## 3.1 Unemployment Persistence

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### Introduction and motivation
- Conventional assumption: demand shocks have temporary effects on unemployment (natural rate hypothesis; Friedman (1968)).
- Empirical motivation: unemployment rates proved very persistent in many advanced economies (references: Ball (2009); Cerra and Saxena (2008, 2017); Blanchard and Summers (1987); Layard and Nickell (1987); Blanchard (2018)).
- Motivating quote: “Any reasonable reader of the data has to recognize that this financial crisis has confirmed the doctrine of hysteresis more strongly than anyone could have anticipated.” — Larry Summers, April 2, 2014.

### Research questions and contribution
- Primary question: How relevant is unemployment hysteresis?
- Contribution:
  - Tests and argues unemployment dynamics can be approximated by unit root processes in most of the 23 advanced economies in the sample since the 1990s.
  - Identifies aggregate demand shocks to unemployment through a modified insider/outsider model that does not restrict demand disturbances to have zero long-run effects on unemployment.
  - Estimates impacts allowing for cross-country heterogeneous dynamics in a panel structural vector autoregressive (PSVAR) model.
  - Exploits heterogeneity to investigate which institutional settings soften or amplify the effects of demand shocks.
- Main empirical finding: Strong evidence of unemployment hysteresis, challenging the natural rate hypothesis.

### Theoretical setup and identification logic
- Model building blocks (selected equations as in the source):
  - Aggregate demand: y_t = φ(d_t − p_t) + a θ_t  (equation (1))
  - Aggregate supply: y_t = n_t + θ_t  (equation (2))
  - Prices and wages: p_t = w_t − θ_t  (equation (3))
  - Wage-setting (expected employment): w_t = arg w_t : n_t^e = λ l_{t−1} + (1 − λ) n_{t−1} − z_t^w + s_t^w  (equation (4))
  - Institutional factors enter via z_t^w = Σ_{Z}^{N} ξ_Z Z_t and s_t^w = Σ_{S}^{M} ψ_S S_t  (equations (5)–(6))
  - Labor supply (participation): l_t = α(w_t − p_t^e) − b u_{t−1} + z_t^l − s_t^l + τ_t  (equation (7))
  - Disturbances follow random walks: Δθ_t = ε_t^s; Δd_t = ε_t^d; Δτ_t = ε_t^l  (equation (8))
- Reduced-form implication for unemployment (selected):
  - u_t = z_t^w − s_t^w + Δ z_t^l − Δ s_t^l + (1 − φ − α) ε_t^s + ε_t^l − φ ε_t^d + α ε_{t−1}^s all multiplied by factor (1 − (1 + b + λ) L − b L^2)^{-1}  (equation (11))
- Identification logic:
  - If unemployment is I(0): identify aggregate demand shocks under the assumption they do not have long-run effects on real output (consistent with natural rate).
  - If unemployment is I(1): allow aggregate demand shocks to have long-run effects on real output (consistent with hysteresis).
  - Therefore assessing unit-root properties of unemployment is critical for identification.

### Stylized implications from the theory
- Unemployment dynamics increase with:
  - discouragement effect b,
  - impact of past employment on wages λ,
  - wage push factor z_t^w.
- Unemployment dynamics decrease with wage pull factor s_t^w.
- Inclusion of wage push and pull factors allows full or partial hysteresis for a broader set of parameter values than earlier models.

### Empirical approach overview
- Two-stage empirical strategy:
  - Stage 1: Use model restrictions to identify demand shocks to unemployment, allowing nonzero long-run effects.
  - Stage 2: Estimate impact of identified shocks in a PSVAR allowing cross-country heterogeneous dynamics; relate heterogeneous responses to institutional proxies via cross-section regressions.

### Visual and time-series evidence (stylized facts)
- Sample: 23 advanced economies since the 1990s.
- Persistence summary:
  - Over a number of quarters ranging between 61 and 114 depending on data availability across countries, the lines denoting the unemployment rates cross the country-specific means less than four times on average.
  - Changes in unemployment rates appear stationary around their mean.
  - Autocorrelation analysis: the autocorrelation coefficient remains statistically different from zero for a minimum of one and a half years up to about two and a half years, indicating the random walk nature of the unemployment series.
  - Rolling panel AR(1) regression (with country- and time-fixed effects) shows the coefficient hovers around one for the sample; in the few periods where the coefficient is statistically different from one, the point estimate does not fall below 0.9.

### Unit-root and cointegration test evidence
- ADF unit root tests (levels and changes; intercept and intercept+trend):
  - For the great majority of the advanced economies, the null hypothesis of a unit root in unemployment rates cannot be rejected.
  - When including the trend, only Finland, Netherlands, and Sweden show results suggesting the unemployment rate is stationary.
  - For changes in unemployment rates, Greece, Ireland, and Latvia: the null hypothesis cannot be rejected at the 10 percent significance level.
  - Lag structure based on the Schwartz information criterion; ***, **, * denote significance at 1, 5, 10 percent.
- Panel unit-root tests (allowing heterogeneous parameters):
  - Im et al. (2003): Levels: -1.492*; Changes: -11.993***; Levels (Intercept and trend): -0.382; Changes (Intercept and trend): -9.896***.
  - Maddala and Wu (1999): Levels: 51.991; Changes: 242.325***; Levels (Intercept and trend): 49.622; Changes (Intercept and trend): 188.241***.
  - Panel tests confirm unemployment rates are not stationary, while changes in unemployment rates are stationary.
- Johansen cointegration framework (real wages, real output, unemployment with unrestricted linear trend):
  - Results confirm presence of a unit root for most advanced economies.
  - For Denmark, Estonia, the United Kingdom, Luxembourg, and the United States, the I(0) nature of the unemployment series cannot be rejected.
  - Authors note mismatches between ADF and Johansen outcomes for several countries.
- Panel cointegration (Pedroni tests; intercept and intercept+trend specifications):
  - Intercept specification: Group ρ-Statistic: -2.042**; Group PP-Statistic: -2.509***; other panel statistics mixed.
  - Intercept and trend specification: Panel v-Statistic: 5.739***; other statistics mixed.
  - Summary: majority of panel cointegration results suggest unemployment rates and wage inflation do not share a long-run relationship.

### Summary interpretation of the unit-root and cointegration evidence
- Panel unit-root evidence that unemployment rates are I(1) (levels nonstationary; changes stationary), combined with lack of robust long-run cointegration between unemployment and wage inflation, provides prima facie evidence consistent with unemployment hysteresis and raises skepticism about the natural rate hypothesis.

_Source: wp18169 — Authors’ calculations._

### 3.1    Unemployment Persistence    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### 3.1    Unemployment Persistence

### Introduction and motivation
- Conventional macroeconomic analysis assumes demand shocks have temporary effects on unemployment (natural rate hypothesis; Friedman (1968)).
- Empirical evidence shows unemployment rates proved very persistent in many advanced economies.
- Key observations and references:
  - Ball (2009): large increases in NAIRU associated with monetary tightenings.
  - Cerra and Saxena (2008) and Cerra and Saxena (2017): output losses after large shocks often closer to permanent than merely persistent.
  - Blanchard and Summers (1987): wage bargaining under strong unions can produce permanent effects of demand shocks (hysteresis).
  - Layard and Nickell (1987): longer unemployment duration → skill loss, hiring disinterest, discouragement → increased persistence.
  - Blanchard (2018): lower R&D spending during slowdowns can permanently lower total factor productivity.
- Motivating quote:
  - “Any reasonable reader of the data has to recognize that this financial crisis has confirmed the doctrine of hysteresis more strongly than anyone could have anticipated.” — Larry Summers, April 2, 2014.

### Research questions and contribution
- How relevant is unemployment hysteresis?
- This paper:
  - Tests and argues that unemployment dynamics can be approximated by unit root processes in most of the 23 advanced economies in the sample since the 1990s.
  - Identifies aggregate demand shocks to unemployment through a modified insider/outsider model (Balmaseda et al., 2000; Amisano and Serati, 2003) that does not restrict demand disturbances to have zero long-run effects on unemployment.
  - Estimates the impact of these shocks allowing for cross-country heterogeneous dynamics in a panel structural vector autoregressive (PSVAR) model.
  - In a second stage, exploits heterogeneity to investigate which institutional settings soften or amplify the effects of demand shocks.
- Main empirical finding summarized:
  - Strong evidence of unemployment hysteresis, raising skepticism about the natural rate hypothesis.

### Stylized empirical and policy-relevant implications from the introduction
- Institutional interactions matter for persistence:
  - Factors that provide suggestive evidence of amplifying demand-shock effects:
    - generosity of unemployment benefits,
    - labor taxation,
    - union density,
    - more coordinated wage-setting bargaining.
  - Factors that provide suggestive evidence of curbing demand-shock effects:
    - diffusion of part-time employment,
    - length of maternity leave,
    - higher statutory retirement age,
    - more generous pension systems,
    - more migrant-friendly policies,
    - higher spending on active labor market programs (ALMP).
- Literature on institutions:
  - Ljungqvist and Sargent (1995): unemployment duration longer when benefits are generous and labor taxes increase.
  - Mortensen and Pissarides (1999): unemployment benefits and employment protection lengthen duration under demand shocks.
  - Blanchard and Wolfers (2000): interactions of common shocks and institutions crucial to explain heterogeneity in unemployment dynamics across Europe.
  - Nunziata et al. (2002) and Nickell et al. (2005): do not find robust evidence for interactions between shocks and institutions (empirical evidence mixed).

### Theoretical setup and identification logic
- Model building blocks (drawing from Blanchard and Summers (1987), Balmaseda et al. (2000), Amisano and Serati (2003)):
  - Aggregate demand equation:
    - y_t = φ(d_t − p_t) + a θ_t  (equation (1))
  - Aggregate supply (output as labor plus productivity):
    - y_t = n_t + θ_t  (equation (2))
  - Prices tied to wages and productivity:
    - p_t = w_t − θ_t  (equation (3))
  - Wage-setting: wages set to obtain expected employment n_t^e, a function of past participation l_{t−1}, past employment n_{t−1}, wage-push z_t^w, and wage-pull s_t^w:
    - w_t = arg w_t : n_t^e = λ l_{t−1} + (1 − λ) n_{t−1} − z_t^w + s_t^w  (equation (4))
  - Institutional factors enter via:
    - z_t^w = Σ_{Z}^{N} ξ_Z Z_t  (equation (5))
    - s_t^w = Σ_{S}^{M} ψ_S S_t  (equation (6))
    - Z_t and S_t are vectors of N and M variables proxying institutional settings.
  - Labor supply (participation) depends on expected real wages, past unemployment, wage push/pull factors, and a stochastic disturbance:
    - l_t = α(w_t − p_t^e) − b u_{t−1} + z_t^l − s_t^l + τ_t  (equation (7))
  - Disturbances follow random walk processes:
    - Δθ_t = ε_t^s
    - Δd_t = ε_t^d
    - Δτ_t = ε_t^l  (equation (8))
    - ε_t^s, ε_t^d, ε_t^l interpreted as productivity, aggregate demand, and labor supply shocks, respectively.
- Solved reduced-form implications (selected equations):
  - Δ(w_t − p_t) = ε_t^s  (equation (9))
  - Δy_t = [φ ε_t^d + (φ + α) ε_t^s − z_t^w + s_t^w] + λ [z_{t−1}^w − s_{t−1}^w + Δ z_{t−1}^l − Δ s_{t−1}^l] * (1 − (1 + b + λ) L − b L^2)^{-1} ... (equation (10))
  - u_t = z_t^w − s_t^w + Δ z_t^l − Δ s_t^l + (1 − φ − α) ε_t^s + ε_t^l − φ ε_t^d + α ε_{t−1}^s all multiplied by factor (1 − (1 + b + λ) L − b L^2)^{-1}  (equation (11))
- Interpretation of the model implications:
  - Equation (11) implies unemployment dynamics increase with the discouragement effect b, the impact of past employment on wages (via λ), and the wage push factor z_t^w; and decrease with the wage pull factor s_t^w.
  - Inclusion of wage push and pull factors allows full or partial hysteresis for a broader set of parameter values than in earlier models: full hysteresis is not limited to λ = 0 for any given b.
  - Aggregate demand vs. supply shock identification depends on the order of integration of unemployment:
    - If unemployment is I(0): assume aggregate demand shocks do not have long-run effects on real output (consistent with natural rate hypothesis).
    - If unemployment is I(1): aggregate demand shocks have long-run effects on real output; labor supply shocks assumed to have no long-run effect on real output.
  - Therefore, assessing persistence/unit-root properties of unemployment rates is critical for choosing an identification strategy.

### Empirical approach overview (as stated)
- Two-stage empirical strategy:
  - Stage 1: Use the restrictions implied by the theoretical model to identify demand shocks to unemployment, allowing demand disturbances to have nonzero long-run effects.
  - Stage 2: Estimate the impact of identified shocks in a PSVAR framework allowing cross-country heterogeneous dynamics; exploit heterogeneity to investigate which institutional settings soften or amplify demand-shock effects.

### Summary of stylized-fact assessment (preview)
- Authors indicate they will:
  - Test for unit roots and find unemployment dynamics approximated by unit root processes in most of the 23 advanced economies since the 1990s.
  - Use this finding to guide shock identification consistent with possible hysteresis.
  - Present Section 3 as a list of stylized facts suggesting unemployment rates in advanced economies tend to be very persistent.

*Source: wp18169 - 3.1 Unemployment Persistence (PDF chapter)*

### 3.1    Unemployment Persistence

### 3.1    Unemployment Persistence

### Visual and time-series evidence
- Visual inspection of unemployment rates in 23 advanced economies since the 1990s reveals a great deal of persistence.
- Over a number of quarters ranging between 61 and 114 depending on data availability across countries, the lines denoting the unemployment rates cross the lines representing the country-specific means less than four times on average.
- Changes in unemployment rates appear stationary around their mean.
- Autocorrelation analysis: the autocorrelation coefficient remains statistically different from zero for a minimum of one and a half years up to about two and a half years, indicating the random walk nature of the unemployment series.
- Rolling panel AR(1) regression of unemployment on its lag (with country- and time-fixed effects) shows the coefficient hovers around one for the length of the sample; in the few periods for which the coefficient is statistically different from one, the point estimate does not fall below 0.9, confirming that the average country displays a unit root process for the unemployment rate.

### ADF unit root test results (summary)
- Augmented Dickey-Fuller (ADF) tests were performed including (i) intercept and (ii) intercept and trend, for both levels of unemployment rates and changes.
- For the great majority of the advanced economies in the sample, the null hypothesis of a unit root in unemployment rates cannot be rejected.
- When including the trend, only Finland, Netherlands, and Sweden show results suggesting the unemployment rate is stationary.
- For the changes in unemployment rates, Greece, Ireland, and Latvia: the null hypothesis cannot be rejected at the 10 percent significance level, indicating some persistence even in the changes for those countries.
- Notes on implementation: the lag structure is based on the Schwartz information criterion; ***, **, and * indicate statistical significance at 1, 5, and 10 percent, respectively.

### Johansen cointegration test results (summary)
- A Johansen (1991) cointegration framework was specified with a VAR in levels including real wages, real output, and unemployment plus an unrestricted linear trend.
- If unemployment is I(0) while the other variables are I(1) and there is no cointegration, the unemployment series is permanent-I(0) in this formulation; alternative cointegrating vector forms imply unemployment is I(1).
- Results in Table 2 confirm the presence of a unit root for most advanced economies.
- For Denmark, Estonia, the United Kingdom, Luxembourg, and the United States, however, the I(0) nature of the unemployment series cannot be rejected.
- The authors note there is no match between the ADF and Johansen test outcomes for several countries.

### Panel unit root tests and reconciliation
- To address heterogeneity in persistence across countries, panel unit root tests that allow for heterogeneous parameters were employed: Im et al. (2003) and Maddala and Wu (1999).
- Panel test results confirm that unemployment rates are not stationary, while changes in unemployment rates are stationary.
- Based on this evidence, the authors conclude that some shocks seem to trigger permanent effects in unemployment rates.

_ Source: Authors' calculations._

### 3.2    Unemployment and Wage Inflation

### 3.2 Unemployment and Wage Inflation

### Unit root evidence for unemployment rates
- Panel unit root tests (Table 3):
  - Im et al. (2003): Levels: -1.492*; Changes: -11.993***; Levels (Intercept and trend): -0.382; Changes (Intercept and trend): -9.896***.
  - Maddala and Wu (1999): Levels: 51.991; Changes: 242.325***; Levels (Intercept and trend): 49.622; Changes (Intercept and trend): 188.241***.
- Notes: Lag structure based on the Schwartz information criterion. ***, **, and * indicate statistical significance at 1, 5, and 10 percent, respectively.

### Phillips-curve relationships (reduced-form evidence)
- Country-specific reduced-form wage Phillips curve estimated as equation (12): πw_t = α + β ̄πp_{t-4,t-1} + γ u_t + ε_t, where πw_t is year-on-year wage inflation, ̄πp_{t-4,t-1} is average year-on-year price inflation over last four quarters, and u_t is the unemployment rate.
- Cross-country findings from reduced-form estimations (Table 4):
  - A significant negative relationship between unemployment rate and wage inflation is found for most countries, but:
    - Austria, Czech Republic, France, the United Kingdom, Slovak Republic, and Sweden show either negative and not significant or positive coefficients on the unemployment rate.
  - When negative and significant, the slope of the Phillips curve ranges from -2.5 to -0.2.
  - A panel estimation returns a coefficient of 0.4.
- Individual coefficient examples from Table 4 (selected):
  - Past price inflation coefficients vary across countries (examples): 0.629*** (AUT), 0.527*** (DEU), 0.691** (FIN), -1.264*** (GRC).
  - Unemployment rate coefficients vary across countries (examples): -0.488*** (DEU), -0.532*** (DNK), -1.217*** (FIN), -2.526*** (LVA), 0.414** (SVK).
- Observations and R-squared vary by country (Table 4), aggregated panel: Observations 1,865; Countries 23.

### Cointegration analysis: long-run relationship between unemployment and wage inflation
- Country-level Engle-Granger and Johansen test results (Table 5):
  - Countries with evidence of cointegration (Johansen number of coint. vectors = 1): DEU, FIN, HUN, ITA, LUX, PRT.
  - Engle-Granger statistics (selected): AUT -3.987** (Obs 82); DEU -4.618*** (Obs 98); PRT -4.649*** (Obs 82).
  - Notes: Tests include four lags. Johansen model includes an unrestricted constant. ***, **, and * indicate statistical significance at 1, 5, and 10 percent, respectively.
- Panel cointegration tests (Pedroni 1999 and 2004) (Table 6) — versions not weighted by member-specific long-run conditional variances:
  - Intercept specification:
    - Panel v-Statistic: 0.157
    - Panel ρ-Statistic: -1.073
    - Panel PP-Statistic: -1.040
    - Panel ADF-Statistic: 1.145
    - Group ρ-Statistic: -2.042**
    - Group PP-Statistic: -2.509***
    - Group ADF-Statistic: -0.941
  - Intercept and trend specification:
    - Panel v-Statistic: 5.739***
    - Panel ρ-Statistic: 0.481
    - Panel PP-Statistic: 0.132
    - Panel ADF-Statistic: 2.012
    - Group ρ-Statistic: 1.529
    - Group PP-Statistic: 1.447
    - Group ADF-Statistic: 2.640
  - Notes: Lag structure based on the Schwartz information criterion. ***, **, and * indicate statistical significance at 1, 5, and 10 percent, respectively.
- Summary interpretation:
  - The great majority of panel cointegration test results suggest that unemployment rates and wage inflation do not share a long-run relationship.
  - Combined with unit root evidence for unemployment rates, this constitutes prima facie evidence supporting the hysteresis hypothesis and raising skepticism about the natural rate hypothesis.

### Heterogeneous PSVAR identification and empirical strategy
- First-stage: heterogeneous PSVAR (Pedroni 2013) to allow country-specific dynamics and recover unconditional structural responses R_i(L) to shocks (productivity, aggregate demand, labor supply).
- Long-run identification (equation (15)):
  - Δz_{i,t} = R_i(1) ε_{i,t} with structure imposing that:
    - Aggregate demand shocks can have permanent effects on real output and unemployment (consistent with I(1) unemployment).
    - Real wages are determined only by productivity shocks in the long run.
    - Labor supply shocks have no permanent effects on output.
- Second-stage: cross-section regressions (equation (16)) of unemployment responses Y_{i,h} on institutional proxies X_i (union density, coordination of wage setting, labor taxation, unemployment benefits, public spending on ALMP, migration policy friendliness, part-time employment, length of maternity leave, statutory retirement age, pension generosity). Horizon-fixed effects included.

### PSVAR results: heterogeneous impulse responses and variance decomposition
- Real wages:
  - Productivity shocks increase real wages in short and long run; dispersion sizable (75th percentile effect about 2.5 times 25th percentile).
  - Aggregate demand shocks: average response of real wages is counter-cyclical; median effect about one third of average; 25th percentile shows positive effect for a quarter of countries.
  - Labor supply shocks: tend to have a positive effect on real wages, but effect is dispersed with a quarter of sample showing a negative effect.
- Real output:
  - Short-run effect positive for all shocks.
  - Labor supply shock effects converge to zero over long run (consistent with restrictions).
  - Productivity and aggregate demand shocks have persistent effects; productivity shock shows larger cross-country variation.
- Unemployment responses (focus on aggregate demand shocks):
  - Median responses show persistence for all shocks.
  - For productivity shocks: dispersed; over one quarter of countries display a zero effect.
  - For an aggregate demand shock:
    - Large, negative, and persistent median effect — evidence of strong hysteretic effects.
    - A one standard deviation increase in aggregate demand is associated with a fall in the unemployment rate by about 0.6 percentage points after two years for the median country.
    - Cross-country dispersion: half of the countries exhibit a response ranging between about 0.4 and 1 percentage points.
  - Statistical significance:
    - Median responses are statistically significant; bootstrapped 95 percent confidence intervals confirm significance (Figure 7 referenced).
- Forecast error variance decomposition (FEVD) for unemployment variability (Figure 8):
  - Short run (on average): 70 percent of variability in unemployment rates due to labor supply shocks; 20 percent due to aggregate demand shocks; 10 percent due to productivity shocks.
  - Over time: proportion explained by aggregate demand shocks increases and reaches about 40 percent one year and a half after the shock, mostly offset by a fall in variation associated with labor supply shocks.
  - Cross-country distribution: median and interquartile range for contribution of aggregate demand shocks indicate little difference between mean and median; for half of sample aggregate demand shocks can explain between 30 and 50 percent of total variability in unemployment rates in the long run.
  - Bootstrapped 95 percent confidence interval for the median contribution of aggregate demand shocks confirms it is statistically different from zero.

### Implications and interpretation (from the analysis)
- Empirical regularities consistent with hysteresis:
  - Unemployment rates exhibit unit root behavior in panel tests.
  - Lack of robust long-run cointegration between unemployment rates and wage inflation in most countries.
  - Persistent, heterogeneous unemployment responses to aggregate demand shocks and a sizable long-run share of unemployment variability attributable to aggregate demand shocks imply that demand shocks can leave long-lasting scars on unemployment (hysteresis).
- Heterogeneity matters:
  - Country-specific institutional settings (wage bargaining, labor taxation, unemployment benefits, ALMP, and other labor market institutions) are posited as determinants of the cross-country dispersion in unemployment persistence; the two-stage strategy is designed to identify which institutional features are associated with larger unemployment responses to aggregate demand shocks.

*Source: Authors’ calculations from "3.2 Unemployment and Wage Inflation", wp18169.*

### 5.2    The Role of Labor Market Institutions

### 5.2    The Role of Labor Market Institutions

### Methodology
- Dependent variable: IRF coefficients (responses of unemployment rate to an aggregate demand shock).
- Estimation approach:
  - Pool all IRF coefficients and run panel regressions.
  - Ordinary least squares (OLS) with autocorrelation and heteroskedasticity consistent (HAC) standard errors.
  - Weighted least squares (WLS) with weights equal to the inverse of the IRFs’ squared standard error.
- Specifications include horizon-fixed effects.
- Sample note: second-stage sample excludes Estonia, Hungary, Latvia, Poland, and Slovenia due to missing explanatory-variable data.

### Main empirical findings (Table 7)
- Estimated signs generally in expected directions. Variables that amplify the effects of aggregate demand shocks on unemployment:
  - Tax wedge: OLS coefficient -0.004 (0.000); WLS coefficient -0.010 (0.002)
  - Unemployment replacement ratio: OLS coefficient -0.028 (0.002); WLS coefficient -0.006 (0.002)
  - Restrictiveness of migrant integration policies: OLS coefficient -0.033 (0.002); WLS coefficient -0.009 (0.003)
  - Union density: OLS coefficient -0.003 (0.000); WLS coefficient -0.005 (0.001)
  - Coordination of wage setting: OLS coefficient -0.159 (0.0006); WLS coefficient -0.083 (0.015)
- Variables that curb the effects of aggregate demand shocks on unemployment:
  - Public spending on ALMP: OLS coefficient 0.007 (0.002); WLS coefficient 0.004 (0.001)
  - Share of part-time employment: OLS coefficient 0.025 (0.003); WLS coefficient 0.017 (0.003)
  - Job-protected maternity leave: OLS coefficient 0.003 (0.000); WLS coefficient 0.002 (0.000)
  - Statutory retirement age: OLS coefficient 0.136 (0.007); WLS coefficient 0.033 (0.012)
  - Public spending on old-age pensions: OLS coefficient 0.180 (0.010); WLS coefficient 0.179 (0.014)
- Sample and fit (Table 7):
  - Observations: 432
  - R-squared: 0.754 (OLS); 0.715 (WLS)
- Notes on interpretation:
  - A negative IRF coefficient describes a fall in unemployment in response to an aggregate demand shock.
  - **Counter-intuitive result:** coordination of wage setting appears to amplify the effect of shocks (possible inefficiencies associated with coordinated wage setting).

### Robustness checks and horizon-specific results (Section 5.3 and Table 8)
- Alternative identification:
  - For countries where unit-root in unemployment is rejected, VARs imposing no long-run effects of aggregate demand shocks produce average and median dynamics similar to baseline.
  - Under identification imposing zero long-run effect for all countries, median IRFs take four years to die out.
- Second-stage regressions at specific horizons (Table 8): coefficients are imprecisely estimated due to reduced observations, but signs broadly consistent with Table 7. Selected coefficients across horizons (h = 0, 4, 8, 12, 16, 20, 23) with HAC standard errors in parentheses:
  - Tax wedge:
    - h“0: -0.001 (0.007)
    - h“4: -0.004 (0.011)
    - h“8: -0.008 (0.013)
    - h“12: -0.006 (0.014)
    - h“16: -0.003 (0.015)
    - h“20: -0.003 (0.015)
    - h“23: -0.004 (0.015)
  - Unemployment replacement ratio:
    - h“0: -0.007 (0.004)
    - h“4: -0.017 (0.005)
    - h“8: -0.025 (0.008)
    - h“12: -0.032 (0.010)
    - h“16: -0.035 (0.012)
    - h“20: -0.037 (0.013)
    - h“23: -0.038 (0.014)
  - Public spending on ALMP:
    - h“0: 0.003 (0.004)
    - h“4: -0.001 (0.006)
    - h“8: 0.006 (0.007)
    - h“12: 0.006 (0.009)
    - h“16: 0.015 (0.011)
    - h“20: 0.017 (0.012)
    - h“23: 0.015 (0.012)
  - Restrictiveness of migrant integration policies:
    - h“0: -0.005 (0.006)
    - h“4: -0.025 (0.008)
    - h“8: -0.038 (0.018)
    - h“12: -0.039 (0.022)
    - h“16: -0.038 (0.025)
    - h“20: -0.039 (0.028)
    - h“23: -0.040 (0.029)
  - Share of part-time employment:
    - h“0: 0.003 (0.005)
    - h“4: 0.025 (0.011)
    - h“8: 0.047 (0.014)
    - h“12: 0.034 (0.016)
    - h“16: 0.019 (0.017)
    - h“20: 0.017 (0.015)
    - h“23: 0.020 (0.014)
  - Job-protected maternity leave:
    - h“0: 0.002 (0.001)
    - h“4: 0.003 (0.001)
    - h“8: 0.004 (0.002)
    - h“12: 0.004 (0.002)
    - h“16: 0.003 (0.002)
    - h“20: 0.003 (0.002)
    - h“23: 0.004 (0.002)
  - Statutory retirement age:
    - h“0: 0.044 (0.021)
    - h“4: 0.109 (0.045)
    - h“8: 0.150 (0.060)
    - h“12: 0.166 (0.067)
    - h“16: 0.155 (0.070)
    - h“20: 0.146 (0.070)
    - h“23: 0.142 (0.070)
  - Public spending on old-age pensions:
    - h“0: 0.061 (0.032)
    - h“4: 0.162 (0.069)
    - h“8: 0.241 (0.091)
    - h“12: 0.222 (0.095)
    - h“16: 0.184 (0.096)
    - h“20: 0.168 (0.094)
    - h“23: 0.167 (0.093)
- Table 8 sample and fit:
  - Observations: 18 (for each horizon column)
  - R-squared by horizon: 0.700, 0.826, 0.843, 0.802, 0.746, 0.739, 0.748 (for h“0, h“4, h“8, h“12, h“16, h“20, h“23 respectively)
- Robustness summary:
  - Despite reduced observations for horizon-specific second-stage regressions, coefficient signs are the same as in Table 7 and magnitudes broadly consistent.
  - Some coefficients remain statistically significant at specific horizons: unemployment benefits, restrictiveness of migration policies, share of part-time employment, job-protected maternity leave, statutory retirement age, and public spending on old-age pensions.

### Policy implications and conclusions (Section 6 summary)
- Evidence of unemployment hysteresis: demand shocks show persistent effects on unemployment.
- Institutional determinants:
  - Disincentives for firms to hire and workers to be employed (e.g., labor taxation, unemployment benefits) and impediments to wage adjustment (e.g., union density) tend to amplify the effects of demand shocks.
  - Programs that improve matching (public spending on ALMP) and incentives for particular worker groups (diffusion of part-time employment, length of maternity leave, higher statutory retirement age, more generous pension systems, more migrant-friendly policies) tend to curb the effects of demand shocks.
- Policy message:
  - Strengthening labor market institutions can lead to less severe effects of demand shocks on unemployment and a faster reversion to pre-crisis unemployment levels.

*Source: Authors’ calculations (from IMF working paper content unit "5.2    The Role of Labor Market Institutions").*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18169.pdf_