## _wp1536 — Uncertainty Shocks and U.S. Unemployment

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---

### Introduction and research question
- Paper examines the effect of uncertainty shocks on the U.S. labor market using U.S. stock market data.
- Two uncertainty measures constructed and compared:
  - Aggregate uncertainty: realized volatility of aggregate stock returns (S&P500).
  - Sectoral uncertainty: cross-industry volatility of stock returns (weighted cross-sectional volatility).
- Estimation framework: structural vector autoregressive (VAR) model for 1957Q1–2014Q3.
- Key high-level result: aggregate and sectoral uncertainty shocks have different effects on the U.S. unemployment rate; sectoral uncertainty has more significant, persistent effects and is especially important for long-term unemployment (longer than 26 weeks).

### Theoretical mechanism and motivation
- Uncertainty given structural interpretation following Bloom and others (2012): an increase in the variance of underlying shocks to the economy.
- Firm-level production and shock processes (notation preserved):
  - y_t,j = A_t f_t,j(k_{t,j}, l_{t,j}) with aggregate productivity A_t and idiosyncratic productivity z_{t,j}.
  - Log autoregressive processes:
    - log(A_t) = ρ_A log(A_{t-1}) + σ_A,t ε_{t-1}
    - log(z_{t,j}) = ρ_Z log(z_{t-1,j}) + σ_Z,t ε_{t-1,j}
  - A_t σ and Z_t σ denote time-varying aggregate and idiosyncratic uncertainty.
- Mechanisms:
  - Wait-and-see option value: higher uncertainty raises the option value of waiting, reducing hiring and firing.
  - Reallocation costs: inter-industry labor reallocation is more costly than intra-industry reallocation; sectoral shocks increase costly reallocation and thus persistent unemployment.

### Construction and properties of uncertainty indices
- Aggregate uncertainty index:
  - Realized volatility of the S&P500 index returns.
  - Quarterly RV_t = [ (1/S) Σ_s (R_{t,s} - R_t)^2 ]^{1/2} annualized by factor 252^{1/2}.
  - S = number of trading days in the quarter; R_{t,s} = market returns on day s; R_t = average market returns during quarter.
- Sectoral uncertainty index:
  - Regress industry returns R_{t,i} on market returns R_t: R_{t,i} = α_i + β_i R_t + ε_{t,i}.
  - Excess-return residuals: η_{t,i} = α̂_i + ε̂_{t,i}.
  - Sectoral index WCSV_t = [ (1/n) Σ_i (η_{t,i} - η_t)^2 ]^{1/2} weighted by industry employment shares i_W.
  - Uses quarterly industry returns; controls for differing betas across industries.
- Distributional and persistence statistics (indices normalized to same mean and variance):
  - Aggregate index: skewness = 3.30; kurtosis = 20.27; AR(1) coefficient = 0.58.
  - Sectoral index: skewness = 1.71; kurtosis = 7.04; AR(1) coefficient = 0.53.
  - Correlation between indices: 0.54.

### Empirical approach (structural VAR)
- Sample: 1957Q1 to 2014Q3 (quarterly).
- Baseline 7-variable VAR ordering (Cholesky): stock market returns → aggregate uncertainty → sectoral uncertainty → inflation → federal funds rate → real GDP growth → unemployment rate.
- Lag length: 4; robustness with 8 lags.
- Identification: evaluate marginal role of each uncertainty index by controlling for the other; parametric bootstrap with 500 repetitions for standard errors.
- Parsimonious 4-variable VAR (robustness): real GDP growth, both uncertainty indices, unemployment rate.

### Main empirical findings — effects on unemployment and macro variables
- Qualitative macro responses:
  - Both aggregate and sectoral uncertainty shocks produce dynamics consistent with a negative aggregate demand shock for inflation, federal funds rate, GDP growth, and unemployment.
  - Responses of inflation and federal funds rate are statistically insignificant for aggregate shocks; sectoral shocks show similar dynamics.
- Unemployment responses (marginal effect of one standard deviation uncertainty shocks):
  - Aggregate uncertainty shock:
    - Instant increase in unemployment: 0.06 percentage point.
    - Becomes statistically insignificant after three quarters.
    - Forecast-error-variance decomposition: explains 1.5 percent of variance in unemployment forecast errors (over 20 quarters).
    - Contribution to unemployment variation decreases monotonically with unemployment duration.
  - Sectoral uncertainty shock:
    - Instant increase in unemployment: nearly 0.2 percentage point.
    - Effect remains statistically significant for more than three years.
    - Forecast-error-variance decomposition: explains approximately 15 percent of variance in unemployment forecast errors (over 20 quarters).
    - Contribution increases monotonically with unemployment duration.
    - Explains virtually none of short-term unemployment variation but explains more than 30 percent of forecast-error variance when unemployment lasts longer than 26 weeks.
- Great Recession and long-term unemployment:
  - Long-term unemployment share: 18 percent of total unemployment in 2007Q4; 32 percent in 2014Q3.
  - VAR decomposition (2007Q4 baseline to 2014Q3, 27 quarters): sectoral uncertainty shocks are important in explaining realized deviations of the long-term unemployment rate from baseline; aggregate uncertainty shocks contribute little.

### Robustness checks and additional results
- Subsample analyses:
  - Estimation on 1984Q1–2014Q3:
    - Effect of aggregate uncertainty shocks declines substantially.
    - Effect of sectoral uncertainty shocks remains strong.
  - Estimation on 1984Q1–2007Q4 (dropping the Great Recession):
    - Persistent effect of sectoral uncertainty shocks on unemployment remains.
- Model specification checks:
  - Parsimonious 4-variable VAR: sectoral uncertainty shocks continue to have strong, persistent effects on unemployment after controlling for real GDP growth.
  - Reverse VAR ordering (placing uncertainty indices at the end): conservative estimates—aggregate uncertainty significant only short term; sectoral uncertainty significant up to three years.
  - Increasing lags to 8: qualitative results remain similar.
- Additional methodological notes:
  - Results robust when estimating model in levels with quadratic trends (impacts decrease somewhat but remain statistically significant).
  - Sectoral uncertainty index construction choices (employment-weighted vs unweighted) yield indices with correlation exceeding 0.9.
  - Index coverage: 50 U.S. industries (S&P500 industry indexes present in the composite at the end of the sample period).

### Conclusions and policy-relevant implications
- Main conclusions:
  - Aggregate uncertainty shocks have short-lived impacts on U.S. unemployment.
  - Sectoral (cross-industry) uncertainty shocks have more significant and persistent impacts, and are particularly important for long-term unemployment dynamics.
- Interpretation:
  - Aggregate uncertainty effects align with the wait-and-see option value channel (short-lived adjustments).
  - Sectoral uncertainty effects align with costly inter-industry reallocation, producing persistent increases in long-term unemployment.
- Implications for policy and research:
  - Policy responses and macroeconomic interpretation should distinguish between aggregate and sectoral uncertainty shocks because their persistence and effects across unemployment durations differ.
  - Future research: develop an integrated model that jointly evaluates both types of uncertainty to better identify independent channels through which aggregate and sectoral uncertainty affect unemployment.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1536.pdf*

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

### _wp1536 - References .............................................................................................................

### Introduction and research question
- Paper examines the effect of uncertainty shocks on the U.S. labor market using U.S. stock market data.
- Two types of uncertainty constructed and compared:
  - Aggregate uncertainty: realized volatility of aggregate stock returns.
  - Sectoral uncertainty: cross-industry volatility of stock returns.
- Estimated using a structural vector autoregressive (VAR) model from 1957Q1 to 2014Q3.
- Key high-level result: aggregate and sectoral uncertainty shocks have different effects on the U.S. unemployment rate; sectoral uncertainty has more significant, persistent effects and is especially important for long-term unemployment (longer than 26 weeks).

### Theoretical mechanism and motivation
- Labor adjustment costs and the wait-and-see mechanism: when uncertainty is high, the option value of waiting increases, reducing hiring and firing (cites Bloom 2009).
- Distinction between aggregate and sectoral uncertainty:
  - Aggregate uncertainty often proxied by volatility of the S&P500 (Bloom 2009).
  - Sectoral uncertainty proxied by cross-sectional volatility of stock returns (Loungani and others 1990; Brainard and Cutler 1993).
- Rationale for stronger sectoral effects: workers accumulate industry-specific human capital, making inter-industry labor reallocation costlier than intra-industry reallocation (Black 1995).

### Empirical approach
- Structural VAR estimated for the U.S. economy covering 1957Q1–2014Q3.
- Two uncertainty indices constructed from a common source (U.S. stock market volatility) to capture different types of uncertainty.
- Robustness checks discussed (figures and appendices listed for alternative samples, variable orderings, and lag lengths).

### Main empirical findings (three new findings)
- Different dynamic responses of unemployment to the two uncertainty shocks:
  - Aggregate uncertainty shocks: immediate but short-lived increase in the unemployment rate (peaking in two quarters and becoming statistically insignificant after four quarters).
  - Sectoral uncertainty shocks: more persistent effect (peaking in two years and becoming statistically insignificant after three years).
- Composition of unemployment fluctuations by duration:
  - Share of unemployment fluctuations attributed to sectoral uncertainty increases when moving from short-term to long-term unemployment.
  - Aggregate uncertainty shocks show monotonic decreases in contribution when moving from long- to short-term unemployment.
- Role in the Great Recession and long-term unemployment:
  - The substantial increase in the long-term unemployment rate since 2007 can be attributed largely to sectoral, not aggregate, uncertainty.
  - In 2014Q3, the long-term unemployment rate remained above 2 percent, compared with 0.7 percent in 2007.
  - This sectoral-focus explains why prior studies that considered only aggregate uncertainty (Born and others 2014; Caldara and others 2014) find uncertainty shocks played a minor role in employment fluctuations during the Great Recession.

### Implications and interpretation
- Sectoral uncertainty captures a need for inter-industry labor reallocation on top of economy-wide uncertainty; thus, sectoral uncertainty shocks are expected to have more persistent effects than aggregate shocks on the unemployment rate.
- Differences in persistence and duration-specific contributions imply that policy responses and macroeconomic interpretation should distinguish between aggregate and sectoral uncertainty shocks.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1536.pdf*

### references to policy uncertainty (Baker and others 2013), direct consumer survey data (Leduc

### _wp1536 - references to policy uncertainty (Baker and others 2013), direct consumer survey data (Leduc

### Key definitions and theoretical framework
- Uncertainty is given a structural interpretation following Bloom and others (2012): an increase in the variance of underlying shocks to the economy.
- Firm-level production specification:
  - y_t,j = A_t f_t,j(k_{t,j}, l_{t,j}) where A_t is aggregate productivity and z_{t,j} is idiosyncratic productivity.
  - Log autoregressive processes:
    - log(A_t) = ρ_A log(A_{t-1}) + σ_A,t ε_{t-1} (notation preserved from source)
    - log(z_{t,j}) = ρ_Z log(z_{t-1,j}) + σ_Z,t ε_{t-1,j}
  - A_t σ and Z_t σ stand for time-varying aggregate and idiosyncratic uncertainty.
- Aggregate uncertainty: all firms affected by more volatile shocks.
- Idiosyncratic/sectoral uncertainty: larger productivity dispersion across firms/industries.
- Hypothesized channels:
  - Wait-and-see (investment/hiring scaled back when uncertainty rises).
  - Reallocation costs: inter-industry labor reallocation is more costly than intra-industry reallocation; sectoral shocks can increase unemployment via costly reallocation.

### Construction of uncertainty indices (U.S. stock market)
- Aggregate uncertainty index:
  - Defined as the realized volatility of the S&P500 index returns.
  - Quarterly construction:
    - RV_t = [ (1/S) Σ_s (R_{t,s} - R_t)^2 ]^{1/2} annualized by factor 252^{1/2} (formula notation preserved).
    - S = number of trading days in the quarter; R_{t,s} = market returns on day s; R_t = average market returns during quarter.
  - Note: not aggregated from monthly frequency to avoid mechanical reduction in volatility.
- Sectoral (cross-industry) uncertainty index:
  - Regress industry returns R_{t,i} on market returns R_t: R_{t,i} = α_i + β_i R_t + ε_{t,i}.
  - Compute excess-return residuals: η_{t,i} = α̂_i + ε̂_{t,i} (notation preserved).
  - Sectoral index: WCSV_t = [ (1/n) Σ_i (η_{t,i} - η_t)^2 ]^{1/2} weighted by industry employment shares i_W.
  - Uses quarterly industry returns to capture long-term swings; controls for different betas across industries.

- Distributional statistics and persistence (indices normalized to same mean and variance for comparison):
  - Aggregate index: skewness = 3.30; kurtosis = 20.27.
  - Sectoral index: skewness = 1.71; kurtosis = 7.04.
  - AR(1) coefficients (persistence): aggregate uncertainty index: 0.58; sectoral uncertainty index: 0.53.
  - Correlation between indices: 0.54.

### Empirical approach: structural VAR
- Sample: quarterly U.S. data from 1957Q1 to 2014Q3.
- Baseline VAR variables (7-variable baseline): stock market returns (S&P500 returns), aggregate uncertainty index, sectoral uncertainty index, inflation, federal funds rate, real GDP growth, unemployment rate.
- System ordering (recursive/Cholesky): stock market returns → two uncertainty indices → inflation → federal funds rate → real GDP growth → unemployment rate.
- Lag length: 4 (quarterly data); also re-estimated with 8 lags for robustness.
- Identification: evaluate marginal role of each uncertainty index by controlling for the other; identification assumption described for orthogonalization when evaluating CSV vs RV.
- Standard errors: parametric bootstrap with 500 repetitions.
- Parsimonious VAR variant: 4-variable model including real GDP growth, both uncertainty indices, and unemployment rate (used in robustness checks).

### Main empirical findings: effects on unemployment and macro variables
- Qualitative effects:
  - Aggregate and sectoral uncertainty shocks have similar qualitative effects on inflation, federal funds rate, GDP growth, and unemployment consistent with uncertainty shocks behaving like a negative aggregate demand shock.
  - Responses of inflation and federal funds rates are statistically insignificant for aggregate shocks; sectoral shocks share similar dynamics.
- Unemployment responses (marginal effects of one standard deviation uncertainty shocks):
  - Aggregate uncertainty shock:
    - Instant increase in unemployment: 0.06 percentage point.
    - Becomes statistically insignificant after three quarters.
    - Forecast-error-variance decomposition: explains only 1.5 percent of variance in unemployment forecast errors (over 20 quarters).
    - Pattern: variation explained decreases monotonically with unemployment duration.
  - Sectoral uncertainty shock:
    - Instant increase in unemployment: nearly 0.2 percentage point.
    - Effect remains statistically significant for more than three years.
    - Forecast-error-variance decomposition: explains approximately 15 percent of variance in unemployment forecast errors (over 20 quarters).
    - Pattern: proportion of variance explained increases monotonically with unemployment duration.
    - Sectoral shocks explain virtually none of short-term unemployment variation but explain more than 30 percent of forecast-error variance when unemployment lasts longer than 26 weeks.
- Long-term unemployment and the Great Recession:
  - Long-term unemployment share: 18 percent of total unemployment in 2007Q4; 32 percent in 2014Q3.
  - VAR analysis (2007Q4 baseline, horizon to 2014Q3 = 27 quarters):
    - Baseline projection: conditional expectation for long-term unemployment as of 2007Q4.
    - Contribution decomposition: sectoral uncertainty shocks emerge as important in explaining realized deviations from baseline; aggregate uncertainty shocks contribute little.
    - Conservative identification: aggregate uncertainty index placed before sectoral index in VAR.

### Robustness checks and additional results
- Subsample and period tests:
  - Estimation on 1984Q1–2014Q3:
    - Effect of aggregate uncertainty shocks declines substantially (consistent with Beetsma and Giuliodori 2012; Choi 2013).
    - Effect of sectoral uncertainty shocks remains strong.
  - Estimation on 1984Q1–2007Q4 (dropping Great Recession):
    - Persistent effect of sectoral uncertainty shocks on unemployment remains.
- Model specification checks:
  - Parsimonious 4-variable VAR (real GDP growth, both uncertainty indices, unemployment): sectoral uncertainty shocks still have a strong and persistent effect on unemployment even after controlling for real GDP growth.
  - Reverse ordering of VAR (placing uncertainty indices at the end of Cholesky ordering) yields more conservative estimates:
    - Aggregate uncertainty: statistically significant effect on unemployment only in short term.
    - Sectoral uncertainty: significant effect up to three years.
  - Increasing lags to 8: qualitative results remain similar.
- Additional methodological notes:
  - Results robust when estimating model in levels with quadratic trends (impacts decrease somewhat but remain statistically significant).
  - Skewness and kurtosis differences indicate aggregate index contains more extreme values.

### Conclusions and implications
- Main conclusion:
  - Aggregate uncertainty shocks have short-lived impacts on U.S. unemployment.
  - Sectoral (cross-industry) uncertainty shocks have more significant and persistent impacts, particularly relevant for long-term unemployment dynamics.
- Interpretations linked to theoretical channels:
  - Aggregate uncertainty effects align with wait-and-see option value (short-lived response).
  - Sectoral uncertainty effects align with costly inter-industry reallocation leading to persistent and long-term unemployment increases.
- Suggested future research direction:
  - Develop an integrated model that jointly evaluates both types of uncertainty to strengthen understanding of independent channels through which aggregate and sectoral uncertainty affect unemployment.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1536.pdf*

### REFERENCES

### _wp1536 - REFERENCES

### References cited
- Bibliographic compilation of research on uncertainty, sectoral shifts, investment, unemployment, stock market volatility, and macroeconomic dynamics. Key recurring authors and themes include:
  - Uncertainty and its macroeconomic effects (e.g., Bloom; Baker, Bloom, and Davis; Jurado, Ludvigson, and Ng; Caldara et al.).
  - Sectoral shifts and cyclical unemployment (e.g., Abraham and Katz; Brainard and Cutler; Lilien; Shin).
  - Investment under uncertainty and irreversibility (e.g., Bernanke; Dixit and Pindyck; Abel and Eberly; Caballero and Engel).
  - Stock market volatility and its macroeconomic links (e.g., Schwert; Hamilton and Lin; Campbell and Hentschel).
  - Methodological contributions on measuring uncertainty and decomposing shocks (e.g., Beetsma and Giuliodori; Fernández-Villaverde et al.; Leduc and Liu).

### Figures and empirical output (listed)
- Figure 1. Uncertainty Index
- Figure 2. Distribution of Aggregate and Sectoral Uncertainty Indices
  - Plot labels include "Aggregate Uncertainty" and "Sectoral Uncertainty" with Density vertical axis and range indicators like 0 .2 .4 .6 and horizontal label "-202468".
- Figure 3. Unemployment Rate (Percent)
- Figure 4. Response to Aggregate Uncertainty Shocks (7 Variable VAR)
- Figure 5. Response to Sectoral Uncertainty Shocks (7 Variable VAR)
- Figure 6. Forecast Error Decomposition of Unemployment Rate by Aggregate Uncertainty
- Figure 7. Forecast Error Decomposition of Unemployment Rate by Sectoral Uncertainty
- Figure 8. The Response of the Long-term Unemployment Rate to Uncertainty Shocks
- Figure 9. Contribution of Uncertainty Shocks to the Long-term Unemployment Rate during the Great Recession (%)
- Figure 10A. Robustness Check: Estimation with Data from 1984Q1 to 2014Q3
- Figure 10b. Robustness Check: Estimation with Data from 1984Q1 to 2007Q4
- Figure 11. Robustness Check: 4 Variable VAR
- Figure 12. Robustness Check: The Reverse Ordering of the Baseline VAR System
- Figure 13. Robustness Check: Using 8 Lags instead of 4 Lags

### Appendix A — Construction of the Sectoral Uncertainty Index
- Baseline coverage and data constraints:
  - Baseline series cover 1957Q1 to 2014Q3.
  - Disaggregated industry-level employment data are consistently available only after 1990.
- Main challenges and methodological responses:
  - Industry composition changes over time in the S&P500 Composite Index; authors obtain dates of changes in the S&P to account for this.
  - Weights are based on BLS employment data using SIC industry codes, but S&P500 industry-level indexes do not correspond exactly to SIC codes.
    - The procedure: determine weights by two-digit SIC codes and divide the weight evenly among the component industries at the end of the sample period.
    - Example: if one S&P500 industry at the end of the sample consists of ten firms, including six firms in one two-digit industry, three in another, and one in a third, then the employment-share weight for that S&P500 industry is computed as the weighted average of the employment shares of the three two-digit SIC industries for each period with weights 0.6, 0.3, and 0.1 respectively.
  - Because disaggregated employment data are consistently available only after 1990, the authors use the average of employment share of two-digit SIC codes between 1990 and 2009.
  - Weights are not time-varying and thus can be subject to bias in a time trend; however, the sectoral uncertainty index based on the average employment share and the unweighted index are highly correlated.
    - The correlation between indices based on different employment weights exceeds 0.9.
- Coverage of industries in the index:
  - The index contains only S&P500 industry indexes included in the composite at the end of the sample period.
  - S&P500 industries added to the S&P500 Composite were excluded, resulting in 50 U.S. industries at the end of the sample period.
- Additional notes:
  - Table A.1 (not reproduced here) shows the name of industry, S&P500 industry code, starting date, and employment share, when applicable.

*Source: _wp1536 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1536.pdf_