## 1. Average Duration of Unemployment (Weeks)

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---

### Introduction and research question
- Central question: Are persistent increases in unemployment cyclical or structural?
- Context and observed facts:
  - U.S. unemployment rose from 4.4 percent in May 2007 to 10.1 percent in October 2009.
  - Recent readings show average unemployment spells in excess of 30 weeks.
  - These readings are more than 10 weeks above the previous highest duration seen in data going back to the early 1960s.

### Breakdown of duration and cross-country heterogeneity
- Duration composition:
  - Short-term spells: less than 5 weeks (showed an uptick).
  - Medium-term and long-term spells: greater than 27 weeks (noted as particularly alarming and responsible for much of the increase in average duration).
- Cross-country comparison:
  - The increase in U.S. unemployment during the Great Recession is compared with that in 12 other industrialized countries, showing both increases elsewhere and considerable heterogeneity in unemployment outcomes.

### Prior literature and quantitative estimates of structural factors
- Sahin, Song, Topa and Violante (2011):
  - Estimate that between 0.8 and 1.4 percentage points of the increase in U.S. unemployment during the Great Recession can be attributed to mismatch.
  - This corresponds to between 20% and 25% of the observed increase in unemployment.
  - For the U.K., they find that 0.8 percent of the increased unemployment— which corresponds to a third of the increase—during the Great Recession was due to mismatch.
- Kirkegaard (2009):
  - Finds a sharp increase in “the relative employment weight of industries undergoing structural change in the current cycle,” implying greater need for reallocation of workers across industries.
- Estevao and Tsounta (2011):
  - Find that increases in skill mismatches in [U.S.] states with worse housing market conditions are associated with even higher unemployment rates.
  - Estimate that the combined impact of skill mismatches and higher foreclosure rates might have raised the U.S. natural rate of unemployment by about 1 ½ percentage points since 2007.
- Barnichon and Figura (2011):
  - Find that until 2006 changes in matching efficiency were largely due to composition of the unemployed; since 2006 composition played a diminished role relative to “dispersion in labor market conditions.”
  - They estimate that in the 2008-2009 recession, the decline in aggregate matching efficiency added 1 ½ percentage points to the unemployment rate.

### Measurement approach: stock market dispersion and uncertainty indices
- Motivating conjecture:
  - Based on Black (1987) and Beaudry and Portier (2004): greater cross-industry dispersion in stock returns signals shocks that affect sectors differently and that investors expect to be permanent, motivating labor reallocation.
- Empirical strategy:
  - Use a stock market dispersion index (cross-industry dispersion of stock returns) as a measure of intensity of structural shocks.
  - Compare effects with an uncertainty index (stock market volatility in the time dimension), following Bloom (2009).
- Index construction (summary):
  - Data: Standard and Poor‘s indexes of industry stock prices covering over 50 industries (manufacturing and nonmanufacturing).
  - Dispersion_t = [ sum_{i=1}^n W_i (R_it - R_t)^2 ]^{1/2} where R_it is the growth rate of industry i‘s stock price index; R_t is the growth rate of the S&P500; W_i is a weight based on the industry‘s share in total employment.
  - Interpretation: weighted standard deviation of industry stock returns emphasizing persistent (permanent) shocks to expected profitability.
- Key comparative findings on indices:
  - The stock market dispersion measure accounts for a significant part of U.S. unemployment fluctuations after controlling for aggregate factors.
  - The dispersion index exerts a much greater impact on long-term unemployment than on short-term unemployment.
  - The uncertainty (volatility) index raises short-duration unemployment but has almost no effect on long-duration unemployment.
  - The stock market dispersion index has a larger effect on aggregate unemployment than Bloom’s uncertainty index.

### Univariate evidence for the U.S.
- Method: regress ΔU on four lags of ΔU and lagged shocks (lag length: 4 quarters). Estimated shocks include monetary policy shocks (Romer and Romer identification), fiscal (tax rate) policy shocks (Romer and Romer identification), oil price shock (percentage change in the real price of oil), and stock price dispersion index changes.
- Key univariate impulse-response findings (impact on overall unemployment):
  - A one standard deviation monetary policy tightening → increase in unemployment of about 0.6 percent after 2 years.
  - Fiscal policy shocks → small and insignificant effects.
  - A one standard deviation increase in the real price of oil → increases unemployment, peak at 2 years.
  - A one standard deviation increase in the dispersion index → increase in unemployment of about 0.2 percent after a year and a half.
- Long-term unemployment (duration > 26 weeks) in univariate regressions:
  - Responses to monetary, fiscal, and oil shocks are small, often of opposite sign, and generally not significant at the 90 percent confidence interval.
  - A one standard deviation increase in the dispersion index → gradual increase in long-term unemployment, peaking at around 0.1 percentage points after two years.
  - Context: average long-term unemployment in the U.S. for the last 40 years is about 0.9 percent.

### VAR evidence for the U.S. (1963:Q1–2010:Q2)
- Baseline VAR variables (6): real GDP growth, growth rate of the S&P500, unemployment rate, inflation, federal funds rate, stock market dispersion index (dispersion placed last in ordering). Lag length: 6 quarters.
- Impulse responses:
  - Output growth shock: one standard deviation increase → 0.3 percentage point decrease in unemployment after one year.
  - Fed funds rate innovations → higher unemployment.
  - Dispersion shock → unemployment gradually increases, peaking at about 0.3 percentage points two years after the shock.
  - Long-term unemployment (VAR): hump-shaped response to dispersion innovations; peak around three years after shock; peak magnitude higher than in univariate regressions.
- Variance decompositions — Unemployment rate (forecast-error variance decomposition):
  - Horizon 5 quarters: Growth 41.9%; Market Return 14.8%; Unemployment Rate 34.7%; Inflation 2.6%; Fed Funds Rate 1.9%; Dispersion 4.1%
  - Horizon 10 quarters: Growth 24.9%; Market Return 16.0%; Unemployment Rate 15.1%; Inflation 10.0%; Fed Funds Rate 8.2%; Dispersion 25.8%
  - Horizon 20 quarters: Growth 16.6%; Market Return 10.3%; Unemployment Rate 9.8%; Inflation 23.3%; Fed Funds Rate 14.4%; Dispersion 25.6%
- Variance decompositions — Long-term unemployment rate (forecast-error variance decomposition):
  - Horizon 5 quarters: Growth 6.4%; Market Return 2.6%; Long-Term Unemployment Rate 88.8%; Inflation 0.2%; Fed Funds Rate 0.6%; Dispersion 1.3%
  - Horizon 10 quarters: Growth 26.6%; Market Return 6.4%; Long-Term Unemployment Rate 46.5%; Inflation 0.6%; Fed Funds Rate 0.3%; Dispersion 19.5%
  - Horizon 20 quarters: Growth 19.3%; Market Return 3.9%; Long-Term Unemployment Rate 32.9%; Inflation 1.3%; Fed Funds Rate 1.7%; Dispersion 40.9%
- Duration-specific pattern (Figure 9 summary):
  - Up to 5 weeks: less than 5% of variance explained by dispersion shocks.
  - 26+ weeks: about 40% explained by dispersion shocks.

### Great Recession decomposition (2007Q4–2010Q2)
- Long-term unemployment share:
  - 2007Q4: long-term unemployment constituted 16 percent of total unemployment.
  - 2010Q2: long-term unemployment constituted 40 percent of total unemployment.
- VAR forecasts (base at 2007Q4, horizon to 2010Q2):
  - For first year, long-term unemployment close to baseline (deviation at most around .06 percentage points).
  - By 2010Q2, realized long-term unemployment was more than 2 ½ percentage points higher than baseline.
  - Orthogonalized dispersion shocks over 2008Q1–2010Q2, if known at 2007Q4, would explain more than half the deviation of realized long-term unemployment from baseline from beginning of 2009 to 2010Q2.
  - Contribution of shocks to GDP growth averaged about 15 percent during the same period.

### Structural vs cyclical decomposition
- Structural unemployment definition in framework: baseline unemployment rate + contribution of dispersion shocks (U*).
- Findings:
  - Short-duration unemployment (less than 5 weeks): structural unemployment fairly constant; actual rate strongly cyclical.
  - Long-duration unemployment (26+ weeks): structural unemployment moves closely with actual unemployment.
  - Cyclical factors more important in early 1980s and early 1990s recessions; less important in mid-1970s and the Great Recession.

### Comparison with Bloom‘s uncertainty index
- Distinction between indexes:
  - Bloom‘s index: time series volatility measure (1962–1985: monthly standard deviation of daily S&P500; 1986 onwards: VXO implied volatility).
  - This paper’s dispersion index: cross-section volatility (how individual industry returns differ from aggregate at a point in time).
- Joint behavior: the two series tend to move together, especially later in the sample.
- VAR evidence comparing indexes — long-term unemployment response:
  - Dispersion shock: peaks at about 12 to 13 quarters; effect statistically distinguishable from zero for about 5 years; peak magnitude ~3 times that of uncertainty shock.
  - Uncertainty shock: peaks earlier (about 6 to 7 quarters); effect statistically indistinguishable from zero after about 2 years.
- Variance decomposition highlights (horizon 20 / duration-specific):
  - Uncertainty index explains more than one fifth of variance for unemployment duration ≤ 5 weeks (horizon 20).
  - For durations ≥ 15 weeks, uncertainty explains noticeably less than one tenth of variance.
  - Dispersion index explains roughly 40% of variance for longest duration unemployment.
  - Dispersion explains about 25% of overall unemployment variance; uncertainty explains less than 10%.
- Augmented VAR (both indexes included; uncertainty ordered above dispersion) — Long-term unemployment variance decomposition:
  - Horizon 5 quarters: Growth 11.2%; Market Return 0.2%; Long-Term Unemployment Rate 76.5%; Inflation 2.5%; Fed Funds Rate 3.6%; Uncertainty 5.5%; Dispersion 0.4%
  - Horizon 10 quarters: Growth 30.6%; Market Return 8.5%; Long-Term Unemployment Rate 37.3%; Inflation 1.2%; Fed Funds Rate 2.6%; Uncertainty 6.0%; Dispersion 13.8%
  - Horizon 20 quarters: Growth 22.0%; Market Return 6.8%; Long-Term Unemployment Rate 31.3%; Inflation 4.1%; Fed Funds Rate 4.8%; Uncertainty 3.7%; Dispersion 27.2%
- Conclusion: dispersion index retains a significant role for long-term unemployment even after controlling for uncertainty.

### International panel VAR evidence (advanced economies)
- Sample: Australia, Austria, Denmark, Finland, France, Germany, Italy, Netherlands, Norway, Portugal, Sweden, United Kingdom (U.S. inclusion not material to results).
- Data and methodology notes:
  - Weighting: industry stock returns weighted by industry share of market capitalization; rolling 10-year average used to smooth shares.
  - Real interest rate (ex-post) used to proxy monetary policy.
  - Long-term unemployment data not consistently available internationally; analysis limited to overall unemployment rate.
  - Panel VAR: country fixed effects, coefficients common across countries; lag length: 12 quarters; estimation period: 1965:Q2–2008:Q3.
- Panel VAR impulse-response findings:
  - A one standard deviation dispersion shock → maximum increase of about 0.3 percentage points in the unemployment rate, similar magnitude to U.S. result.
  - Response is more delayed and persistent internationally: peak impact reached after 6 years (vs. 2 years for U.S.).
- International variance decomposition (Table 4):
  - Horizon 10 quarters: Growth 15.2%; Market Return 0.8%; Unemployment Rate 75.3%; Real Interest Rate 7.6%; Dispersion 1.1%
  - Horizon 20 quarters: Growth 12.8%; Market Return 1.1%; Unemployment Rate 66.1%; Real Interest Rate 12.0%; Dispersion 8.0%
  - Horizon 40 quarters: Growth 11.4%; Market Return 0.7%; Unemployment Rate 57.0%; Real Interest Rate 13.0%; Dispersion 17.9%
  - At horizon 40 quarters, dispersion shocks explain about 17.9% of unemployment variation in the international panel (about three-fourths of the U.S. value at same horizon).

### Key conclusions and implications
- The cross-section (stock market) dispersion index captures structural sectoral shocks that materially affect unemployment, especially long-duration unemployment.
- Quantitative impacts (U.S. VAR):
  - Dispersion shocks account for about 25 percent of forecast-error variance of overall unemployment at a 5-year (20-quarter) horizon.
  - Dispersion shocks account for up to 40.9 percent of forecast-error variance of long-term unemployment at a 20-quarter horizon.
- During the Great Recession, sectoral (dispersion) shocks explain about half of the increase in long-duration unemployment between 2009 and 2010Q2; GDP shocks contributed about 15 percent on average during this period.
- Comparison with uncertainty:
  - Time-series uncertainty (Bloom) affects short-term unemployment more and has shorter-lived effects.
  - Cross-sectional dispersion affects longer-duration unemployment more and has more persistent effects.
- International evidence: dispersion shocks matter for unemployment across advanced economies, with delayed but persistent effects; at long horizons dispersion contributes substantially (17.9% at 40 quarters).

*Source: IMF Working Paper — section titled "Average Duration of Unemployment (Weeks)".*

### 1. Average Duration of Unemployment (Weeks) ......................................... 22

### 1. Average Duration of Unemployment (Weeks)

### Introduction and research question
- Central question: Are persistent increases in unemployment cyclical or structural?
- Context: U.S. unemployment rose from 4.4 percent in May 2007 to 10.1 percent in October 2009, accompanied by a sharp increase in the duration of unemployment.
- Observed facts:
  - Recent readings show average unemployment spells in excess of 30 weeks.
  - These readings are more than 10 weeks above the previous highest duration seen in data going back to the early 1960s.

### Breakdown of duration and cross-country heterogeneity
- Duration composition:
  - Short-term spells: less than 5 weeks (showed an uptick).
  - Medium-term and long-term spells: greater than 27 weeks (noted as particularly alarming and responsible for much of the increase in average duration).
- Cross-country comparison:
  - The increase in U.S. unemployment during the Great Recession is compared with that in 12 other industrialized countries, showing both increases elsewhere and considerable heterogeneity in unemployment outcomes.

### Prior literature and quantitative estimates of structural factors
- Sahin, Song, Topa and Violante (2011):
  - Estimate that between 0.8 and 1.4 percentage points of the increase in U.S. unemployment during the Great Recession can be attributed to mismatch.
  - This corresponds to between 20% and 25% of the observed increase in unemployment.
  - For the U.K., they find that 0.8 percent of the increased unemployment— which corresponds to a third of the increase—during the Great Recession was due to mismatch.
- Kirkegaard (2009):
  - Finds a sharp increase in “the relative employment weight of industries undergoing structural change in the current cycle,” implying greater need for reallocation of workers across industries.
- Estevao and Tsounta (2011):
  - Find that increases in skill mismatches in [U.S.] states with worse housing market conditions are associated with even higher unemployment rates.
  - Estimate that the combined impact of skill mismatches and higher foreclosure rates might have raised the U.S. natural rate of unemployment by about 1 ½ percentage points since 2007.
- Barnichon and Figura (2011):
  - Find that until 2006 changes in matching efficiency were largely due to composition of the unemployed; since 2006 composition played a diminished role relative to “dispersion in labor market conditions.”
  - They estimate that in the 2008-2009 recession, the decline in aggregate matching efficiency added 1 ½ percentage points to the unemployment rate.

### Measurement approach: stock market dispersion and uncertainty indices
- Motivating conjecture:
  - Based on Black (1987) and Beaudry and Portier (2004): greater cross-industry dispersion in stock returns signals shocks that affect sectors differently and that investors expect to be permanent, motivating labor reallocation.
- Empirical strategy:
  - Use a stock market dispersion index (cross-industry dispersion of stock returns) as a measure of intensity of structural shocks.
  - Compare effects with an uncertainty index (stock market volatility in the time dimension), following Bloom (2009).
- Key findings on indices:
  - The stock market dispersion measure accounts for a significant part of U.S. unemployment fluctuations after controlling for aggregate factors.
  - The dispersion index exerts a much greater impact on long-term unemployment than on short-term unemployment.
  - The uncertainty (volatility) index raises short-duration unemployment but has almost no effect on long-duration unemployment.
  - The stock market dispersion index has a larger effect on aggregate unemployment than Bloom’s uncertainty index.

### Cross-country extension and broader implications
- Extension to a sample of 12 developed economies:
  - Finds that the unemployment rate increases significantly following an increase in stock market dispersion, after controlling for aggregate factors.
- Theoretical relevance:
  - Results provide support for models in which permanent sectoral shifts and uncertainty shocks matter for aggregate labor market outcomes (e.g., Phelan and Trejos (2000); Bloom (2009); Bloom, Floetotto and Jaimovich (2009)).
  - Empirical evidence suggests structural shocks (as proxied by dispersion) are especially important for long-term unemployment, while uncertainty shocks are more relevant for short-term unemployment.

*Source: IMF Working Paper — section titled "Average Duration of Unemployment (Weeks)".*

### Section II describes the construction of the stock market dispersion index. The next

### _wp11106 - Section II describes the construction of the stock market dispersion index. The next

### Construction of the stock market dispersion index
- Data: Standard and Poor‘s indexes of industry stock prices covering over 50 industries (manufacturing and nonmanufacturing).
- Index definition: Dispersion_t = [ sum_{i=1}^n W_i (R_it - R_t)^2 ]^{1/2} where:
  - R_it is the growth rate of industry i‘s stock price index.
  - R_t is the growth rate of the S&P500.
  - W_i is a weight based on the industry‘s share in total employment.
- Interpretation: the index is the weighted standard deviation of industry stock returns; it is designed to emphasize persistent (permanent) shocks to expected profitability rather than temporary cyclical disturbances.
- Empirical behavior (U.S., 1963–2010): index displays some cyclical behavior; recessions typically associated with increases in the index, but magnitude of increases is not tightly correlated with output loss (examples: 1974-75 and 1990 recessions show larger increases than 1981 recession). The index also rose in expansionary periods (dot-com boom).

### Univariate evidence for the U.S.: regressions on unemployment
- Method: regress ΔU on four lags of ΔU and lagged shocks (lag length: 4 quarters). Estimated shocks:
  - Monetary policy shocks (Romer and Romer identification).
  - Fiscal (tax rate) policy shocks (Romer and Romer identification).
  - Oil price shock: percentage change in the real price of oil.
  - Stock price dispersion index changes.
- Key univariate impulse-response findings (impact on overall unemployment):
  - A one standard deviation monetary policy tightening → increase in unemployment of about 0.6 percent after 2 years.
  - Fiscal policy shocks → small and insignificant effects.
  - A one standard deviation increase in the real price of oil → increases unemployment, peak at 2 years.
  - A one standard deviation increase in the dispersion index → increase in unemployment of about 0.2 percent after a year and a half.
- Long-term unemployment (duration > 26 weeks) in univariate regressions:
  - Responses to monetary, fiscal, and oil shocks are small, often of opposite sign, and generally not significant at the 90 percent confidence interval.
  - A one standard deviation increase in the dispersion index → gradual increase in long-term unemployment, peaking at around 0.1 percentage points after two years.
  - Context: average long-term unemployment in the U.S. for the last 40 years is about 0.9 percent.

### VAR evidence for the U.S. (1963:Q1–2010:Q2)
- Baseline VAR variables (6): real GDP growth, growth rate of the S&P500, unemployment rate, inflation, federal funds rate, stock market dispersion index (dispersion placed last in ordering). Lag length: 6 quarters.
- A. Effects of sectoral shocks (identified VAR):
  - Output growth shock: one standard deviation increase → 0.3 percentage point decrease in unemployment after one year.
  - Fed funds rate innovations → higher unemployment.
  - Dispersion shock → unemployment gradually increases, peaking at about 0.3 percentage points two years after the shock.
  - Long-term unemployment (VAR): hump-shaped response to dispersion innovations; peak around three years after shock; peak magnitude higher than in univariate regressions.
- Variance decompositions (selected exact values from Tables):
  - Table 1 — Unemployment rate, Forecast-error variance decomposition:
    - Horizon 5 quarters: Growth 41.9%; Market Return 14.8%; Unemployment Rate 34.7%; Inflation 2.6%; Fed Funds Rate 1.9%; Dispersion 4.1%
    - Horizon 10 quarters: Growth 24.9%; Market Return 16.0%; Unemployment Rate 15.1%; Inflation 10.0%; Fed Funds Rate 8.2%; Dispersion 25.8%
    - Horizon 20 quarters: Growth 16.6%; Market Return 10.3%; Unemployment Rate 9.8%; Inflation 23.3%; Fed Funds Rate 14.4%; Dispersion 25.6%
  - Table 2 — Long-term unemployment rate, Forecast-error variance decomposition:
    - Horizon 5 quarters: Growth 6.4%; Market Return 2.6%; Long-Term Unemployment Rate 88.8%; Inflation 0.2%; Fed Funds Rate 0.6%; Dispersion 1.3%
    - Horizon 10 quarters: Growth 26.6%; Market Return 6.4%; Long-Term Unemployment Rate 46.5%; Inflation 0.6%; Fed Funds Rate 0.3%; Dispersion 19.5%
    - Horizon 20 quarters: Growth 19.3%; Market Return 3.9%; Long-Term Unemployment Rate 32.9%; Inflation 1.3%; Fed Funds Rate 1.7%; Dispersion 40.9%
  - Figure 9 pattern: the contribution of dispersion shocks to forecast-error variance of unemployment increases monotonically with duration:
    - Up to 5 weeks: less than 5% explained by dispersion shocks.
    - 26+ weeks: about 40% explained by dispersion shocks.

### Great Recession decomposition (2007Q4–2010Q2)
- Long-term unemployment share:
  - 2007Q4: long-term unemployment constituted 16 percent of total unemployment.
  - 2010Q2: long-term unemployment constituted 40 percent of total unemployment.
- VAR forecasts (base at 2007Q4, horizon to 2010Q2):
  - For first year, long-term unemployment close to baseline (deviation at most around .06 percentage points).
  - By 2010Q2, realized long-term unemployment was more than 2 ½ percentage points higher than baseline.
  - Orthogonalized dispersion shocks over 2008Q1–2010Q2, if known at 2007Q4, would explain more than half the deviation of realized long-term unemployment from baseline from beginning of 2009 to 2010Q2.
  - Contribution of shocks to GDP growth averaged about 15 percent during the same period.

### Structural vs cyclical decomposition
- Structural unemployment definition in framework: baseline unemployment rate + contribution of dispersion shocks (U*).
- Findings:
  - Short-duration unemployment (less than 5 weeks): structural unemployment fairly constant; actual rate strongly cyclical.
  - Long-duration unemployment (26+ weeks): structural unemployment moves closely with actual unemployment.
  - Cyclical factors more important in early 1980s and early 1990s recessions; less important in mid-1970s and the Great Recession.

### Comparison with Bloom‘s uncertainty index
- Distinction:
  - Bloom‘s index: time series volatility measure (1962–1985: monthly standard deviation of daily S&P500; 1986 onwards: VXO implied volatility).
  - This paper’s dispersion index: cross-section volatility (how individual industry returns differ from aggregate at a point in time).
- Joint behavior: the two series tend to move together, especially later in the sample.
- VAR evidence comparing indexes:
  - Long-term unemployment response:
    - Dispersion shock: peaks at about 12 to 13 quarters; effect statistically distinguishable from zero for about 5 years; peak magnitude ~3 times that of uncertainty shock.
    - Uncertainty shock: peaks earlier (about 6 to 7 quarters); effect statistically indistinguishable from zero after about 2 years.
  - Variance decompositions at horizon 20 (Figure 14 summary):
    - Uncertainty index explains more than one fifth of variance for unemployment duration ≤ 5 weeks (horizon 20).
    - For durations ≥ 15 weeks, uncertainty explains noticeably less than one tenth of variance.
    - Dispersion index explains roughly 40% of variance for longest duration unemployment.
    - Dispersion explains about 25% of overall unemployment variance; uncertainty explains less than 10%.
  - Augmented VAR (both indexes included; uncertainty ordered above dispersion) — Table 3:
    - Horizon 5 quarters: Growth 11.2%; Market Return 0.2%; Long-Term Unemployment Rate 76.5%; Inflation 2.5%; Fed Funds Rate 3.6%; Uncertainty 5.5%; Dispersion 0.4%
    - Horizon 10 quarters: Growth 30.6%; Market Return 8.5%; Long-Term Unemployment Rate 37.3%; Inflation 1.2%; Fed Funds Rate 2.6%; Uncertainty 6.0%; Dispersion 13.8%
    - Horizon 20 quarters: Growth 22.0%; Market Return 6.8%; Long-Term Unemployment Rate 31.3%; Inflation 4.1%; Fed Funds Rate 4.8%; Uncertainty 3.7%; Dispersion 27.2%
  - Conclusion: dispersion index retains a significant role for long-term unemployment even after controlling for uncertainty.

### International panel VAR evidence (advanced economies)
- Sample countries: Australia, Austria, Denmark, Finland, France, Germany, Italy, Netherlands, Norway, Portugal, Sweden, United Kingdom (U.S. inclusion not material to results).
- Data and methodology notes:
  - Weighting: industry stock returns weighted by industry share of market capitalization; rolling 10-year average used to smooth shares.
  - Real interest rate (ex-post) used to proxy monetary policy.
  - Long-term unemployment data not consistently available internationally; analysis limited to overall unemployment rate.
  - Panel VAR estimated with country fixed effects, coefficients common across countries; lag length: 12 quarters; estimation period: 1965:Q2–2008:Q3 (stock market data often start in 1973 for many countries).
- Panel VAR impulse-response findings:
  - A one standard deviation dispersion shock → maximum increase of about 0.3 percentage points in the unemployment rate, similar magnitude to U.S. result.
  - Response is more delayed and persistent internationally: peak impact reached after 6 years (vs. 2 years for U.S.).
- International variance decomposition (Table 4):
  - Horizon 10 quarters: Growth 15.2%; Market Return 0.8%; Unemployment Rate 75.3%; Real Interest Rate 7.6%; Dispersion 1.1%
  - Horizon 20 quarters: Growth 12.8%; Market Return 1.1%; Unemployment Rate 66.1%; Real Interest Rate 12.0%; Dispersion 8.0%
  - Horizon 40 quarters: Growth 11.4%; Market Return 0.7%; Unemployment Rate 57.0%; Real Interest Rate 13.0%; Dispersion 17.9%
  - At horizon 40 quarters, dispersion shocks explain about 17.9% of unemployment variation in the international panel (about three-fourths of the U.S. value at same horizon).

### Key conclusions and implications
- The cross-section (stock market) dispersion index captures structural sectoral shocks that materially affect unemployment, especially long-duration unemployment.
- Quantitative impacts (U.S. VAR):
  - Dispersion shocks account for about 25 percent of forecast-error variance of overall unemployment at a 5-year (20-quarter) horizon.
  - Dispersion shocks account for up to 40.9 percent of forecast-error variance of long-term unemployment at a 20-quarter horizon.
- During the Great Recession, sectoral (dispersion) shocks explain about half of the increase in long-duration unemployment between 2009 and 2010Q2; GDP shocks contributed about 15 percent on average during this period.
- Comparison with uncertainty:
  - Time-series uncertainty (Bloom) affects short-term unemployment more and has shorter-lived effects.
  - Cross-sectional dispersion affects longer-duration unemployment more and has more persistent effects.
- International evidence: dispersion shocks matter for unemployment across advanced economies, with delayed but persistent effects; at long horizons dispersion contributes substantially (17.9% at 40 quarters).

*Source: _wp11106 - Section II describes the construction of the stock market dispersion index. The next*

### REFERENCES

### _wp11106 - REFERENCES

### References

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*Source: _wp11106 - REFERENCES*

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