarters by mid-2021, and reaching zero by early 2022 when the Fed began its tightening cycle. This shorter expected duration reflects the faster recovery and different nature of the COVID recession compared to the financial crisis.

Between these two episodes (2016-2019), the expected duration remains at zero as interest rates were above the ELB. Gray shaded regions indicate NBER-dated recessions (2020 recession visible). The series is constructed from Blue Chip Economic Indicators survey data (2008-2010) and the Federal Reserve Bank of New York's Survey of Primary Dealers (2011 onward).

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Figure A.3: Model-Based Flexible-Price Gaps
(a) Employment
(b) Unemployment
(c) Unemployment Rate
(d) LFPR
(e) Total Hours Worked
(f) Work Week Hours
(g) Vacancies
(h) Labor Market Tighness
(i) Output
Notes: The figure plots the model-based flexible-price gaps. The horizontal axis represents time and the vertical axis represents percentage point deviations from the flexible-price variable. Shaded areas represent NBER recession dates.

This figure contains nine subplots showing individual labor market gaps from 1990 to 2025:

(a) Employment Gap: Time series line chart with y-axis ranging from -8 to +2 percentage points. The employment gap shows negative values (slack) during recessions: approximately -2% in 1991, -2% in 2001, -7% during the 2008-2009 crisis (the deepest negative value), and -6% in 2020. The gap returns to near zero during expansions, with brief periods of positive values (tightness) in the mid-2000s and late 2010s. Recent values (2024-2026) fluctuate around zero. Gray shaded regions indicate NBER recessions.

(b) Unemployment Level Gap: Time series line chart with y-axis ranging from -1 to +5. The unemployment level gap (excess unemployment above the natural level) shows large positive spikes during recessions: approximately +1.5 in 1991, +2 in 2001, +4.5 during 2009 (the largest spike), and +4 in 2020. Between recessions, the gap fluctuates near zero with some negative excursions (unemployment below natural rate) in the late 1990s and mid-2000s. Recent values hover around zero. Gray shaded regions indicate NBER recessions.

(c) Unemployment Rate Gap: Time series line chart with y-axis ranging from -2 to +8 percentage points. Pattern similar to unemployment level gap but expressed as a rate. Shows positive spikes during recessions: approximately +2 percentage points in 1991, +2.5 in 2001, +6 in 2009, and +7 in 2020 (the largest deviation). Negative values appear during tight labor markets in the late 1990s (approximately -1 percentage point) and briefly in the mid-2000s. Recent values near zero. Gray shaded regions indicate NBER recessions.

(d) Labor Force Participation Rate (LFPR) Gap: Time series line chart with y-axis ranging from -4 to +1 percentage points. The LFPR gap shows substantial variation, generally negative (below equilibrium) during and after recessions: approximately -1 percentage point in the early 1990s, -1.5 in the early 2000s, declining to -3 percentage points during the 2008-2015 period (the largest and most persistent negative values), and -3.5 in 2020. The gap has recovered somewhat in recent years but remains negative around -1 percentage point in 2024-2026. The persistent negative values during the 2010s reflect structural decline in participation not fully captured by cyclical factors. Gray shaded regions indicate NBER recessions.

(e) Total Hours Worked Gap: Time series line chart with y-axis ranging from -10 to 0 percentage points. Total hours gap combines employment and hours-per-worker adjustments. Shows large negative values during recessions: approximately -3% in 1991, -4% in 2001, -8% in 2009, and -9% in 2020 (the deepest slack). Returns toward zero during expansions with some positive values in the late 1990s. Recent values fluctuate near zero. This gap exhibits larger volatility than employment alone, reflecting variation in both the extensive and intensive margins. Gray shaded regions indicate NBER recessions.

(f) Workweek Hours Gap: Time series line chart with y-axis ranging from -10 to +2. The average workweek gap shows negative values during recessions: approximately -2 to -3 during early 1990s, -4 in 2001, -8 during 2009 (the largest negative value), and -7 in 2020. The gap generally fluctuates around zero during expansions with some positive excursions in the mid-2000s. Recent values near zero with slight negative bias. This intensive margin captures firms' adjustments in hours per worker separate from employment changes. Gray shaded regions indicate NBER recessions.

(g) Vacancies Gap: Time series line chart with y-axis ranging from -30 to +5 percentage points. Vacancies gap exhibits high volatility and large swings. Shows deep negative values (vacancy posting below equilibrium) during recessions: approximately -8 in 1991, -10 in 2001, -25 in 2009 (the deepest), and -20 in 2020. During expansions, the gap can be substantially positive, reaching approximately +5 in the late 1990s and briefly positive in the mid-2000s. Following the 2020 recession, vacancies surged above equilibrium before normalizing in recent years to slightly negative values. Vacancies are the most volatile labor market margin. Gray shaded regions indicate NBER recessions.

(h) Labor Market Tightness Gap: Time series line chart with y-axis ranging from -200 to +50. Labor market tightness (defined as vacancies relative to job searchers) shows extreme volatility. Large negative values (excess labor supply) during recessions: approximately -30 in 1991, -40 in 2001, -150 in 2009 (by far the largest negative value), and -100 in 2020. Positive values (excess labor demand) appear during tight labor markets: approximately +20 in the late 1990s, small positive values in mid-2000s, and notably approximately +30 in 2021-2022 post-COVID recovery before normalizing. Recent values fluctuate near zero to slightly negative. This measure amplifies cyclical swings by combining vacancy and unemployment movements. Gray shaded regions indicate NBER recessions.

(i) Output Gap: Time series line chart with y-axis ranging from -25 to +5 percentage points. This is the same output gap shown in Figure 2 for comparison. Shows deep negative values during recessions: approximately -5% in 1991, -7% in 2001, -20% in 2009, and -23% in 2020 (the largest gap). Returns toward zero during expansions with brief positive excursions in the late 1990s and mid-2000s. Recent values slightly negative around -2%. Gray shaded regions indicate NBER recessions.

Note: All gaps are defined as deviations from flexible-price-and-wage equilibrium. Shaded areas represent NBER recession dates.

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Figure A.4:
Notes: The x-axis represents the unemployment rate gap, while the y-axis represents the output gap. Blue dots are our estimated gaps, while red and yellow dots represent the estimated gaps by the Federal Reserve and the CBO, respectively.

This figure is a scatter plot showing the relationship between two variables (Okun's Law):

The x-axis represents the unemployment rate gap, ranging from -2 to +8 percentage points. The y-axis represents the output gap, ranging from -25 to +5 percentage points.Three series are plotted with different markers:

All three series display a clear negative linear relationship, consistent with Okun's Law—when unemployment rises above its natural rate (positive unemployment gap), output falls below potential (negative output gap), and vice versa.

The blue dots (model estimates) form the densest scatter, spanning the full range of both axes. They show a tight negative relationship with slope approximately -1.7, meaning each 1 percentage point increase in the unemployment gap corresponds to roughly 1.7 percentage points decline in the output gap. The scatter extends from unemployment gaps of approximately -1 to +7 percentage points and output gaps from approximately -23% to +5%.

The red dots (Federal Reserve estimates) show a steeper relationship with slope approximately -1.68, clustering more tightly around the regression line. They span unemployment gaps from approximately 0 to +6 percentage points and output gaps from approximately -15% to +3%. The FED estimates show less extreme values than the model during the COVID recession.

The yellow dots (CBO estimates) display the shallowest slope at approximately -1.0, with scatter from unemployment gaps of approximately -0.5 to +6 percentage points and output gaps from approximately -8% to +3%. CBO estimates show the least extreme values and tightest clustering.

The model-based Okun coefficient of -1.7 aligns closely with the Federal Reserve's estimate and the model's predicted unconditional relationship. All three measures confirm the robust negative relationship between unemployment and output gaps, with differences primarily in magnitudes during extreme episodes rather than the fundamental relationship structure.

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Figure A.5: Double decomposition SLMI

This figure contains eight stacked area charts showing joint shock-data decompositions from 1990 to 2025:

Each subplot shows how a specific structural shock affects the SLMI through different observable variables. Within each panel, different colored areas represent contributions from:

Subplot descriptions:

(Top Left) Risk Premium (RP) Shock: Y-axis ranges from -15 to +5. Risk premium shocks show their largest negative contributions during financial crises, reaching approximately -12 to -15 during 2008-2009 and approximately -8 during 2020. The unemployment rate, LFPR, and GDP are the primary transmission channels. During the 2008-2009 crisis, these three variables account for most of the negative contribution. Credit spreads also play a meaningful role. The decomposition shows risk premium shocks work primarily through labor market quantities and aggregate demand channels. Recent years show modest negative contributions around -2 to -3.

(Top Right) Government Spending Shock: Y-axis ranges from -6 to +6. Government spending shocks show both positive and negative contributions throughout the sample, with magnitudes typically in the ±2 to ±4 range. Notable negative contribution of approximately -4 in early 1990s and positive contribution of approximately +3 to +5 in early 2000s. Transmission occurs through multiple channels including GDP, consumption, and investment, with no single dominant variable. The effects are more balanced across variables than other shocks. Recent years show small negative contributions around -1.

(Middle Left) Investment Efficiency Shock: Y-axis ranges from -10 to +2. Investment efficiency shocks show substantial negative contributions during the 2001 recession (approximately -4) and especially during the 2008-2015 period, reaching approximately -8 to -10. The primary transmission occurs through investment (I) itself, with supporting contributions from GDP, LFPR, and unemployment. These shocks capture supply-side disturbances affecting capital formation. Recent years show negative contributions around -3 to -4, suggesting persistent investment headwinds. The 2020 episode shows more modest impact (approximately -3) than the financial crisis.

(Middle Right) Monetary Policy Shock: Y-axis ranges from -8 to +6. Monetary policy shocks show meaningful contributions in the pre-2013 period, with magnitudes reaching ±4 to ±6, particularly in the early 1990s, early 2000s, and during the financial crisis. Transmission occurs primarily through the federal funds rate (FFR) itself, with secondary effects through GDP, investment, and unemployment. Notably, contributions become negligible after 2013 when time-varying Taylor rule coefficients are introduced, consistent with these coefficients better capturing systematic policy changes. Recent years show virtually zero contribution from monetary policy shocks.

(Bottom Left) Productivity Shock: Y-axis ranges from -10 to +8. Productivity shocks display both positive and negative contributions throughout the sample. Largest negative contribution of approximately -6 to -8 in early 1990s. Positive contributions of approximately +4 to +6 in mid-to-late 1990s. Modest contributions during the 2000s and financial crisis. The 2020-2022 period shows negative contributions around -4 to -6. Transmission occurs primarily through GDP, with contributions from LFPR, unemployment, and real wages. These shocks capture technology-driven labor market adjustments. Recent years show negative contributions around -2 to -3.

(Top Panel, Second Row) Price Markup Shock: Y-axis ranges from -2 to +8. Price markup shocks show predominantly positive contributions (tightness signals) in multiple episodes. Notable positive contributions of approximately +4 to +6 in the late 1990s, +2 to +4 in mid-2000s, and substantially large positive values of approximately +6 to +8 during 2021-2023 (post-COVID inflation period). Transmission occurs primarily through inflation measures (PCE and CPI), with these shocks capturing pricing power and markup variations. The large 2021-2023 contribution reflects markup-driven inflation pressures interpreted by the model as labor market tightness. Recent years show contributions declining toward zero as inflation normalized.

(Middle Panel, Second Row) Wage Markup Shock: Y-axis ranges from -0.25 to +0.1. Wage markup shocks show very small magnitude contributions throughout the entire sample period, typically in the range of ±0.05 to ±0.1. Slightly negative contributions in some periods (early 2000s, 2008-2009) and slightly positive in others (mid-2010s). Transmission occurs through wage variables (RCPRHW) and has minimal impact on the overall SLMI. The limited contribution suggests wage markups play a minor role in labor market slack dynamics relative to other shocks. Recent years show near-zero contributions.

(Bottom Panel, Second Row) Labor Supply LFPR Shock: Y-axis ranges from -0.6 to +0.8. Labor supply shocks affecting participation show modest contributions throughout the sample, typically ±0.2 to ±0.5. Positive contributions (suggesting slack from low participation) of approximately +0.4 to +0.6 during the 2009-2015 recovery period. Negative contributions in some earlier periods. Transmission occurs primarily through LFPR itself. These shocks capture exogenous shifts in labor force attachment preferences. The positive contributions during the 2010s recovery reflect persistent participation shortfalls interpreted as supply-side slack. Recent years show small positive contributions around +0.2.

(Bottom Right) Labor Supply Hours Shock: Y-axis ranges from -8 to +4. Labor supply shocks affecting the intensive margin (hours) show substantial variation. Large negative contributions of approximately -6 during the 2020 recession, capturing the extreme hours reduction. Positive contributions of approximately +2 to +3 in the mid-2000s. Transmission occurs through the hours/workweek variables. These shocks capture preferences for working longer or shorter hours independent of employment status. Recent years show contributions near zero to slightly negative.

General Note: Each subplot's colored areas sum to the contribution of that specific shock to the total SLMI. The double decomposition methodology simultaneously attributes SLMI variation to specific shocks and specific observables, revealing both the economic forces driving slack and their empirical manifestation in the data. This analysis follows Chung et al. (2021).

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