## wpiea2019167-print-pdf

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---

### Introduction
- Output gap defined as the difference between actual and potential output; potential output equals the maximum level without generating inflationary pressures (Okun, 1962).
- Output gap estimates inform fiscal and monetary policy to keep the economy at full potential while avoiding inflationary pressures.
- Labor market slack is a key determinant of the output gap; tight labor markets create upward pressure on wages and prices, idle labor market resources reduce output and inflationary pressures.
- In Korea, traditional unemployment measures weakly capture cyclical labor market conditions; the Phillips curve relationship between inflation and unemployment is relatively weak (Bhattarai, 2016).
- Two reasons traditional unemployment may understate slack:
  - Excludes workers outside the labor force who are ready to work (discouraged workers).
  - Excludes part-time workers who wish to work longer hours (involuntary part-time workers).
- Paper introduces a broader labor market slack measure including discouraged workers and uses two multivariate filter (MVF) models to estimate revised output gaps:
  - MVF model 1: simple production function with augmented unemployment and an estimated TFP gap (based on Blagrave et al., 2015).
  - MVF model 2: augmented unemployment plus capacity utilization (based on Alichi et al., 2017).
- Result: output gap estimates using the augmented measure are more negative than those derived using traditional unemployment.

### Measuring Labor Market Slack
- Traditional unemployment in Korea (survey data) broadly stable around 3-4 percent of the labor force since 1980, with a spike to 7 percent during the Asia crisis in 1998-99.
- International definition of unemployment requires (i) without work, (ii) available to start within two weeks, (iii) actively searching (International Labor Organization, 2018).
- Broader definitions:
  - Intensive margin: discouraged workers (without work but not able to start within two weeks or not actively searching).
  - Extensive margin: involuntary part-time workers (want more hours).
- Constructed broader measure by augmenting traditional unemployment with discouraged workers (expressed in percent of the labor force plus discouraged workers).
- Characteristics of the broader measure:
  - Hovers around 5 percent.
  - Variance at business cycle frequency approximately twice that of regular unemployment.
  - Variance values: unemployment = 0.06; augmented unemployment = 0.11 (business cycle frequency defined as deviation from HP-filtered trend with lambda = 6.25).
  - Comparable to "Labor Utilization Indicator 2" published by Statistics Korea.
- Data issue: level break in discouraged workers series in 2014; series spliced by backing out pre-2014 levels using growth rate of earlier series.
- Phillips curve evidence:
  - Traditional unemployment vs. core inflation: weak/non-negative relationship since 2001.
  - Augmented unemployment vs. core inflation: downward-sloping Phillips Curve since 2001 (regression y = -0.1846x + 5.2796, R² = 0.1144 for 2001-18).

### Output Gap Estimates Using a Multivariate Filter
- Period covered: 2007-2023 using broader labor market slack.
- MVF model (modified Blagrave et al., 2015) includes a TFP gap to capture innovations in trend productivity.
- Data: annual data from 2001 for GDP, inflation, employment, TFP, unemployment, and alternative labor slack measures; historical data up to 2017, estimate for 2018, and forecast for 2019-23 from April 2019 WEO.
- Estimation: Bayesian estimation; priors for Korea based on Blagrave et al. (2015).
- Steady-state parameter values:
  - Steady state level for TFP growth set equal to historical average of 1.5 percent.
  - Steady state level for structural component of underutilized labor market resources set equal to historical average labor market slack: 3.4 percent (regular unemployment) and 5.5 percent (broader measure).
- Key findings:
  - Output gap based on broader labor market slack is generally more negative than that based on traditional unemployment.
  - Both measures show a positive output gap before the Global Financial Crisis (GFC); both turn negative during the GFC.
  - Augmented measure yields a more negative output gap during the GFC and does not turn positive immediately after the GFC, reflecting slow labor market recovery.
  - Augmented measure produces a more negative output gap in recent years, suggesting aggregate demand insufficient to reach full potential.
- Inflation context:
  - Headline and core inflation mostly below target since 2012 with brief exceptions.
  - Negative and persistent output gap consistent with prolonged low inflation via reduced wage pressures.

### Multivariate Filter with Capacity Utilization
- Motivation: TFP is unobservable and its estimation is uncertain; alternative MVF excludes a TFP gap and uses observed capacity utilization as an additional signal for potential output (Alichi et al., 2017).
- Estimation uses the augmented labor market slack including discouraged workers.
- Findings:
  - After the GFC, estimated output gap widened to about -2 percent and quickly closed in 2010 while unemployment gap remained negative longer.
  - Discrepancy explained by a sharp surge in capacity utilization immediately after the crisis (strong rebound in demand) while labor market recovery was slower.
  - By 2018, estimated output gap remained negative, reflecting deterioration of labor market slack and capacity underutilization in the industrial sector.

### Uncertainty in Estimating the Output Gap and Potential
- Sources of uncertainty: (i) model choice, (ii) model parameters, (iii) quality and quantity of information.
- Robustness assessment: construct confidence bands around output gap estimates and compare MVF with HP filter using methodology from Blagrave et al. (2015) and Alichi et al. (2017).
- Monte Carlo simulation design:
  - 1000 draws of all variables from the model for a sufficiently-long period (1000 years).
  - First 500 draws discarded to alleviate burn-in bias.
  - HP filter applied with signal-noise ratio = 6.25 to GDP series in each sample.
  - Deviations of HP filter estimates of potential growth and output gap from the assumed true path computed for 77 percent and 98 percent demand shocks (typical values in literature for emerging markets and advanced economies).
  - Similar steps implemented for MVF to allow fair comparison.
- Confidence band results:
  - Average 95 percent confidence bands for potential growth and for the output gap compared MVF vs HP.
- MVF standard errors (uncertainty magnitudes):
  - Standard error around potential growth:
    - "more than 0.8 percent" for a 77 percent demand shock
    - "only 0.3 percent" for a 98 percent demand shock
  - Standard error around the output gap:
    - 1.4 percent for the 77 percent demand shock
    - 0.9 percent for the 98 percent demand shock
  - Interpretation: these magnitudes "suggest that the estimates should be taken with caution."
- Comparison with HP filter:
  - Confidence bands around estimates of potential output and the output gap from the MVF are narrower than those from an HP filter, "regardless of the choice of shocks."
  - Conclusion: this result "confirms the theoretical and empirical literature" that a MVF is superior to a univariate filter given a richer information set.

### MVF Specifications and Model Structure
- Two MVF models:
  - Model 1: output gap tied with labor market slack using a production function and TFP shocks.
  - Model 2: output gap estimated using both labor market slack and capacity utilization.
- MVF model structure (key components):
  - Core production function: Cobb-Douglas with inputs capital (K), employment (E), and total factor productivity (A).
  - Employment E replaced by potential labor force (PLF) times non-employed fraction U; PLF and U definitions vary with labor slack measure.
  - Output gap (y) decomposed as sum of TFP gap (a) and labor market slack (U) plus stochastic shocks.
  - TFP process: trend component stochastic with long-term deterministic growth rate ܩௌௌ = 1.5 percent and stochastic shocks.
  - Structural underutilization steady states: ܷഥ௦௦ = 3.4/5.5/10.7 percent corresponding to different labor slack definitions.
  - A New Keynesian Phillips curve links the output gap to inflation, including current, future, and past inflation, output gap term, and a shock term.

### Parametrization, Estimation, and Key Coefficients
- Long-run steady state levels:
  - ܩௌௌ: 1.5 percent
  - ܷഥ௦௦: 3.4/5.5/10.7 percent
- Selected posterior estimates (Table D.2) for model with regular unemployment measure:
  - ߙ: Prior 0.3 | Posterior 0.3
  - ߶: Prior 0.6 | Posterior 0.56
  - ߠ: Prior 0.10 | Posterior 0.13
  - ߣ: Prior 0.25 | Posterior 0.34
  - ߚ: Prior 0.25 | Posterior 0.29
  - ߬ସ: Prior 0.10 | Posterior 0.10
  - ߬ଷ: Prior 0.10 | Posterior 0.10
  - ߬ଶ: Prior 0.20 | Posterior 0.25
  - Std(߳௧௒): Prior 0.80 | Posterior 0.79
  - ߳(݀ݐܵ௧஺̅): Prior 0.20 | Posterior 0.196
  - ߳(݀ݐܵ௧ீ): Prior 0.20 | Posterior 0.198
  - ߳(݀ݐܵ௧గ): Prior 0.25 | Posterior 0.466
  - ߳(݀ݐܵ௧ௌ̅): Prior 0.10 | Posterior 0.09
  - ߳(݀ݐܵ௧௚ௌ̅): Prior 0.50 | Posterior 0.49
  - ߳(݀ݐܵ௧௨): Prior 0.49 | Posterior 0.49

### Use of Consensus Forecasts and Data Notes
- Use of consensus forecasts to improve end-of-sample expectations:
  - Output growth expectations: Consensus Economics forecasts five years ahead starting from the end of historical observations.
  - CPI inflation: Consensus Economics one year ahead forecasts.
  - Consensus forecasts benchmarked against model-consistent forward-looking expectations; their "signaling power" determined by historical standard deviations of error terms and can be tuned.
- Data sources:
  - OECD, IMF, and Statistics Korea
  - Real GDP, inflation, employment, and unemployment: IMF’s World Economic Outlook
  - Capital stock: OECD Economic Outlook
- TFP computation:
  - Backed out using production function ܭܣ = ܻ ஈ ܮ ଵିఈ with OECD data for capital and employment and assumption ߙ = 0.3
- Discouraged workers series:
  - Data from Statistics Korea; "level break in the time series for discouraged workers in 2014"; series spliced by "backing out the levels prior to 2014 using the growth rate of the earlier time series."

### Policy Implications and Official Measures
- Policy implications:
  - Using the broader measures of labor market slack suggests "the Korean economy has not yet reached a point where inflationary pressures are significant," implying "policies can remain accommodative for a longer."
- Official published broader measures (Statistics Korea):
  - Labor Underutilization Indicator 1: augments unemployment along the intensive margin (part-time workers willing to work longer hours); expressed in percent of the total labor force.
  - Labor Underutilization Indicator 2: augments unemployment along the extensive margin (workers potentially in the labor force); expressed as a share of the labor force extended with the potential labor force.
  - Labor Underutilization Indicator 3: extends unemployment along both intensive and extensive margins (involuntary part-time + potentially in labor force).
  - Effect on measured slack: these indicators "lift the measure of labor market slack from around 4 percent to up to 12 percent."
  - Data limitation: "The period for the measures is too short to make them useful as input to the model presented in section II."
  - Figure metadata: "Latest observation: July 2018."

*Source: wpiea2019167-print-pdf - References (extracted content).*

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

### wpiea2019167-print-pdf - References

### Introduction
- Output gap defined as the difference between actual and potential output; potential output equals the maximum level without generating inflationary pressures (Okun, 1962).
- Output gap estimates inform fiscal and monetary policy to keep the economy at full potential while avoiding inflationary pressures.
- Labor market slack is a key determinant of the output gap; tight labor markets create upward pressure on wages and prices, idle labor market resources reduce output and inflationary pressures.
- In Korea, traditional unemployment measures weakly capture cyclical labor market conditions; the Phillips curve relationship between inflation and unemployment is relatively weak (Bhattarai, 2016).
- Two reasons traditional unemployment may understate slack:
  - Excludes workers outside the labor force who are ready to work (discouraged workers).
  - Excludes part-time workers who wish to work longer hours (involuntary part-time workers).
- This paper introduces a broader labor market slack measure including discouraged workers and uses two multivariate filter (MVF) models to estimate revised output gaps:
  - MVF model 1: simple production function with augmented unemployment and an estimated TFP gap (based on Blagrave et al., 2015).
  - MVF model 2: augmented unemployment plus capacity utilization (based on Alichi et al., 2017).
- Result: output gap estimates using the augmented measure are more negative than those derived using traditional unemployment.

### Measuring Labor Market Slack
- Traditional unemployment in Korea (survey data) has been broadly stable around 3-4 percent of the labor force since 1980, with a spike to 7 percent during the Asia crisis in 1998-99.
- International definition of unemployment requires (i) without work, (ii) available to start within two weeks, (iii) actively searching (International Labor Organization, 2018).
- Broader definitions include:
  - Intensive margin: discouraged workers (without work but not able to start within two weeks or not actively searching).
  - Extensive margin: involuntary part-time workers (want more hours).
- Broader measure constructed by augmenting traditional unemployment with discouraged workers (expressed in percent of the labor force plus discouraged workers).
- Characteristics of the broader measure:
  - Hovers around 5 percent.
  - Variance at business cycle frequency approximately twice that of regular unemployment.
  - Variance values: unemployment = 0.06; augmented unemployment = 0.11 (business cycle frequency defined as deviation from HP-filtered trend with lambda = 6.25).
  - Comparable to "Labor Utilization Indicator 2" published by Statistics Korea.
- Data issue: level break in discouraged workers series in 2014; series spliced by backing out pre-2014 levels using growth rate of earlier series.
- Phillips curve evidence:
  - Traditional unemployment vs. core inflation: weak/non-negative relationship since 2001 (Figure 3a).
  - Augmented unemployment vs. core inflation: downward-sloping Phillips Curve since 2001 (regression y = -0.1846x + 5.2796, R² = 0.1144 shown for modified Phillips curve in 2001-18).

### Output Gap Estimates Using a Multivariate Filter
- Period covered: 2007-2023 using broader labor market slack.
- MVF model (Appendix B) is a modified Blagrave et al. (2015) model including a TFP gap to capture innovations in trend productivity.
- Data: annual data from 2001 for GDP, inflation, employment, TFP, unemployment, and alternative labor slack measures; historical data up to 2017, estimate for 2018, and forecast for 2019-23 from April 2019 WEO.
- Estimation: Bayesian estimation; priors for Korea based on Blagrave et al. (2015).
- Steady-state parameter values:
  - Steady state level for TFP growth set equal to historical average of 1.5 percent.
  - Steady state level for structural component of underutilized labor market resources set equal to historical average labor market slack: 3.4 percent (regular unemployment) and 5.5 percent (broader measure).
- Key findings:
  - Output gap based on broader labor market slack is generally more negative than that based on traditional unemployment (Figure 4).
  - Both measures show a positive output gap before the Global Financial Crisis (GFC); both turn negative during the GFC.
  - Augmented measure yields a more negative output gap during the GFC and does not turn positive immediately after the GFC, reflecting slow labor market recovery.
  - Augmented measure also produces a more negative output gap in recent years, suggesting aggregate demand insufficient to reach full potential.
- Inflation context:
  - Headline and core inflation mostly below target since 2012 with brief exceptions (Figure 5).
  - Negative and persistent output gap consistent with prolonged low inflation via reduced wage pressures.

### Multivariate Filter with Capacity Utilization
- Motivation: TFP is unobservable and its estimation is uncertain; alternative MVF excludes a TFP gap and uses observed capacity utilization as an additional signal for potential output (Alichi et al., 2017).
- Estimation uses the augmented labor market slack including discouraged workers.
- Findings:
  - After the GFC, estimated output gap widened to about -2 percent and quickly closed in 2010 while unemployment gap remained negative longer.
  - Discrepancy explained by a sharp surge in capacity utilization immediately after the crisis (strong rebound in demand) while labor market recovery was slower.
  - By 2018, estimated output gap remained negative, reflecting deterioration of labor market slack and capacity underutilization in the industrial sector (Figure 6).

### Uncertainty in Estimating the Output Gap and Potential
- Sources of uncertainty: (i) model choice, (ii) model parameters, (iii) quality and quantity of information.
- Robustness assessment: construct confidence bands around output gap estimates and compare MVF with HP filter using methodology from Blagrave et al. (2015) and Alichi et al. (2017).
- Monte Carlo simulation design:
  - 1000 draws of all variables from the model for a sufficiently-long period (1000 years).
  - First 500 draws discarded to alleviate burn-in bias.
  - HP filter applied with signal-noise ratio = 6.25 to GDP series in each sample.
  - Deviations of HP filter estimates of potential growth and output gap from the assumed true path computed for 77 percent and 98 percent demand shocks (typical values in literature for emerging markets and advanced economies).
  - Similar steps implemented for MVF to allow fair comparison.
- Confidence band results:
  - Average 95 percent confidence bands for potential growth shown in Figure 7 (comparison MVF vs HP).
  - Average 95 percent confidence bands for output gap shown in Figure 8 (comparison MVF vs HP).
- Note: MVF has an analytical covariance matrix, but Monte Carlo simulations were used to enable direct comparison with HP filter.

*Source: wpiea2019167-print-pdf - References (extracted content).*

### 19.      The estimates of potential growth and output gap coming from the MVF are

### 19.      The estimates of potential growth and output gap coming from the MVF are

### Uncertainty in MVF estimates
- Standard error around potential growth:
  - "more than 0.8 percent" for a 77 percent demand shock
  - "only 0.3 percent" for a 98 percent demand shock
- Standard error around the output gap:
  - 1.4 percent for the 77 percent demand shock
  - 0.9 percent for the 98 percent demand shock
- Interpretation:
  - These magnitudes "suggest that the estimates should be taken with caution."

### Comparison with HP filter
- Confidence bands:
  - Confidence bands around estimates of potential output and the output gap from the MVF are narrower than those from an HP filter, "regardless of the choice of shocks."
- Conclusion:
  - This result "confirms the theoretical and empirical literature" that a MVF is superior to a univariate filter given a richer information set.

### Broader measure of labor market slack and implications
- Motivation:
  - Traditional labor market slack measure: unemployment rate — "well-defined" but incomplete.
  - Does not capture workers outside the labor force who are able and willing to work but not engaged in active job search (discouraged workers).
- Constructed alternative:
  - Augment regular unemployment with discouraged workers to form a broader measure of labor market slack.
- Empirical implication:
  - The broader measure produces the expected negative relationship between unemployment and inflation (a downward-sloping Phillips curve), "unlike the traditional measure of unemployment."

### MVF specifications and estimation of the output gap
- Two MVF models used to estimate Korea's output gap:
  - Model 1: output gap tied with labor market slack using a production function and TFP shocks.
  - Model 2: output gap estimated using both labor market slack and capacity utilization.
- Effects of using the broader labor slack measure:
  - Augmenting unemployment with discouraged workers makes the estimated output gap "more negative in recent years."
    - Interpretation: "there is more idle capacity in the economy than suggested by the standard measure of unemployment."
  - The unemployment gap computed using broader measures of labor market utilization displays "higher variation at business cycle frequency."

### Policy implications
- Using the broader measures of labor market slack suggests:
  - "the Korean economy has not yet reached a point where inflationary pressures are significant,"
  - implying "policies can remain accommodative for a longer."

### Official published broader measures (Statistics Korea)
- Statistics Korea publishes three alternative measures of labor market slack (available since the first quarter of 2015):
  - Labor Underutilization Indicator 1: augments unemployment along the intensive margin (part-time workers willing to work longer hours); expressed in percent of the total labor force.
  - Labor Underutilization Indicator 2: augments unemployment along the extensive margin (workers potentially in the labor force); expressed as a share of the labor force extended with the potential labor force.
  - Labor Underutilization Indicator 3: extends unemployment along both intensive and extensive margins (involuntary part-time + potentially in labor force).
- Effect on measured slack:
  - These indicators "lift the measure of labor market slack from around 4 percent to up to 12 percent."
- Data limitation:
  - "The period for the measures is too short to make them useful as input to the model presented in section II." Model estimates rely on the constructed measure in Section II.
- Figure metadata:
  - "Latest observation: July 2018."

### MVF model structure (key equations and components)
- Core production function:
  - Cobb-Douglas with inputs capital (K), employment (E), and total factor productivity (A).
- Employment representation:
  - Employment E replaced by potential labor force (PLF) times non-employed fraction U; definition of PLF and U varies with the chosen labor slack measure.
- Output gap decomposition:
  - Output gap (y) written as sum of TFP gap (a) and labor market slack (U) (see equation (3’) in source).
  - Output gap is allowed to be affected by stochastic shocks (error term ߳).
- TFP process:
  - Trend component of TFP modelled as stochastic with:
    - long-term deterministic growth rate ܩௌௌ
    - stochastic level shock ߳௧஺̅
    - stochastic growth shock ߳௧ீ
  - Long-run growth rate (Table D.1): ܩௌௌ = 1.5 percent
- Structural underutilization process:
  - Structural level governed by long-run steady state ܷഥ௦௦ and affected by transitory shocks (߳௧௎ഥ) and a stochastic trend (ܷ݃ഥ௧).
  - Long-run steady states for Korea (Table D.1): ܷഥ௦௦ = 3.4/5.5/10.7 percent (three alternative steady-state values corresponding to different labor slack definitions).
- Labor market gap:
  - Defined as difference between actual and structural underutilization of labor market resources, with its own stochastic shock process.
- Phillips Curve:
  - A New Keynesian Phillips curve links the output gap to inflation, including current, future, and past inflation, output gap term, and a shock term.

### Use of consensus forecasts to improve end-of-sample expectations
- Consensus inputs:
  - Output growth expectations: Consensus Economics forecasts five years ahead starting from the end of historical observations.
  - CPI inflation: Consensus Economics one year ahead forecasts.
- Implementation:
  - Consensus forecasts (model inputs) are benchmarked against model-consistent forward-looking expectations; their "signaling power" is determined by historical standard deviations of error terms and can be tuned.

### Alternative MVF with capacity utilization (Appendix C)
- Okun’s law variant:
  - Output gap written as a function of the augmented labor market gap and stochastic term (equation (4a)).
- Capacity utilization role:
  - Manufacturing capacity utilization used to gauge capital slack and signal labor market state in Korea's context.
- Capacity utilization system:
  - Equations (3a), (5a), (6a), (6b) describe dynamics of capacity utilization, equilibrium capacity utilization rate, its change term, shocks, and the capacity utilization gap correlated with overall economic slack.

### Parametrization and estimated coefficients (Appendix D)
- Parameter types:
  - Long-run steady state levels: computed using long-run averages.
  - Model coefficients and shock variables: estimated by Bayesian methods; priors from Blagrave et al (2017); posteriors presented in Table D.2.
- Table D.1: Long Run Steady State Levels (Korea)
  - ܩௌௌ: 1.5 percent
  - ܷഥ௦௦: 3.4/5.5/10.7 percent
- Table D.2: Model Coefficients [for model with regular unemployment measure] — Prior and Posterior (Korea)
  - ߙ: Prior 0.3 | Posterior 0.3
  - ߶: Prior 0.6 | Posterior 0.56
  - ߠ: Prior 0.10 | Posterior 0.13
  - ߣ: Prior 0.25 | Posterior 0.34
  - ߚ: Prior 0.25 | Posterior 0.29
  - ߬ସ: Prior 0.10 | Posterior 0.10
  - ߬ଷ: Prior 0.10 | Posterior 0.10
  - ߬ଶ: Prior 0.20 | Posterior 0.25
  - Std(߳௧௒): Prior 0.80 | Posterior 0.79
  - ߳(݀ݐܵ௧஺̅): Prior 0.20 | Posterior 0.196
  - ߳(݀ݐܵ௧ீ): Prior 0.20 | Posterior 0.198
  - ߳(݀ݐܵ௧గ): Prior 0.25 | Posterior 0.466
  - ߳(݀ݐܵ௧ௌ̅): Prior 0.10 | Posterior 0.09
  - ߳(݀ݐܵ௧௚ௌ̅): Prior 0.50 | Posterior 0.49
  - ߳(݀ݐܵ௧௨): Prior 0.49 | Posterior 0.49

### Data and practical notes (Appendix E)
- Data sources:
  - OECD, IMF, and Statistics Korea
  - Real GDP, inflation, employment, and unemployment: IMF’s World Economic Outlook
  - Capital stock: OECD Economic Outlook
- TFP computation:
  - Backed out using production function ܭܣ = ܻ ஈ ܮ ଵିఈ with OECD data for capital and employment and assumption ߙ = 0.3
- Discouraged workers series:
  - Data on discouraged workers and other non-active persons from Statistics Korea
  - There is a "level break in the time series for discouraged workers in 2014"; series were spliced by "backing out the levels prior to 2014 using the growth rate of the earlier time series."

*Source: wpiea2019167-print-pdf - 19.      The estimates of potential growth and output gap coming from the MVF are (IMF working paper content provided in the source content).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019167-print-pdf.pdf_