## _wp1693 - Appendix A

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---

### Cointegration tests and structural breaks
- Cointegration between unemployment and vacancies is sensitive to structural breaks; the Gregory and Hansen (1996) procedure was used to detect cointegration under breaks and to identify break dates.
- When accounting for a break (intercept level shift or intercept and slope regime shift), unemployment and vacancies are cointegrated for: Australia, Finland, Germany, Hungary, Norway, Portugal, Sweden, the United Kingdom, and the United States; and for Austria, Finland, and Poland when considering the Z statistic.
- Countries for which no cointegration was found: the Czech Republic and Norway.
- Breaks tend to cluster around the global financial crisis.
- Selected break statistics and dates (level shift / regime shift; ADF and Z statistics; estimated break dates):
  - Australia: ADF stat -6.97*, estimated break date 2008Q3; Z stat -55.906*, estimated break date 2008Q4. Regime shift ADF -6.75*, 2008Q3; Z -55.613*, 2008Q4.
  - Austria: ADF -3.80, 2004Q4; Z -38.54*, 2004Q3. Regime shift ADF -3.88, 2006Q4; Z -38.45, 2004Q2.
  - Czech Republic: level ADF -3.73, 2010Q3; Z -17.89, 2007Q3. Regime ADF -3.59, 2010Q1; Z -15.56, 2009Q1.
  - Finland: level ADF -3.93, 2010Q2; Z -92.57*, 2004Q3. Regime ADF -4.05, 2010Q4; Z -94.20*, 2004Q3.
  - Germany: level ADF -4.86*, 2009Q1; Z -11.06, 2008Q1. Regime ADF -5.36*, 2001Q4; Z -18.27, 2005Q2.
  - Hungary: level ADF -4.13, 2011A1; Z -35.43, 2010Q3. Regime ADF -3.47, 2011Q1; Z -42.34*, 2011Q1.
  - Norway: level ADF -4.17, 2007Q3; Z -32.14, 2008Q2. Regime ADF -3.57, 2007Q4; Z -36.95, 2005Q2.
  - Poland: level ADF -3.68, 2004Q1; Z -37.65*, 2003Q3. Regime ADF -3.75, 2004Q1; Z -37.29, 2003Q3.
  - Portugal: level ADF -5.59*, 2007Q3; Z -22.41, 2006Q3. Regime ADF -5.32*, 2007Q3; Z -23.84, 2010Q4.
  - Sweden: level ADF -4.92*, 2008Q1; Z -39.93*, 2006Q1. Regime ADF -4.66, 2008Q1; Z -39.78, 2005Q3.
  - United Kingdom: level ADF -5.98*, 2005Q3; Z -26.77, 2001Q3. Regime ADF -5.85*, 2002Q3; Z -31.43, 2001Q3.
  - United States: level ADF -5.04*, 2008Q3; Z -36.46*, 2008Q3. Regime ADF -5.18*, 2008Q3; Z -39.21, 2006Q3.
- Note: critical values for 1% confidence: ADF (constant, no trend) -3.55; PP -3.55; ADF (constant and trend) -4.137; PP -4.133.

### Non-linear estimation and identified shifts in the Beveridge curve
- Non-linear (hyperbolic) estimation was applied to Beveridge curves incorporating shift dummies based on visual and cointegration-identified break dates; the coefficient associated with the shift is significant for all countries examined.
- Direction and timing of identified breaks (from Table 5):
  - Australia: break date 2008Q3 — Outward
  - Austria: 2004Q3 — Outward
  - Czech Republic: 2008Q2 — Inward
  - Finland: No break — No break
  - Germany: 2009Q1 — Inward
  - Hungary: 2011Q1 — Outward
  - Norway: No break — No break
  - Poland: 2002Q3 and 2008Q4 — Outward then Inward
  - Portugal: 2007Q3 — Outward
  - Sweden: 2008Q1 — Outward
  - United Kingdom: 2005Q3 — Outward
  - United States: 2008Q3 — Outward
- Overall summary:
  - Ten shifts identified across twelve countries.
  - Most shifts are outward (deterioration in matching); inward for the Czech Republic and Germany.
  - Poland exhibits two breaks: an outward shift followed by an inward shift.
  - Except for Austria and the United Kingdom, deterioration occurred around the global financial crisis.

- Selected non-linear estimation coefficients (Table 4a: Vertical Shift; constants and shift coefficients):
  - Australia: Constant 6.112*** (0.0173); Shift 0.122*** (0.0272)
  - Austria: Constant 4.727*** (0.0222); Shift 0.246*** (0.0269)
  - Czech Republic: Constant 5.697*** (0.0262); Shift -0.127*** (0.0409)
  - Finland: Constant 5.143*** (0.0180); Shift -0.106*** (0.0218)
  - Germany: Constant 8.040*** (0.0216); Shift -0.245*** (0.0419)
  - Hungary: Constant 5.421*** (0.0270); Shift 0.460*** (0.0583)
  - Poland: Constant 7.239*** (0.0437); Shift 0.351*** (0.0697)
  - Portugal: Constant 5.338*** (0.0496); Shift 0.730*** (0.0728)
  - Sweden: Constant 5.330*** (0.0286); Shift 0.354*** (0.0420)
  - UK: Constant 7.140*** (0.0345); Shift 0.305*** (0.0461)
  - US: Constant 8.777*** (0.0207); Shift 0.522*** (0.0318)
- Selected non-linear estimation with slope (Table 4b: Vertical Shift with Slope Coefficient; constants, shift, slope):
  - Australia: Constant 3.931*** (0.191); Shift 0.249*** (0.0185); Slope 11.51*** (0.921)
  - Austria: Constant 3.754*** (0.198); Shift 0.286*** (0.0239); Slope 4.180*** (0.644)
  - Czech Republic: Constant 4.346*** (0.109); Shift -0.235*** (0.0226); Slope 6.500*** (0.441)
  - Finland: Constant 5.199*** (0.117); Shift -0.113*** (0.0262); Slope 0.833** (0.343)
  - Germany: Constant 6.095*** (0.297); Shift -0.208*** (0.0309); Slope 12.30*** (1.721)
  - Hungary: Constant 4.350*** (0.158); Shift 0.555*** (0.0451); Slope 4.785*** (0.553)
  - Poland: Constant 6.331*** (0.0946); Shift 0.373*** (0.0415); Slope 3.907*** (0.291)
  - Portugal: Constant 4.063*** (0.408); Shift 0.880*** (0.0827); Slope 4.019*** (0.961)
  - Sweden: Constant 5.450*** (0.196); Shift 0.342*** (0.0465); Slope 0.611 (0.625)
  - UK: Constant 3.685*** (0.545); Shift 0.299*** (0.0342); Slope 22.74*** (3.423)
  - US: Constant 6.042*** (0.690); Shift 0.477*** (0.0302); Slope 17.36*** (4.125)

### Determinants of shifts — main empirical findings
- Business cycle:
  - Output gap (contemporaneous and lagged) is generally not statistically significant — outward or inward shifts do not occur systematically at specific business cycle phases.
- Labor force and fiscal balance:
  - Labor force growth is highly significant and negative across almost all specifications; this helps explain why Beveridge curves have not shifted back after the crisis.
  - Overall fiscal balance is mostly significant with a negative sign.
  - Selected reported coefficients:
    - Labor force (growth) coefficient: -0.411*** (0.109)
    - Overall balance coefficient: -0.217*** (0.0396)
- Composition effects:
  - Higher share of young unemployed → associated with outward movements (worsening matching).
  - Higher share of old-age unemployed → associated with less outward movement (improvement).
  - Female unemployment shows evidence supportive of male-biased labor matching preference.
  - Long-term unemployment → makes matching more difficult.

### Fiscal and labor market policy effects (quantified results)
- Social security contributions and tax wedge increase the likelihood of outward shifts (Panel logit (RE), Shift size specification):
  - ESSC_100 2.485*** (0.354); ESSC_167 2.419*** (0.326); ESSC_67 2.304*** (0.372)
  - WSSC_100 1.940*** (0.289); WSSC_167 2.571*** (0.369); WSSC_67 1.949*** (0.290)
  - TW_100 0.241** (0.113); TW_167 0.813*** (0.149); TW_67 0.128* (0.0726)
- Unemployment benefits increase the likelihood of outward shifts:
  - Unempl benefits 0.0194*** (0.00357) — baseline panel probit.
  - Robustness: 0.00144*** (0.000285) when Shift size/mismatch used as dependent variables.
- Active labor market programs that reduce frictions (Panel logit (RE), Shift size):
  - Job creation: -0.141** (0.0620)
  - Rehabilitation: -0.257*** (0.0779)
  - Job sharing: -2.587** (1.074)
  - Start-up incentives: -0.255*** (0.0589)
  - Training: statistically insignificant in baseline.
  - Incentives: small/insignificant in some specifications.
- Robustness checks:
  - Employment protection, long-term unemployment, and education results are robust.
  - Social security contributions remain significant across estimations.
  - Tax wedge retains detrimental impact in many specifications (notably TW_167).
  - Active labor market policies are somewhat less robust but start-up incentives and job sharing/rehabilitation often retain significance.

### Shocks, institutions, and interactions during the global financial crisis
- Interactions with crisis time dummies (2008Q3 and 2008Q4) show:
  - At the trough of the crisis the level of education and the length of unemployment had a less strong impact on the likelihood of an outward shift (columns 1–4, Table 10).
  - The detrimental impact of unemployment benefits was stronger during the crisis:
    - 2008Q3*Unemployment benefits 0.0161* (0.009)
    - 2008Q4*Unemployment benefits 0.0142* (0.008)
  - For many other variables, the incidence of the financial crisis did not materially alter their impact on labor market dynamics.
- Attempts to identify complementarities (e.g., share of temporary contracts interacted with EPL variants) yielded statistically insignificant or inconclusive results.

### Principal conclusions and policy implications
- Factors associated with faster matching / lower frictional unemployment (negative impact on likelihood of outward shift):
  - Higher labor force growth.
  - Stronger employment protection legislation (EPL).
  - An older unemployed population.
  - Government spending in active labor market policies such as job sharing programs and start-up incentives.
- Factors associated with worse matching / higher likelihood of outward shift:
  - Larger share of long-term unemployed.
  - Female and young unemployed.
  - More employees with intermediate education in the labor force.
  - Higher social security contributions and tax wedge.
  - Higher unemployment benefits.
- Policy recommendations:
  - Prefer active labor market policies over passive ones.
  - Give preference to programs for job sharing and incentives for start-up activities to reduce frictional unemployment.
  - Reconsider unemployment benefits and labor taxation (social security contributions and tax wedge) given their association with worse matching.
  - Caveat on EPL: tighter protection is associated with lower frictional unemployment but may raise flows into and out of unemployment, possibly increase overall unemployment, lower average productivity, and raise entry barriers for young workers.
- Caveats:
  - Analysis is based on a limited number of shifts over 13 years; most shifts occurred around the global financial crisis.
  - No backward shifts observed yet for curves shifted outward during the crisis; the slower pace of labor market recovery relative to output recovery remains an open question.

### Key calibration, long-run estimates, and summary statistics
- Selected VAR lag/criteria (examples):
  - Australia: Selected 2, AIC -6.4161, LR 7.498*, FPE 5.61e-06*, SIC -6.027*, HQ -6.269*
  - United Kingdom: Selected 3, AIC -7.00*, LR 16.29*, FPE 3.12e-06*, SIC -6.43*, HQ -6.79*
  - United States: Selected 2, AIC -5.76*, LR 48.63*, FPE 1.07e-05*, SIC -5.36*, HQ -5.61*
- Selected cointegration long-run estimates (β, s.e., μC, s.e., 2R):
  - Australia: β -0.159, s.e. 0.108, μC 7.147***, s.e. 0.536, 2R 0.285
  - Czech Republic: β -0.303***, s.e. 0.0677, μC 7.103***, s.e. 0.271, 2R 0.643
  - Germany: β -0.488***, s.e. 0.145, μC 11.004***, s.e. 0.851, 2R 0.499
  - Poland: β -0.491***, s.e. 0.060, μC 9.326***, s.e. 0.207, 2R 0.822
  - United Kingdom: β -0.970***, s.e. 0.251, μC 13.600***, s.e. 1.591, 2R 0.538
  - United States: β -1.847***, s.e. 0.661, μC 20.146***, s.e. 3.924, 2R 0.398
- Selected summary statistics (means and ranges):
  - wages: Mean 89.92, Min 41.34, Max 123.83
  - EPL: Mean 2.24, Min 0.256, Max 4.58
  - Unemployment young: Mean 28.92, Min 14.72, Max 45.56
  - Female unemployment: Mean 46.62, Min 37.5, Max 59.615
  - Long term: Mean 8.09, Min 1.44, Max 14.491
  - Advanced education: Mean 23.33, Min 5.27, Max 61.86
  - Intermediate education: Mean 52.53, Min 11.99, Max 79.16
  - Basic education: Mean 19.78, Min 5.24, Max 74.30
  - Overall_balance: Mean -1.43, Min -18.18, Max 38.82
  - ESSC_100: Mean 21.02, Min 5.94, Max 41.81
  - WSSC_100: Mean 11.24, Min 0, Max 22.17
  - TW_100: Mean 40.59, Min 26.65, Max 55.8
  - Job-creation: Mean 0.0069, Min -0.0018, Max 0.0325
  - Start-up incentives: Mean 0.0025, Min -0.00045, Max 0.027
  - Unemployment benefits: Mean 0.193, Min 0.0336, Max 0.556

*Source: _wp1693 - Appendix A*

### References .............................................................................................................

### _wp1693 - References

### Tables (listed)
- 1. Unit Root Tests ........................................................................................................................................................... 17
- 2. Johansen-Juselius Cointegration Tests ............................................................................................................. 17
- 3. Testing for Regime Shifts in Cointegration: Gregory-Hansen .................................................................. 18
- 4a. Nonlinear Estimation: Vertical Shift .................................................................................................................. 19
- 4b. Nonlinear Estimation: Vertical Shift with Slope Coefficient .................................................................... 19
- 5. Identifying Shifts in the Beveridge Curve ......................................................................................................... 20
- 6. Labor Market Characteristics ................................................................................................................................. 22
- 7. Fiscal and Labor Market Policies .......................................................................................................................... 22
- 8. Robustness—Labor Market Characteristics ..................................................................................................... 24
- 9. Robustness—Fiscal and Labor Market Policies .............................................................................................. 25
- 10. The Role of Shocks and Labor Market Institutions in the Matching Process .................................. 27

### Figures (listed)
- 1. OECD Average Unemployment and Vacancies in the Great Recession .................................................. 4
- 2. Beveridge Curves (I) .................................................................................................................................................. 15
- 3. Beveridge Curves (II) ................................................................................................................................................. 16

### Appendices
- A ............................................................................................................................................................................................ 29
- B ............................................................................................................................................................................................ 30

### Notable excerpt (closing lines)
- "To understand the effects of policy on unemployment in Britain we would have to explain first, how policy has affected the willingness of firms to hire new workers and how it has affected the willingness of the unemployed to look for and accept new jobs."  
  Pissarides 1986

*Source: _wp1693 - References*

### INTRODUCTION

### INTRODUCTION

### Overview
- Post-global financial crisis unemployment increases have been attributed largely to cyclical factors, but mismatches between labor demand and labor supply have become more relevant compared with pre-crisis years.
- Positive recovery signals (e.g., increase in advertised vacancies starting in the last quarter of 2009) coexisted with high unemployment and marked increases in long-term unemployment.
- OECD data: the number of unemployed increased by almost 50 percent between 2007 and 2013; the number of long-term unemployed increased by more than 80 percent.
- Addressing labor mismatches is urgent given path dependency associated with long-term unemployment.

### Conceptual framework: Beveridge curve and movements vs. shifts
- The Beveridge curve relates vacancies to the number of unemployed; typically negative slope (as vacancies increase, unemployment declines).
- Movements along the curve: cyclical changes (recessions → lower vacancies and higher unemployment; recoveries → higher vacancies and lower unemployment).
- Shifts of the curve: structural changes in matching efficiency (inward shift = improvement; outward shift = deterioration).
- Examples:
  - Short-time working schemes can attenuate unemployment increases and may lead to inward shifts if vacancies fall at a given unemployment level.
  - Jobless recoveries can produce outward shifts (vacancies constant, unemployment rising).
- Factors influencing shifts include labor force characteristics, institutional settings, and types of mismatches (skills, geography, sectors).
- Long-term unemployment can shift the curve outward via skill deterioration or employer bias.

### Research goals and scope
- Assess the role of policies and institutions in shifting the Beveridge curve for a sample of 12 OECD countries over the 2000Q1–2013Q4 period.
- Two-step approach:
  1. Detect shifts in each country’s Beveridge curve and determine magnitude and direction using three methodologies: visual examination, cointegration techniques, and non-linear estimation.
  2. Use a panel probit model to assess factors (policies, institutions, labor-market characteristics) influencing the probability of shifts.

### Main empirical findings
- Shifts detected:
  - Out of the 12 OECD countries examined, 10 exhibit a shift of their respective Beveridge curve.
  - Seven countries show outward shifts (deteriorations of labor market matching), often at the onset of the global financial crisis.
  - Two countries show inward shifts (improvements).
  - One country features both an outward and an inward shift.
- Labor market structure:
  - Labor force growth reduces the likelihood of an outward shift across specifications.
  - Higher labor market protection makes outward shifts less likely (negatively associated with frictional unemployment).
  - Outward shifts are more likely with a higher share of employees with intermediate education in the labor force.
- Categories of unemployment:
  - Frictions increase with a larger share of long-term unemployed to total unemployed.
  - Preferred specification also shows matching is more difficult with larger shares of female job seekers and young job seekers, and easier with larger shares of elderly workers.
- Policies:
  - Higher social security contributions and the tax wedge are more likely to shift the Beveridge curve outward, harming matching—especially at higher income levels.
  - Higher unemployment benefits have a similar detrimental effect by lowering urgency to find a job.
  - Spending on active labor market programs reduces frictions, particularly programs aimed at incentives for start-up and promoting job sharing.
- Interactions and crisis effects:
  - During the 2008 global shock the negative impact of unemployment benefits on frictional unemployment was stronger.
  - During the 2008 shock the role of long-term unemployment was smaller as was the impact of low and intermediate levels of education.
  - No significant change was found in the impact of other determinants or evidence of complementarities across labor market institutions (consistent with Bassanini and Duval (2009)).

### Contributions of the study
- First cross-country study on Beveridge curves and their dynamics based on a broad sample of OECD countries (with specific earlier exceptions noted in the literature).
- Introduces a combination of three complementary methodologies to detect shifts: visual inspection, cointegration with endogenously determined breaks, and non-linear (hyperbolic) estimation.
- Adds a fiscal policy angle to analyze conditions that exacerbate matching processes.
- Tests implications of the 2008–09 shock on determinants of frictional unemployment.

### Methodology summary
- Identification of shifts:
  - Visual examination of Beveridge curves (vacancies on horizontal axis, unemployment on vertical axis).
  - Cointegration analysis (Johansen trace test; Stock-Watson-Shin Dynamic OLS for long-term coefficients), with unit root testing including ADF, PP, and Ng and Perron (2001) M-tests; tests for breaks in cointegration using Gregory and Hansen (1996) ADF and PP allowing for breaks.
  - Non-linear estimation using a hyperbolical functional form (convex-to-origin Beveridge curve) following a specification similar to Börsch-Supan (1991) to test the statistical significance and sign of identified breaks.
- Shift variable construction:
  - Binary dummy: value = 1 for quarters after outward shifts (or before inward shifts); value = 0 for quarters before outward shifts (or after inward shifts).
  - Alternative specifications: “Shift size” using estimated coefficients b0 from the non-linear estimation; “Mismatch” variable taking value a0 before the shift and a0 + b0 after the shift.
- Determinants analysis:
  - Limited dependent variable models: panel probit (preferred) and logit (robustness), including time fixed effects, country panel i = 1,...,12; t = 2000:1,...,2013:4.
  - Controls: contemporaneous and lagged output gap, growth in labor force; in fiscal specifications include overall balance.
  - Labor market characteristics examined: real wages (lagged, in growth rates), temporary contracts per labor force, index of strictness of employment protection legislation (EPL), composition of unemployed population by age, gender, long-term status, and education levels (advanced, intermediate, basic).
  - Fiscal/labor-market policies examined: tax wedge and components (employer and employee social security contributions) at different earnings levels; spending on active labor market policies and unemployment benefits (all as percent of GDP). Components of active labor market policies include incentives for start-ups, job creation, rehabilitation, general employment, job rotation and training.
- Data and sample:
  - Sample: 12 OECD countries, 2000Q1–2013Q4 (chosen for vacancy data availability).
  - Data sources: IMF WEO and IFS for GDP, output gap, fiscal balance; OECD quarterly and annual data for wages, unemployment groups, social security contributions, tax wedge, ALMP and passive policy spending, EPL, temporary contracts; ILO annual data for labor force and education structure.
  - Annual-only series interpolated to quarterly using the Denton procedure with appropriate quarterly benchmarks (e.g., quarterly unemployment for labor variables; quarterly spending as share of GDP for ALMP).

### Organization of the paper
- Section 2: theoretical framework and literature review.
- Section 3: econometric methodology.
- Section 4: main findings.
- Last section: conclusions.

*Source: _wp1693 - INTRODUCTION*

### Appendix A.

### Appendix A.

### Cointegration tests and structural breaks
- Cointegration analysis is sensitive to structural breaks; Gregory and Hansen (1996) procedure was used to detect cointegration under breaks and identify break dates.
- When accounting for a break (intercept level shift or intercept and slope regime shift), unemployment and vacancies are cointegrated for: Australia, Finland, Germany, Hungary, Norway, Portugal, Sweden, the United Kingdom, and the United States; and for Austria, Finland, and Poland when considering the Z statistic.
- Countries for which no cointegration was found: the Czech Republic and Norway.
- Breaks tend to cluster around the global financial crisis.
- Selected break dates and test statistics (level shift / regime shift; ADF and Phillips tests) include:
  - Australia: ADF stat -6.97*, estimated break date 2008Q3; Z stat -55.906*, estimated break date 2008Q4. Regime shift ADF -6.75*, 2008Q3; Z -55.613*, 2008Q4.
  - Austria: ADF -3.80, 2004Q4; Z -38.54*, 2004Q3. Regime shift ADF -3.88, 2006Q4; Z -38.45, 2004Q2.
  - Czech Republic: level ADF -3.73, 2010Q3; Z -17.89, 2007Q3. Regime ADF -3.59, 2010Q1; Z -15.56, 2009Q1.
  - Finland: level ADF -3.93, 2010Q2; Z -92.57*, 2004Q3. Regime ADF -4.05, 2010Q4; Z -94.20*, 2004Q3.
  - Germany: level ADF -4.86*, 2009Q1; Z -11.06, 2008Q1. Regime ADF -5.36*, 2001Q4; Z -18.27, 2005Q2.
  - Hungary: level ADF -4.13, 2011A1; Z -35.43, 2010Q3. Regime ADF -3.47, 2011Q1; Z -42.34*, 2011Q1.
  - Norway: level ADF -4.17, 2007Q3; Z -32.14, 2008Q2. Regime ADF -3.57, 2007Q4; Z -36.95, 2005Q2.
  - Poland: level ADF -3.68, 2004Q1; Z -37.65*, 2003Q3. Regime ADF -3.75, 2004Q1; Z -37.29, 2003Q3.
  - Portugal: level ADF -5.59*, 2007Q3; Z -22.41, 2006Q3. Regime ADF -5.32*, 2007Q3; Z -23.84, 2010Q4.
  - Sweden: level ADF -4.92*, 2008Q1; Z -39.93*, 2006Q1. Regime ADF -4.66, 2008Q1; Z -39.78, 2005Q3.
  - United Kingdom: level ADF -5.98*, 2005Q3; Z -26.77, 2001Q3. Regime ADF -5.85*, 2002Q3; Z -31.43, 2001Q3.
  - United States: level ADF -5.04*, 2008Q3; Z -36.46*, 2008Q3. Regime ADF -5.18*, 2008Q3; Z -39.21, 2006Q3.
- Note: critical values for 1% confidence: ADF (constant, no trend) -3.55; PP -3.55; ADF (constant and trend) -4.137; PP -4.133.

### Non-linear estimation and identified shifts in the Beveridge curve
- Non-linear estimation was applied to Beveridge curves incorporating shift dummies based on visual and cointegration-identified break dates.
- The coefficient associated with the shift is significant for all countries examined.
- Direction of shifts (from Table 5 — break date selected and break direction):
  - Australia: break date 2008Q3 — Outward
  - Austria: 2004Q3 — Outward
  - Czech Republic: 2008Q2 — Inward
  - Finland: No break — No break
  - Germany: 2009Q1 — Inward
  - Hungary: 2011Q1 — Outward
  - Norway: No break — No break
  - Poland: 2002Q3 and 2008Q4 — Outward then Inward
  - Portugal: 2007Q3 — Outward
  - Sweden: 2008Q1 — Outward
  - United Kingdom: 2005Q3 — Outward
  - United States: 2008Q3 — Outward
- Overall summary:
  - Ten shifts identified across twelve countries.
  - Shifts are outward (deterioration in matching) for most countries; inward for the Czech Republic and Germany.
  - Poland exhibits two breaks: an outward shift followed by an inward shift.
  - Except for Austria and the United Kingdom, deterioration occurred around the global financial crisis.

Key estimates from non-linear estimation (Table 4a: Vertical Shift)
- Constants and shift coefficients (standard errors in parentheses):
  - Australia: Constant 6.112*** (0.0173); Shift 0.122*** (0.0272)
  - Austria: Constant 4.727*** (0.0222); Shift 0.246*** (0.0269)
  - Czech Republic: Constant 5.697*** (0.0262); Shift -0.127*** (0.0409)
  - Finland: Constant 5.143*** (0.0180); Shift -0.106*** (0.0218)
  - Germany: Constant 8.040*** (0.0216); Shift -0.245*** (0.0419)
  - Hungary: Constant 5.421*** (0.0270); Shift 0.460*** (0.0583)
  - Poland: Constant 7.239*** (0.0437); Shift 0.351*** (0.0697)
  - Portugal: Constant 5.338*** (0.0496); Shift 0.730*** (0.0728)
  - Sweden: Constant 5.330*** (0.0286); Shift 0.354*** (0.0420)
  - UK: Constant 7.140*** (0.0345); Shift 0.305*** (0.0461)
  - US: Constant 8.777*** (0.0207); Shift 0.522*** (0.0318)
- Observations and R-squared:
  - Observations: Australia 57, Austria 56, Czech Rep. 56, Finland 49, Germany 56, Hungary 56, Poland 52, Portugal 50, Sweden 52, UK 50, US 52.
  - R-squared: 0.305, 0.619, 0.298, 0.488, 0.456, 0.567, 0.494, 0.635, 0.545, 0.489, 0.845 respectively.

Key estimates from non-linear estimation with slope (Table 4b: Vertical Shift with Slope Coefficient)
- Constants, shift, and slope (standard errors in parentheses):
  - Australia: Constant 3.931*** (0.191); Shift 0.249*** (0.0185); Slope 11.51*** (0.921)
  - Austria: Constant 3.754*** (0.198); Shift 0.286*** (0.0239); Slope 4.180*** (0.644)
  - Czech Republic: Constant 4.346*** (0.109); Shift -0.235*** (0.0226); Slope 6.500*** (0.441)
  - Finland: Constant 5.199*** (0.117); Shift -0.113*** (0.0262); Slope 0.833** (0.343)
  - Germany: Constant 6.095*** (0.297); Shift -0.208*** (0.0309); Slope 12.30*** (1.721)
  - Hungary: Constant 4.350*** (0.158); Shift 0.555*** (0.0451); Slope 4.785*** (0.553)
  - Poland: Constant 6.331*** (0.0946); Shift 0.373*** (0.0415); Slope 3.907*** (0.291)
  - Portugal: Constant 4.063*** (0.408); Shift 0.880*** (0.0827); Slope 4.019*** (0.961)
  - Sweden: Constant 5.450*** (0.196); Shift 0.342*** (0.0465); Slope 0.611 (0.625)
  - UK: Constant 3.685*** (0.545); Shift 0.299*** (0.0342); Slope 22.74*** (3.423)
  - US: Constant 6.042*** (0.690); Shift 0.477*** (0.0302); Slope 17.36*** (4.125)
- Observations and R-squared:
  - Observations: same counts as Table 4a above.
  - R-squared: 0.796, 0.739, 0.821, 0.491, 0.719, 0.770, 0.824, 0.692, 0.548, 0.725, 0.883 respectively.

### Determinants of shifts — main empirical findings
- Output gap (contemporaneous and lagged) is generally not statistically significant — outward or inward shifts do not occur systematically at specific business cycle phases.
- Labor force growth is highly significant and negative throughout almost all specifications; this helps explain why Beveridge curves have not shifted back after the crisis.
- Overall fiscal balance is mostly significant with a negative sign.
- Exact reported coefficients in baseline/specification block (select):
  - Labor force (growth) coefficient reported in block: -0.411*** (0.109)
  - Overall balance coefficient reported in block: -0.217*** (0.0396)
  - (These coefficients were reported as key negative effects in the baseline regression outputs.)
- Composition effects:
  - Higher share of young unemployed → associated with outward movements (worsening matching).
  - Higher share of old-age unemployed → associated with less outward movement (improvement).
  - Female unemployment shows evidence supportive of male-biased labor matching preference.
  - Long-term unemployment → makes matching more difficult.

### Fiscal and labor market policy effects (key quantified results)
- Social security contributions and tax wedge increase likelihood of outward shifts:
  - ESSC_100 2.485*** (0.354); ESSC_167 2.419*** (0.326); ESSC_67 2.304*** (0.372) — Panel logit (RE), Shift size specification.
  - WSSC_100 1.940*** (0.289); WSSC_167 2.571*** (0.369); WSSC_67 1.949*** (0.290) — Panel logit (RE), Shift size specification.
  - TW_100 0.241** (0.113); TW_167 0.813*** (0.149); TW_67 0.128* (0.0726) — Panel logit (RE), Shift size specification.
- Unemployment benefits increase likelihood of outward shifts:
  - Unempl benefits 0.0194*** (0.00357) — baseline panel probit; robustness: 0.00144*** (0.000285) when Shift size/mismatch used as dependent variables.
- Active labor market programs that improve matching:
  - Job creation: coefficient -0.141** (0.0620) — Panel logit (RE), Shift size.
  - Rehabilitation: -0.257*** (0.0779) — Panel logit (RE), Shift size.
  - Job sharing: -2.587** (1.074) — Panel logit (RE), Shift size.
  - Start-up incentives: -0.255*** (0.0589) — Panel logit (RE), Shift size; robust and strongly significant across specifications.
  - Training: statistically insignificant in baseline.
  - Incentives: small/insignificant in some specifications.
- Robustness checks (Panel logit RE/FE, fixed effects, alternative dependent variables Shift size and Mismatch) broadly confirm:
  - Employment protection, long-term unemployment, and education results are robust.
  - Social security contributions remain significant across estimations.
  - Tax wedge retains detrimental impact in many specifications (notably TW_167).
  - Active labor market policies are somewhat less robust but start-up incentives and job sharing/rehabilitation often retain significance.

### Shocks, institutions, and interactions during the global financial crisis
- Interactions with crisis time dummies (2008Q3 and 2008Q4) show:
  - At the trough of the crisis the level of education and the length of unemployment had a less strong impact on the likelihood of an outward shift (columns 1–4, Table 10).
  - The detrimental impact of unemployment benefits was stronger during the crisis: interaction terms show 2008Q3*Unemployment benefits 0.0161* (0.009) and 2008Q4*Unemployment benefits 0.0142* (0.008) in respective specifications.
  - For many other variables, the incidence of the financial crisis did not materially alter their impact on labor market dynamics.
- Attempts to identify complementarities (e.g., share of temporary contracts interacted with EPL variants) yielded statistically insignificant or inconclusive results.

### Principal conclusions and policy implications
- Factors associated with a negative impact (increasing likelihood of an inward shift — faster matching, less frictional unemployment):
  - Higher labor force growth.
  - Stronger employment protection legislation (EPL).
  - An older unemployed population.
  - Government spending in active labor market policies such as job sharing programs and start-up incentives.
- Factors associated with a positive impact (increasing likelihood of an outward shift — worse matching):
  - Larger share of long-term unemployed.
  - Female and young unemployed.
  - More employees with intermediate education in the labor force.
  - Higher social security contributions and tax wedge.
  - Higher unemployment benefits.
- Policy recommendations emphasized:
  - Prefer active labor market policies over passive ones.
  - Give preference to programs for job sharing and incentives for start-up activities to reduce frictional unemployment.
  - Reconsider unemployment benefits and labor taxation (social security contributions and tax wedge) given their association with worse matching.
  - Note the caveat on EPL: tighter protection is associated with lower frictional unemployment but may raise flows into and out of unemployment, possibly increase overall unemployment, lower average productivity, and raise entry barriers for young workers.
- Caveats:
  - Analysis is based on a limited number of shifts over 13 years; most shifts occurred around the global financial crisis.
  - No backward shifts observed yet for curves shifted outward during the crisis; the slower pace of labor market recovery relative to output recovery remains an open question.

*Source: Appendix A of the referenced IMF working paper (Appendix A).*

### Appendix A

### Appendix A

### Table A1. Lag length Criteria for the Relationship between Unemployment and Vacancies
- Note: AIC (Akaike information criterion), LR (sequential modified likelihood ratio test statistic), FPE (Final prediction error criterion by Lutkepohl, 1993), SIC (Schwarz information criterion), HQ (Hannan-Quinn information criterion).

### Table A2. Estimation of Long-Run Relationships: Stock-Watson-Shin Cointegration
- Note: The  is the Shin (1994) LM statistic which tests for deterministic cointegration. The critical values are taken from Shin (1994), Table 1, for m=1. Standard errors are adjusted for long-run variance. The long-run variance of the cointegrating regression residuals was estimated using the Barlett window with as proposed by Newey and West (1987). The number of leads and lags selected was as proposed in Stock and Watson (1993). *, ** and *** denote significance at 10, 5 and 1% levels, respectively.

- Selected lag / AIC / LR / FPE / SIC / HQ (as presented for countries)
  - Australia: Selected 2, AIC -6.4161, LR 7.498*, FPE 5.61e-06*, SIC -6.027*, HQ -6.269*
  - Austria: Selected 5, AIC -5.97*, LR 17.06*, FPE 8.80e-06*, SIC -5.13*, HQ -5.65*
  - Czech Republic2: AIC -5.29*, LR 30.49*, FPE 1.72e-05*, SIC -4.91*, HQ -5.14*
  - Finland: Selected 5, AIC -6.20*, LR 26.43*, FPE 7.05e-06*, SIC -5.36*, HQ -5.88*
  - Germany: Selected 5, AIC -6.58*, LR 16.48*, FPE 4.83e-06*, SIC -5.68*, HQ -6.25*
  - Hungary: Selected 3, AIC -3.71*, LR 14.18*, FPE 8.42e-05*, SIC -3.17, HQ -3.50*
  - Norway: Selected 5, AIC -4.63, LR 32.48*, FPE 3.37e-05, SIC -3.79*, HQ -4.31*
  - Poland: Selected 6, AIC -5.45*, LR 8.93, FPE 1.50e-05*, SIC -4.46, HQ -5.07*
  - Portugal: Selected 5, AIC -5.27*, LR 17.67*, FPE 1.78e-05*, SIC -4.43*, HQ -4.95*
  - Sweden: Selected 5, AIC -4.51*, LR 31.13*, FPE 3.81e-05*, SIC -3.64*, HQ -4.18*
  - United Kingdom: Selected 3, AIC -7.00*, LR 16.29*, FPE 3.12e-06*, SIC -6.43*, HQ -6.79*
  - United States: Selected 2, AIC -5.76*, LR 48.63*, FPE 1.07e-05*, SIC -5.36*, HQ -5.61*

- Cointegration estimates by country (, s.e., C, s.e., 2R)
  - Australia:  -0.159, s.e. 0.108, C 7.147***, s.e. 0.536, 2R 0.285
  - Austria:  -0.144, s.e. 0.185, C 5.691***, s.e. 0.626, 2R 0.188
  - Czech Republic:  -0.303***, s.e. 0.0677, C 7.103***, s.e. 0.271, 2R 0.643
  - Finland:  -0.363***, s.e. 0.053, C 6.572***, s.e. 0.177, 2R 0.748
  - Germany:  -0.488***, s.e. 0.145, C 11.004***, s.e. 0.851, 2R 0.499
  - Hungary:  -0.498***, s.e. 0.170, C 7.583***, s.e. 0.615, 2R 0.428
  - Norway:  -0.303***, s.e. 0.091, C 5.306***, s.e. 0.266, 2R 0.437
  - Poland:  -0.491***, s.e. 0.060, C 9.326***, s.e. 0.207, 2R 0.822
  - Portugal:  0.397, s.e. 0.444, C 5.087***, s.e. 1.124, 2R 0.126
  - Sweden:  0.244, s.e. 0.198, C 4.946***, s.e. 0.683, 2R 0.123
  - United Kingdom:  -0.970***, s.e. 0.251, C 13.600***, s.e. 1.591, 2R 0.538
  - United States:  -1.847***, s.e. 0.661, C 20.146***, s.e. 3.924, 2R 0.398

- Additional calibration notes (as presented)
  - )(6 2/1 TINTl
  - )(3 3/1 TINTq

### Appendix B — Table B1. Summary Statistics
- Variable / Observations / Mean / Std. Deviation / Min / Max
  - wages: 681, Mean 89.92, Std. Deviation 14.54, Min 41.34, Max 123.83
  - EPL: 672, Mean 2.24, Std. Deviation 0.98, Min 0.256, Max 4.58
  - EPL individual: 672, Mean 2.24, Std. Deviation 0.98, Min 0.256, Max 4.58
  - EPL collective: 672, Mean 2.77, Std. Deviation 0.53, Min 1.625, Max 3.625
  - Unemployment young: 650, Mean 28.92, Std. Deviation 8.01, Min 14.72, Max 45.56
  - Unemployment old: 655, Mean 1.19, Std. Deviation 0.95, Min 0.035, Max 4.496
  - Female unemployment: 670, Mean 46.62, Std. Deviation 4.22, Min 37.5, Max 59.615
  - Long term: 504, Mean 8.09, Std. Deviation 3.41, Min 1.44, Max 14.491
  - Advanced education: 632, Mean 23.33, Std. Deviation 12.11, Min 5.27, Max 61.86
  - Intermediate education: 640, Mean 52.53, Std. Deviation 16.42, Min 11.99, Max 79.16
  - Basic education: 604, Mean 19.78, Std. Deviation 15.52, Min 5.24, Max 74.30
  - Overall_balance: 613, Mean -1.43, Std. Deviation 5.74, Min -18.18, Max 38.82
  - ESSC_100: 672, Mean 21.02, Std. Deviation 9.83, Min 5.94, Max 41.81
  - ESSC_167: 672, Mean 20.51, Std. Deviation 9.63, Min 5.94, Max 40.09
  - ESSC_67: 672, Mean 21.02, Std. Deviation 10.01, Min 5.94, Max 43.96
  - WSSC_100: 672, Mean 11.24, Std. Deviation 6.05, Min 0, Max 22.17
  - WSSC_167: 672, Mean 10.39, Std. Deviation 5.69, Min 0, Max 22.17
  - WSSC_67: 672, Mean 11.16, Std. Deviation 6.01, Min 0, Max 22.17
  - TW_100: 672, Mean 40.59, Std. Deviation 7.83, Min 26.65, Max 55.8
  - TW_167: 672, Mean 45.13, Std. Deviation 7.55, Min 32.2, Max 59.14
  - TW_67: 672, Mean 36.94, Std. Deviation 7.55, Min 20.6, Max 51.38
  - Job-creation: 440, Mean 0.0069, Std. Deviation 0.0069, Min -0.0018, Max 0.0325
  - Incentives: 440, Mean 0.030, Std. Deviation 0.0373, Min -0.0004, Max 0.167
  - Rehabilitation: 412, Mean 0.0059, Std. Deviation 0.0063, Min 0, Max 0.023
  - Job-sharing: 412, Mean 0.0022, Std. Deviation 0.0048, Min -0.0008, Max 0.018
  - Start-up incentives: 440, Mean 0.0025, Std. Deviation 0.0042, Min -0.00045, Max 0.027
  - Training: 440, Mean 0.0495, Std. Deviation 0.0426, Min 0.00047, Max 0.018
  - Unemployment benefits: 464, Mean 0.193, Std. Deviation 0.121, Min 0.0336, Max 0.556

*Appendix A (content unit: _wp1693 - Appendix A)*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1693.pdf_