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---

### Dataset: Burning Glass Technologies (BGT)
- Coverage:
  - Tracks online vacancy postings from over 45,000 online job boards; removes duplicates and cleans data.
  - Covers the near universe (≈70%) of all U.S. online vacancy postings.
  - Comprises ≈250 million job vacancy postings for the years of 2007 and 2010-2019.
  - All postings include date posted, employer name, and FIPS county code; analysis uses Commuting Zones rather than counties.
  - NAICS industry and ONET occupation breakdowns; many vacancies list education or software skill requirements.
- Reporting and imputation:
  - Education reported for approximately half of vacancies; when missing, imputed within the finest occupational breakdown.
  - Wage information reported for 17% of vacancies; midpoint used when a wage range is listed.
  - Wage data reflect annual compensation and exclude bonuses and other benefits.
- Aggregation and unit of analysis:
  - Vacancy-level data collapsed into a panel of firm-commuting zone-quarter observations (establishment-level).
  - Over 15 million firm-commuting zone-quarter observations.
  - Over 380,000 firms.
  - Just over 700 commuting zones.
  - Average commuting zone has postings from 22,000 firms (unevenly distributed).
  - Average firm posts in 170 commuting zones.
- Strengths and limitations:
  - Strengths: extensive coverage, time-stamped posting dates, location identifiers, direct firm postings.
  - Limitations: online postings not fully representative; over-representation of industries (e.g., IT, Education); wage reporting limited to 17%; smaller firms and lower-skill occupations less likely to report wages.

### Compustat merge and cleaning
- Merge procedure:
  - Aggregate BGT vacancies to firm level and fuzzy-merge BGT firm names to Compustat using string cleaning and two-layered matching (exact + Jaro-Winkler).
- Matching results (2008–2019):
  - 8,231 firm matches from 14,983 firms in Compustat.
  - 3,217 exact matches.
  - 5,014 matched using Jaro-Winkler fuzzy matching (string distance threshold of 0.11).
  - Merged companies represent 75% of sales, and 73% of employment of all companies in Compustat.
- Compustat cleaning steps (following Ottonello and Winberry(2020)):
  - Keep only corporations incorporated in the US.
  - Drop firms in the financial and utilities sectors.
  - Drop firm-quarter observations with acquisitions larger than 5 percent of assets.
  - Drop firm-quarter observations where the investment rate is in the top and bottom 1 percent of the distribution.
  - Drop observations where the investment spell is shorter than 40 quarters.
  - Drop firm–quarter observations where liquidity, debt, and sales are outliers.
  - Drop firms with less than 10 million US dollars in assets and firms that are in the sample less than 5 years.
  - Linearly interpolate annual employment data to quarterly data.

### Monetary policy shocks (measures and usage)
- Baseline shocks:
  - Jarociński and Karadi(2020) — JK 2020, focusing on interest rate surprises in the three-month fed funds future.
  - JK 2020 separates pure monetary policy shocks from “Fed information” shocks; Fed information shocks used as a control.
- Robustness alternatives:
  - Nakamura and Steinsson(2018): principal component across yield curve (one-month to two-year).
  - Jarociński(2021): four shocks (standard monetary policy shock plus three orthogonal shocks).
  - Bu et al.(2021): include unconventional policy via a Fama-MacBeth two-step procedure.
- Time-series note:
  - Monetary policy shocks exhibit both significant tightening and loosening; largest tightening and loosening shocks in the sample occurred in 2007; global financial crisis-related loosening cycle started in August 2007.

### Definition and measurement of Labor Market Power (LMP)
- Baseline measure:
  - LMP_{i,c,t} = Vacancy Share_{i,c,t} = (Σ_{τ≤t} v_{i,c,τ}) / (Σ_{τ≤t} Σ_{i} v_{i,c,τ}), where v_{i,c,τ} are vacancies by firm i in commuting zone c at time τ.
  - Local labor market defined as a U.S. census commuting zone.
  - Cumulative vacancy shares used to reduce endogeneity and account for firms that do not post consecutively.
- High-LMP firms:
  - Defined as firms above the 95th percentile across the full distribution of firm-CZ-time observations.
- Vacancy share distribution statistics:
  - Average vacancy share is 0.8%.
  - Median vacancy share is 0.1%.
  - 95th percentile vacancy share is 3.7%.
- Alternative measure:
  - Herfindahl-Hirschman Index (HHI) of vacancy postings at commuting zone level: Σ_{i} (Vacancy Share_{i,c,t})^2.

### Empirical relationship: LMP and posted wages
- Cross-sectional pattern:
  - Higher labor market power tends to correspond to lower posted wages.
  - Example magnitudes:
    - Firms with vacancy share between 0 and 0.00005 (0.005 percentage points) post average wages between US$50,000 and US$48,000 for non-college vacancies.
    - Firms with vacancy share of 0.00005 post 1 out of 20,000 vacancies.
    - Firms controlling more than 0.005 percentage points show strongly declining posted wages.
    - Firm with vacancy share of 0.1% (posting 1 in every 1000 vacancies) posts average wage of less than US$45,000 for non-college vacancies.
    - College vacancies: around US$76,000 for vacancy share of <0.00005 and around US$70,000 for vacancy share of >0.001.
- Vacancy-level regressions:
  - Coefficient on LMP_i,c,t across Table 2 columns: -0.360 ∗∗∗; -0.193 ∗∗; -0.168 ∗∗∗; -0.174 ∗∗; -0.181 ∗∗∗ (t-stats: (-3.85), (-2.44), (-2.83), (-2.31), (-2.81)).
  - Authors interpret vacancy share as a good proxy for actual labor market power after extensive controls.

### Main empirical findings: Monetary policy, LMP, and vacancies
- Baseline cross-sectional specification (Equation 3):
  - Log Vacancies_{i,c,t} = α + β MP_easing_t × LMP_{i,c,t−1} + θ X_{i,c,t} + γ_{i,t} + γ_{c,t} + ε_{i,c,t}.
  - X_{i,c,t} includes the Federal Reserve information shock and interactions; γ_{i,t} firm–time fixed effects; γ_{c,t} CZ–time effects.
- Baseline effect without LMP:
  - Coefficient on monetary policy shock in column 1 = 0.348.
  - Interpretation: for a firm without labor market power, vacancy postings rise by 3.48% in response to a 10 basis points expansionary monetary policy shock.
- Interaction with LMP:
  - Interaction MP_easing × lagged vacancy share positive and statistically significant in most specifications.
  - Preferred-specification interaction coefficient: −7.895 (column 7) — text interprets: for a firm that controls 10% of the local labor market, vacancy postings rise by 7% more in response to a 10 basis point accommodative shock relative to a firm with no LMP (noting 10% vacancy share is very rare).
  - Table 4 interaction coefficients by column: 13.913 ∗∗∗; 3.400 ∗; 5.439 ∗∗∗; 5.442 ∗∗; 7.624 ∗∗∗; 8.722 ∗∗; 7.895 ∗∗ (standard errors reported per column).
- Sample and fixed-effects:
  - Introducing firm-time fixed effects (column 6) reduces sample from 15.7 million to 12.8 million observations and firms from 354,254 to 199,893.
- Robustness:
  - Results robust to alternative monetary policy definitions (Table A1), alternative LMP definitions including industry-local cumulative vacancy share (Table A2 and Figure A2), and excluding Public Administration (Table A3).
  - Footnote: 47% of high LMP firms are in tradable sectors versus 36% of low LMP firms.

### Dynamics and persistence (local projections)
- Local-projection specification sums horizons H:
  - Σ_{h=0}^H Log Vacancies_{i,c,t+h} = α_H + β_H MP_easing_t × LMP_{i,c,t−1} + θ_H X_{i,c,t} + γ_{i,t+H} + γ_{c,t+H} + ε_{i,c,t+H}.
- Dynamic responses:
  - Figure 7: hypothetical firm with 100% LMP shows vacancy response increasing over time relative to firm without LMP.
  - Figure 8: high-LMP (95th percentile) firms increase labor demand by around 3% within first two quarters in response to a 10 basis point loosening; median LMP firms increase by around 2% with effect decaying (additional postings cut in half after six quarters), while high-LMP firms retain almost unchanged initial response after 6 quarters.
  - Table A5 provides point estimates and standard errors across horizons.

### Heterogeneity by vacancy type and skills
- Data coverage:
  - ≈40% of vacancies are college vacancies.
  - ≈28% of vacancies require software skills.
  - Correlation between college and tech-savvy (software) vacancy types ≈29%.
- Triple-interaction specification (Equation 4):
  - Log Vacancies_{i,c,t,j} = α + β MP_easing_t × LMP_{i,c,t−1} + γ MP_easing_t × LMP_{i,c,t−1} × Type_j + X_{i,c,t} + γ_{i,t} + γ_{c,t} + ε_{i,c,t}.
- Key heterogeneous findings (Table 6):
  - College vs non-college:
    - College vacancies respond less strongly to monetary policy than non-college vacancies.
    - Triple interaction implies amplification by LMP is stronger for non-college vacancies.
    - Economic magnitudes in text: effect around −7.8 for non-college vacancies and (−7.8 + 2.9) = −4.9 for college vacancies.
  - Software vs non-software:
    - Software vacancies generally less responsive to monetary policy.
    - Firms with LMP adjust more along the non-software dimension than the software dimension.
- Dynamics by type:
  - Effect of LMP for vacancies not requiring college grows over time; effect for vacancies requiring software skills also becomes stronger (Figure 9 and Table 7).
  - Figure 10: non-college vacancies show persistently larger and increasing responses for LMP firms; for college vacancies differences beyond first quarter are not meaningful.

### Symmetry, compositional effects, and wages
- Symmetry:
  - Authors checked for asymmetries and report no significant evidence of differential effects for positive vs negative surprise shocks.
  - Firms with LMP cut (expand) vacancies by more than firms without LMP following contractionary (expansionary) surprises.
- Compositional effects on aggregate wages:
  - High market-power firms pay lower wages on average and have a higher markdown.
  - Following contractionary (expansionary) shock, share of vacancies by high market-power firms decreases (increases), which dampens the effect of the shock on aggregate wages.

### From vacancies to employment (elasticities and dynamics)
- Contemporaneous elasticity (Equation 5):
  - ∆Employment_{i,t} = α_i + α_t + β_1 Log Vacancies_{i,t} + υ_{i,t}.
  - A doubling in the number of vacancies (Log Vacancies_{i,t} = 1) is associated with a 0.74 percentage point stronger employment growth.
- Back-of-the-envelope translation:
  - Figure 8: after four quarters, a high-LMP firm increased vacancy postings by a factor of 2 in response to a 10 basis point accommodative shock.
  - Translating: (0.74 * 2) = 1.48 percentage points stronger employment growth for a high-LMP firm in response to the accommodative shock; a firm without LMP shows no stronger employment growth by these estimates.
- Caveats:
  - Employment data limited to listed firms (Compustat); translation assumes elasticities constant across merged and non-merged firms.
  - Authors do not find evidence of differential elasticity by LMP.
- Dynamic employment responses (Compustat local projections):
  - LMP_{i,t−1} = 1 if firm is in top 5% of LMP in at least one commuting zone.
  - Result (Figure 12): in response to a 10 bp monetary easing shock, firms with LMP increase employment by 1–2 percentage point more than firms without LMP within the first year (consistent with ~1.5% back-of-the-envelope).

### Posted wages: measurement and response to monetary policy
- Posted wage measure:
  - Posted Wage_{i,c,t} = log(w_{i,c,t}) − log(  ̄w_{c,t} ), deviations from regional average posted wage.
  - BGT coverage: ≈17% of postings include a minimum, maximum, or range for wage; when a range is reported the average of min and max is used.
- Local projections for posted wages:
  - Σ_{h=0}^H Posted Wage_{i,c,t+h}/H = α_H + β_H MP_easing_t × LMP_{i,c,t−1} + θ_H X_{i,c,t} + γ_{i,t+H} + γ_{c,t+H} + ε_{i,c,t+H}.
- Findings:
  - Accommodative monetary policy shock increases posted wages, particularly in the short term (Table 8, Table 9, Figure 13).
  - The response of posted wages to monetary policy shocks is not significantly different for firms with vs without LMP across horizons (Figure A4).
  - Interpretation: firms with more labor market power increase vacancies and employment more in response to easing without posting higher wages relative to regional averages.

### Labor Market Power and the Wage Phillips Curve
- Specification (Equation 6):
  - Wage Growth_{c,t} = α + β1 Unemployment Rate_{c,t} + β2 1LMP_{c,t} + β (Unemployment Rate_{c,t} × 1LMP_{c,t}) + ε_c,t.
  - 1LMP_{c,t} = 1 if commuting zone HHI based on vacancy postings is above the median.
- Main regression evidence (Table 10):
  - Unemployment Rate_{c,t} coefficients: -1.546 ∗∗∗; -1.735 ∗∗∗; -2.745 ∗∗∗; -5.301 ∗∗∗ (standard errors: (0.291); (0.391); (0.394); (0.811)).
  - Unemployment Rate_{c,t} × 1LMP_{c,t}: 1.840 ∗∗∗; 1.619 ∗∗∗; 2.810 ∗∗∗; 2.485 ∗∗∗ (standard errors: (0.529); (0.529); (0.747); (0.728)).
  - Implication: wage Phillips curve is steeper (negative) in Low LMP regions and flat or flatter in High LMP regions.
- Interpretation and mechanism:
  - In commuting zones with High Labor Market Power there is little association between unemployment rate and wage growth.
  - Mechanism consistent with model: firms with LMP can hire more workers by posting more vacancies without increasing wages if they benefit from more efficient matching or lower posting costs.

### Key quantitative summaries from empirical tables
- Panel structure (Table 1):
  - Total Observations: 15,810,352
  - Commuting Zone observations: 387,107
  - Time observations: 70,843
- Wage–LMP relationship (Table 2):
  - LMP coefficients across specifications: -0.360 ∗∗∗; -0.193 ∗∗; -0.168 ∗∗∗; -0.174 ∗∗; -0.181 ∗∗∗.
  - College_v coefficients: 0.238 ∗∗∗; 0.236 ∗∗∗; 0.173 ∗∗∗; 0.170 ∗∗∗; 0.162 ∗∗∗.
- Labor demand effect (Table 4 representative figures):
  - MP easing_t coefficients reported across columns: 0.351 ∗∗∗; 0.647 ∗∗∗; 0.696 ∗∗∗ (SEs reported).
  - LMP_i,c,t−1 coefficients: 23.166 ∗∗∗; 14.505 ∗∗∗; … up to 22.713 ∗∗∗ across columns.
  - Interaction MP easing_t × LMP_i,c,t−1: 13.913 ∗∗∗; 3.400 ∗; 5.439 ∗∗∗; …; 7.895 ∗∗ (SEs reported).
- Cumulative one-year effects (Table 5):
  - MP easing_t coefficients: -0.198; 0.746 ∗∗∗; 0.940 ∗∗∗ (SEs reported).
  - Interaction one-year cumulative MP easing_t × LMP_i,c,t−1: 72.928 ∗∗∗; 30.573 ∗∗∗; 18.408 ∗∗; …; 35.245 ∗∗∗ (SEs reported).
- Wage effects (Table 8 and Table 9):
  - Table 8 MP easing_t: 0.001; 0.146 ∗∗∗; 0.148 ∗∗∗.
  - Table 9 MP easing_t: -0.076; 0.118 ∗∗; 0.121 ∗∗.
  - Interaction MP easing_t × LMP estimates vary across specifications, with some positive and statistically significant coefficients and some not significant.

### Stylized facts on geography and sectors of high-LMP firms
- Regions with high-LMP firms tend to have:
  - Lower GDP per capita.
  - Lower house prices.
  - Smaller labor force.
  - Looser labor markets.
  - Higher HHI.
- Geographic pattern:
  - High-LMP regions mostly in the middle of the country, notably absent on the coasts and around larger cities.
- Sectoral prevalence:
  - Sectors with high market power firms include health care, educational services, agriculture, public administration, retail trade, and mining.
  - High-LMP firms are more likely to be in tradable sectors (47% of high LMP firms vs 36% of low LMP firms).

### Policy implications and interpretation
- Labor market power flattens the wage Phillips curve and helps explain why accommodative monetary policy can stimulate labor demand without generating strong wage growth.
- Implications for monetary policy conduct:
  - In presence of elevated labor market power, monetary policy can stimulate employment without materially driving wages and prices up, increasing the sacrifice ratio between inflation and unemployment.
  - When inflation is very low, reflation is more difficult for monetary policy.
  - A high sacrifice ratio complicates disinflation: unemployment will need to rise more than otherwise.
  - Ongoing monetary policy tightening will likely hurt labor demand more in regions where labor market power is strong.
  - Firms with significant labor market power are more likely to adjust wage bills by reducing headcount rather than lowering wages, potentially diminishing wage-price pass-through.

*Source: wpiea2022128-print-pdf*

### 3.1  Burning Glass Technologies (BGT)

### 3.1  Burning Glass Technologies (BGT)

### Dataset description and coverage
- BGT tracks all online vacancy postings from over 45,000 online job boards, removes duplicates, and cleans the data.
- Resulting dataset covers the near universe (≈70%) of all U.S. online vacancy postings and comprises ≈250 million job vacancy postings for the years of 2007 and 2010-2019.
- All postings include the exact date when the vacancy was posted online, the name of the employer, and the FIPS county code; analysis uses Commuting Zones rather than counties.
- NAICS industry and ONET occupation breakdowns are available; many vacancies list job requirements such as education or software skills.
- Education is reported for approximately half of vacancies; when missing, education is imputed based on existing vacancies using the finest occupational breakdown, assigning the same education requirement within the same occupation.
- Wage information is reported for 17% of vacancies. Some postings list a wage range — the midpoint of the range is taken. Wage data reflect annual compensation and does not include bonuses and other benefits beyond the basic wage.
- Vacancy-level data is collapsed into a panel of firm-, commuting zone- and quarter-level (establishment-level) observations.
- The unit of analysis is the firm-commuting zone-time level:
  - Over 15 million firm-commuting zone-quarter observations.
  - Over 380,000 firms.
  - Just over 700 commuting zones.
  - The average commuting zone has postings from 22,000 firms (unevenly distributed).
  - An average firm posts in 170 commuting zones.

### Data strengths and limitations
- Strengths:
  - Extensive coverage and collected directly from firms’ postings, avoiding limitations of survey datasets that only cover firms of a certain size or publicly traded firms.
  - Time-stamped posting dates and location identifiers enable establishment-level analysis.
- Limitations:
  - Online vacancy postings are not fully representative of all postings and over-represent certain industries (e.g., IT, Education), especially in earlier years.
  - Wage reporting is limited (17%); Hazell et al.(2021) find the wage subset can still replicate occupation-level wage features, though smaller firms and lower-skill occupations are more likely to report wages.
  - Robustness checks (e.g., Hershbein and Kahn(2018)) indicate BGT tracks aggregate and industry trends closely despite shortcomings.

### Compustat merge and cleaning
- Aggregate BGT vacancies to firm level and fuzzy-merge BGT firm names to Compustat using string cleaning and two-layered matching (exact + Jaro-Winkler).
- Matching results (2008–2019):
  - 8,231 firm matches from 14,983 firms in Compustat.
  - 3,217 exact matches.
  - 5,014 matched using Jaro-Winkler fuzzy matching (string distance threshold of 0.11).
  - Merged companies represent 75% of sales, and 73% of employment of all companies in Compustat.
- Compustat cleaning steps (following Ottonello and Winberry(2020)):
  - Keep only corporations incorporated in the US.
  - Drop firms in the financial and utilities sectors.
  - Drop firm-quarter observations with acquisitions larger than 5 percent of assets.
  - Drop firm-quarter observations where the investment rate is in the top and bottom 1 percent of the distribution.
  - Drop observations where the investment spell is shorter than 40 quarters.
  - Drop firm–quarter observations where liquidity, debt, and sales are outliers.
  - Drop firms with less than 10 million US dollars in assets and firms that are in the sample less than 5 years.
  - Linearly interpolate annual employment data to quarterly data.

### Monetary policy shocks (overview used in analysis)
- Baseline shocks: Jarociński and Karadi(2020) — JK 2020, focusing on interest rate surprises in the three-month fed funds future.
  - Three-month future exchanges a constant interest for the average federal funds rate over the course of the third calendar month in the contract; reflects shift in expected federal funds rate after the following policy meeting.
  - JK 2020 shocks separate pure monetary policy shocks from “Fed information” shocks (central bank signaling).
  - Fed information shocks capture signals about the state of the economy and can have effects opposite to pure monetary policy shocks; JK 2020 allows using Fed information shock as a control.
- Robustness checks use alternative measures: Nakamura and Steinsson(2018), Jarociński(2021), Bu et al.(2021).
  - Nakamura and Steinsson(2018): principal component analysis across the yield curve (one-month to two-year).
  - Jarociński(2021): four shocks — standard monetary policy shock plus three orthogonal shocks (Odyssean forward guidance, longer-term treasury yield shock related to asset purchases, Delphic forward guidance).
  - Bu et al.(2021): include unconventional policy via a Fama-MacBeth two-step procedure; conclude their measure does not contain a significant central bank information effect.
- Time series note: monetary policy shocks exhibit both significant tightening and loosening; largest tightening and loosening shocks in the sample occurred in 2007; the global financial crisis-related loosening cycle started in August 2007.

### Treatment of vacancy wages and ranges
- Wage reporting present in 17% of vacancies.
- When a posting lists a wage range, the midpoint of that range is used.
- Wage data reflect annual compensation and exclude bonuses and other benefits.

### Definition and measurement of Labor Market Power (LMP)
- Baseline measure: share of vacancies posted by a single firm in a local labor market out of total vacancies posted in that labor market.
- Local labor market defined as a U.S. census commuting zone.
- Cumulative vacancy shares are used to reduce endogeneity and because some smaller firms do not post in consecutive periods. Labor Market Power is defined as:
  - Labor Market Power_{i,c,t} = Vacancy Share_{i,c,t} = (Σ_{τ≤t} v_{i,c,τ}) / (Σ_{τ≤t} Σ_{i} v_{i,c,τ})
  - where vacancies in commuting zone c for firm i at time τ are denoted by v_{i,c,τ}.
- High labor market power firms: those above the 95th percentile across the full distribution of firm-CZ-time observations.
- Vacancy share distribution statistics:
  - Average vacancy share is 0.8%.
  - Median vacancy share is 0.1%.
  - 95th percentile vacancy share is 3.7%.

### Empirical relationship between LMP and posted wages
- Cross-sectional pattern: higher labor market power tends to correspond to lower posted wages.
- Evidence:
  - Figure summary: firms with vacancy share between 0 and 0.00005 (0.005 percentage points) post average wages between US$50,000 and US$48,000 for non-college vacancies; a firm with vacancy share of 0.00005 posts 1 out of 20,000 vacancies.
  - Once a firm controls more than 0.005 percentage points of the market, posted wages decline strongly.
  - Example: a firm with vacancy share of 0.1% (posting 1 in every 1000 vacancies) posts an average wage of less than US$45,000 for non-college vacancies.
  - College vacancies: higher overall posted wages (around US$76,000 for vacancy share of <0.00005 and around US$70,000 for vacancy share of >0.001) with posted wages declining more linearly but with a large drop at vacancy shares of about 0.005%.
- Controls and robustness:
  - Vacancy-level regressions controlling for a large set of vacancy characteristics show that after controlling for observed and unobserved vacancy, firm, and region characteristics, firms with higher vacancy shares post lower wages (see Table 2).
  - Authors interpret this as evidence that vacancy share is a good proxy for actual labor market power.

### Alternative measures and robustness for LMP
- Alternative local market definition: commuting zone-level with additional industry breakdown — results are robust (see section 5 discussion).
- Herfindahl-Hirschman Index (HHI) of vacancy postings at commuting zone level computed as Σ_{i} (Vacancy Share_{i,c,t})^2 and used to assess whether commuting zones where firms have more market power have flatter Phillips curves.

### Stylized facts on the location and sectors of high-LMP firms
- Regions hosting firms with high labor market power tend to have:
  - Lower GDP per capita.
  - Lower house prices.
  - Smaller labor force.
  - Looser labor markets.
  - Higher HHI.
- Geographic pattern: regions with high labor market power firms are consistently in the middle of the country and notably absent on the coasts and around larger cities.
- Sectoral prevalence: sectors with high market power firms include health care, educational services, agriculture, public administration, retail trade, and mining.
- High labor market power firms are more likely to be in tradable sectors.

### Key empirical result highlighted
- Firms with labor market power raise vacancies by more following a monetary policy shock without having to increase wages by more compared to firms without labor market power.
- Heterogeneity: vacancies that do not require a college degree or tech skills react more to monetary policy in the presence of labor market power.
- Throughout the analysis the focus is on monetary policy easing shocks; a positive coefficient involving monetary policy indicates the variable rises with monetary policy easing.

*Source: wpiea2022128-print-pdf - 3.1  Burning Glass Technologies (BGT)*

### 5.1  Monetary Policy, Labor Market Power and Vacancy

### 5.1  Monetary Policy, Labor Market Power and Vacancy

### Specification and identification
- Baseline cross-sectional specification (Equation 3):
  - Log Vacancies_{i,c,t} = α + β MP_easing_t × LMP_{i,c,t−1} + θ X_{i,c,t} + γ_{i,t} + γ_{c,t} + ε_{i,c,t}
  - LMP is measured by the vacancy share defined in Equation 2.
  - X_{i,c,t} includes the Federal Reserve information shock and its interactions with vacancy share.
  - γ_{i,t} are firm–time fixed effects; γ_{c,t} are commuting zone–time effects.
- Identification strategy:
  - Progressively include fixed effects across specifications (columns 1–7 of Table 4) to control for firm-level, time, and regional confounders.
  - Column 7 (preferred baseline): commuting-zone-time fixed effects plus firm-time fixed effects to condition on regional labor-market tightness and firm-specific time variation.

### Main empirical findings on vacancy responses
- Baseline effect without labor market power:
  - Coefficient on monetary policy shock in column 1 = 0.348.
  - Interpretation given by the authors: for a firm without labor market power, vacancy postings rise by 3.48% in response to a 10 basis points expansionary monetary policy shock.
- Interaction with labor market power:
  - Interaction term (MP_easing × lagged vacancy share) is positive and statistically significant in most specifications, indicating labor market power amplifies vacancy responses to monetary policy easing.
  - Preferred-specification interaction coefficient: −7.895 (column 7). The text interprets this coefficient as: for a firm that controls 10% of the local labor market, vacancy postings rise by 7% more in response to a 10 basis point accommodative monetary policy shock relative to a firm that has no labor market power. (The text notes a 10% vacancy share is very rare.)
- Sample and robustness:
  - Introduction of firm-time fixed effects (column 6) reduces the sample from 15.7 million to 12.8 million observations and the number of firms from 354,254 to 199,893, tightening identification by comparing the same firm across regions at the same time.
  - Results are robust to alternative monetary policy definitions (Table A1), alternative LMP definitions that include industry-local cumulative vacancy share (Table A2 and Figure A2), and excluding the public administration sector (Table A3).
- Contextual note:
  - Footnote: 47% of high LMP firms are in tradable sectors versus 36% of low LMP firms.

### Dynamics and persistence (local projections)
- Local projection specification sums horizons H:
  - Σ_{h=0}^H Log Vacancies_{i,c,t+h} = α_H + β_H MP_easing_t × LMP_{i,c,t−1} + θ_H X_{i,c,t} + γ_{i,t+H} + γ_{c,t+H} + ε_{i,c,t+H}
- Dynamic responses:
  - Figure 7: response of vacancy postings for a hypothetical firm with 100% labor market power increases over time relative to firms without LMP.
  - Figure 8: firms with high LMP (95th percentile) increase labor demand by around 3% within the first two quarters in response to a 10 basis point loosening; median LMP firms increase by around 2% and the effect for median firms decays (additional postings cut in half after six quarters), while high-LMP firms retain almost unchanged their initial response after 6 quarters.
- Point estimates and standard errors available in Table A5.

### Heterogeneity by vacancy type (college, software)
- Data coverage and definitions:
  - ≈40% of vacancies are college vacancies in the sample.
  - ≈28% of vacancies require software skills.
  - Correlation between college and tech-savvy (software) vacancy types ≈29%.
- Triple-interaction specification (Equation 4):
  - Log Vacancies_{i,c,t,j} = α + β MP_easing_t × LMP_{i,c,t−1} + γ MP_easing_t × LMP_{i,c,t−1} × Type_j + X_{i,c,t} + γ_{i,t} + γ_{c,t} + ε_{i,c,t}
  - Type_j = 1 for the vacancy characteristic (college or software) under examination.
- Key heterogeneous findings (Table 6):
  - College vs non-college:
    - Monetary policy interaction with vacancy type is positive and statistically significant: college vacancies respond less strongly to monetary policy than non-college vacancies.
    - Triple interaction (MP_easing × LMP × college dummy) is positive and statistically significant, implying labor-market-power amplification is stronger for non-college vacancies.
    - Economic magnitudes: effect around −7.8 for non-college vacancies and (−7.8 + 2.9) = −4.9 for college vacancies (as reported in text).
  - Software vs non-software:
    - Software vacancies generally less responsive to monetary policy.
    - Firms with labor market power adjust more along the non-software dimension than the software dimension.
- Dynamics by vacancy type:
  - Effect of labor market power for vacancies not requiring college grows over time; effect for vacancies requiring software skills also becomes stronger (Figure 9 and Table 7).
  - Figure 10: for non-college vacancies, firms with LMP show persistently larger and increasing responses relative to non-LMP firms; for college vacancies, differences beyond the first quarter are not meaningful.

### Symmetry, compositional effects, and wages
- Symmetry:
  - Specification assumes symmetric effects of positive and negative surprise monetary policy shocks. The authors checked for asymmetries and report no significant evidence of differential effects (results available upon request).
  - Following a contractionary (expansionary) surprise, firms with LMP cut (expand) vacancies by more than firms without LMP.
- Compositional effects on aggregate wages:
  - High market-power firms pay lower wages on average and have a higher markdown; following a contractionary (expansionary) shock, the share of vacancies by high market-power firms decreases (increases), which dampens the effect of the shock on aggregate wages.

### From vacancies to employment
- Contemporaneous elasticity (Equation 5):
  - ∆Employment_{i,t} = α_i + α_t + β_1 Log Vacancies_{i,t} + υ_{i,t}
  - ∆Employment_{i,t} is log change in employment of firm i between year t and t−1 in Compustat.
  - Log Vacancies_{i,t} is log number of vacancies posted by firm i in year t from BGT.
- Empirical association:
  - A doubling in the number of vacancies (Log Vacancies_{i,t} = 1) is associated with a 0.74 percentage point stronger employment growth.
- Back-of-the-envelope translation:
  - Figure 8: after four quarters, a high-LMP firm increased vacancy postings by a factor of 2 in response to a 10 basis point accommodative shock.
  - Translating vacancies to employment: (0.74 * 2) = 1.48 percentage points stronger employment growth for a high-LMP firm in response to the accommodative shock; a firm without LMP shows no stronger employment growth by these estimates.
- Caveats:
  - Employment data limited to listed firms (Compustat); elasticities assumed constant across merged and non-merged firms for the translation to hold.
  - Potential for differential elasticity by LMP status (monopsonists posting more vacancies but not hiring proportionally) is discussed; authors do not find evidence of differential elasticity by LMP.

### Dynamic employment responses (Compustat)
- Local projection for employment dynamics:
  - Σ_{h=0}^H ∆Employment_{i,t+h} = α_H + β_H MP_easing_t × LMP_{i,t−1} + θ_H X_{i,t} + γ_i + γ_{t+H} + ε_{i,t+H}
  - Here LMP_{i,t−1} = 1 if firm is in top 5% of LMP in at least one commuting zone.
- Result (Figure 12):
  - In response to a 10 bp monetary easing shock, firms with LMP increase employment by 1–2 percentage point more than firms without LMP within the first year.
  - This is consistent with the back-of-the-envelope estimate (~1.5%).

### Posted wages
- Posted wage measure:
  - Posted Wage_{i,c,t} = log(w_{i,c,t}) − log(  ̄w_{c,t} ), deviations from regional average posted wage.
  - BGT coverage: only ≈17% of postings include a minimum, maximum, or range for wage; when a range is reported the average of min and max is used.
- Local projections for posted wages:
  - Σ_{h=0}^H Posted Wage_{i,c,t+h}/H = α_H + β_H MP_easing_t × LMP_{i,c,t−1} + θ_H X_{i,c,t} + γ_{i,t+H} + γ_{c,t+H} + ε_{i,c,t+H}
- Findings:
  - Accommodative monetary policy shock increases posted wages, particularly in the short term (Table 8, Table 9, Figure 13).
  - The response of posted wages to monetary policy shocks is not significantly different for firms with vs without labor market power across horizons (Figure A4).
  - Interpretation: firms with more labor market power increase vacancies and employment more in response to easing without posting higher wages relative to regional averages.

*Source: IMF working paper chapter "5.1  Monetary Policy, Labor Market Power and Vacancy" (wpiea2022128-print-pdf).*

### 5.4  Labor Market Power and the Wage Phillips Curve

### 5.4  Labor Market Power and the Wage Phillips Curve

### Empirical approach
- Objective: Test whether labor market power helps explain the flatter slope of the wage Phillips curve.
- Data and specification:
  - Wage Growth_c,t: annual wage growth of posted vacancies from Burning Glass Technology (BGT) at the commuting zone-year level.
  - Unemployment Rate_c,t: commuting zone-year unemployment rate from BLS.
  - 1LMP_c,t: dummy equal to one if vacancy-posting concentration (HHI) in the commuting zone is above the median.
  - Estimated regression (Equation 6): Wage Growth_c,t = α + β1 Unemployment Rate_c,t + β2 1LMP_c,t + β (Unemployment Rate_c,t × 1LMP_c,t) + ε_c,t.
- Visualization: Figure 14 presents a commuting zone-level binscatter of the wage Phillips curve split by Low Labor Market Power (below median HHI) and High Labor Market Power (above median HHI).

### Regression results
- Wage Phillips curve for low labor market power regions:
  - The coefficient β1 is always negative and statistically significant.
  - β1 ranges from −1.5 to −5.3 depending on the level of fixed effects included.
- Interaction effect:
  - The coefficient on the interaction between labor market power and the unemployment rate is positive and statistically significant.
  - This leads to an entirely flat or flatter wage Phillips curve when labor market power is high.
- Robustness note:
  - The change in β1 across specifications indicates commuting zone and time specific factors correlated with the unemployment rate matter; time fixed effects likely capture inflation expectations (Hazell et al., 2022).

### Interpretation and mechanism
- For commuting zones with Low Labor Market Power (blue diamonds in Figure 14):
  - The wage Phillips curve is steep — strong negative relationship between unemployment rate and wage growth.
- For commuting zones with High Labor Market Power:
  - There is no association between the unemployment rate and wage growth — a flat wage Phillips curve.
- Mechanism consistent with model:
  - Firms with labor market power can hire more workers by posting more vacancies without increasing wages if they benefit from more efficient job matching or lower posting costs.

### Key quantitative finding on vacancies
- A firm with high labor market power in a certain region expands its vacancy postings by about 30% more relative to its counterparts.
- The effect on vacancies is more persistent for firms with high labor market power.
- Labor market power does not significantly amplify the effects of monetary policy shocks on wages.

### Heterogeneity across vacancy types
- Vacancies requiring a college degree and those requiring “tech-skills” are far less responsive to monetary policy than vacancies not requiring a college degree and targeted towards non-tech workers.
- Monetary policy cycles can generate significant heterogeneity in labor demand across the skill distribution.

### Policy implications
- Labor market power flattens the wage Phillips curve and helps explain why accommodative monetary policy can stimulate labor demand without generating strong wage growth.
- Implications for conduct of monetary policy:
  - In the presence of elevated labor market power, monetary policy can stimulate employment without materially driving wages and hence prices up, i.e. labor market power may increase the sacrifice ratio between inflation and unemployment.
  - When inflation is very low, this makes reflation more difficult for monetary policy.
  - Conversely, a high sacrifice ratio complicates disinflation: unemployment will need to rise more than it would otherwise.
  - Ongoing monetary policy tightening will likely hurt labor demand more in regions where labor market power is strong.
  - Firms with significant labor market power are more likely to adjust their wage bill by reducing headcount rather than lowering wages, potentially diminishing the wage-price pass-through of monetary policy.

*Source: 5.4  Labor Market Power and the Wage Phillips Curve (excerpt).*

### References

### wpiea2022128-print-pdf - References

### References (selected citations and themes)
- Research on labor market power, concentration, and wages:
  - Acemoglu, Daron; Joe Hazell; Pascual Restrepo (2021) “Ai and jobs: evidence from online vacancies”, Journal of Labor Economics. 20
  - Azar, José et al. (2019a, 2019b, 2019c, 2020, 2022) — multiple works on estimating labor market power, concentration, and minimum wage effects. 7, 24
  - Berger, David; Kyle Herkenhoff; Simon Mongey (2022) “Labor market power”, American Economic Review, 112 (4), pp. 1147–93.3, 4, 7, 14
  - De Loecker, Jan; Jan Eeckhout; Gabriel Unger (2020) “The rise of market power and the macroeconomic implications”, The Quarterly Journal of Economics, 135 (2), pp. 561–644.6, 18
  - Benmelech, Efraim; Nittai K Bergman; Hyunseob Kim (2022) “Strong employers and weak employees how does employer concentration affect wages?”, Journal of Human Resources, 57 (S), pp. S200–S250.7
  - Hershbein, Brad; Claudia Macaluso; Chen Yeh (2022) “Concentration in us local labor markets: evidence from vacancy and employment data”, American Economic Review (forthcoming). 3, 7
- Monetary policy, labor markets, and distribution:
  - Andersen, Asger Lau et al. (2021) “Monetary policy and inequality”.5, 6
  - Baqaee, David; Emmanuel Farhi; Kunal Sangani (2021) “The supply-side effects of monetary policy”, NBER.6
  - Bu, Chunya; John Rogers; Wenbin Wu (2021) “A unified measure of fed monetary policy shocks”, Journal of Monetary Economics, 118, pp. 331–349.12, 13, 49
  - Jarociński, Marek and Peter Karadi (2020) “Deconstructing monetary policy surprise the role of information shocks”, American Economic Journal: Macroeconomics, 12 (2), pp. 1–43.12, 23, 32–51
  - Nakamura, Emi and Jón Steinsson (2018) “High-frequency identification of monetary non-neutrality: the information effect”, The Quarterly Journal of Economics, 133 (3), pp. 1283–1330.12, 49
  - Duval, Mr Romain A; Davide Furceri; Raphael Lee; Marina M Tavares (2021) Market Power and Monetary Policy Transmission, International Monetary Fund.6
- Wage Phillips curve, job polarization, automation:
  - Blanchard, Olivier (2018) “Should we reject the natural rate hypothesis?”, Journal of Economic Perspectives, 32 (1), pp. 97–120.3
  - Galí, Jordi and Luca Gambetti (2019) “Has the us wage phillips curve flattened? a semi-structural exploration”, NBER.3, 7, 37
  - Jaimovich, Nir and Henry E Siu (2020) “Job polarization and jobless recoveries”, Review of Economics and Statistics, 102 (1), pp. 129–147.5
  - Fornaro, Luca and Martin Wolf (2021) “Monetary policy in the age of automation”.5

### Empirical tables — key findings and exact estimates
- Table 1: Summary of the Panel Structure
  - Total Observations: 15,810,352
  - Commuting Zone observations: 387,107
  - Time observations: 70,843
  - Average Number of Firms: 387,107 - 22,412 103,230
  - Average Number of CZ: 708 170 - 704
  - Average Number of Periods: 432 942 -

- Table 2: Relationship Between Wages and Our Measure of Labor Market Power (vacancy-level regression: Log wage_v,i,c,t)
  - Coefficient on LMP_i,c,t across columns: -0.360 ∗∗∗; -0.193 ∗∗; -0.168 ∗∗∗; -0.174 ∗∗; -0.181 ∗∗∗ (t-stats in parentheses: (-3.85), (-2.44), (-2.83), (-2.31), (-2.81))
  - College_v,i,c,t coefficients: 0.238 ∗∗∗; 0.236 ∗∗∗; 0.173 ∗∗∗; 0.170 ∗∗∗; 0.162 ∗∗∗ (t-stats: (41.46), (31.56), (36.31), (37.33), (40.28))
  - Software Skills_v,i,c,t coefficients: 0.028 ∗∗∗; 0.028 ∗∗∗; 0.015 ∗∗∗; 0.015 ∗∗∗; 0.013 ∗∗∗ (t-stats: (8.13), (7.01), (4.25), (4.34), (4.51))
  - Routine Manual_v,i,c,t coefficients switch sign across specifications: -0.110 ∗∗∗; -0.105 ∗∗∗; 0.037 ∗∗∗; 0.037 ∗∗∗; 0.049 ∗∗∗ (t-stats: (-18.83), (-15.99), (3.36), (3.44), (4.50))
  - Non-Routine Cognitive Analytical_v,i,c,t coefficients: 0.064 ∗∗∗; 0.057 ∗∗∗; 0.103 ∗∗∗; 0.106 ∗∗∗; 0.102 ∗∗∗ (t-stats: (12.20), (9.83), (12.89), (13.88), (12.66))
  - Observations by column: 12,714,694; 12,356,399; 11,862,438; 11,857,790; 11,857,284
  - Number of Firms reported: 173,057; 144,813; 141,764; 141,715; 141,708
  - Notes: Regression includes firm-time, CZ-time, industry-time, occupation-time, occupation-CZ, occupation-industry fixed effects. Standard errors double clustered at firm and CZ. *** p<0.01, ** p<0.05, * p<0.1.

- Table 3: Correlation between regional characteristics and presence of firms with high labor market power
  - Coefficient estimates for 1{High LMP Firm} on regional outcomes:
    - HHI: 0.022 ∗∗∗ (standard error (0.006))
    - GDP per Capita: -0.151 ∗∗ (standard error (0.073))
    - House Prices: -0.446 ∗∗∗ (standard error (0.123))
    - Labor Force: -1.291 ∗∗∗ (standard error (0.258))
    - Tightness: -0.090 ∗∗∗ (standard error (0.019))
    - Unemployment Rate: 0.001 (standard error (0.002))
  - Observations by outcome: 29,315; 26,283; 23,122; 29,277; 29,277; 29,277
  - Notes: 1{High LMP Firm} = 1 if at least one establishment in top 5th percentile of vacancy shares is present. Standard errors clustered at the Commuting Zone level.

- Table 4: Labor Demand Effect of Monetary Policy (Log Vacancies_i,c,t)
  - MP easing_t coefficients (where MP easing_t is the negative of Jarociński and Karadi(2020) shock):
    - Column (1) not reported for MP easing; Columns showing MP easing_t: 0.351 ∗∗∗; 0.647 ∗∗∗; 0.696 ∗∗∗ (standard errors (0.036), (0.032), (0.035))
  - LMP_i,c,t−1 coefficients across columns: 23.166 ∗∗∗; 14.505 ∗∗∗; 14.958 ∗∗∗; 20.318 ∗∗∗; 20.866 ∗∗∗; 21.439 ∗∗∗; 22.713 ∗∗∗ (standard errors (1.816), (1.252), (1.275), (1.534), (1.560), (1.667), (1.639))
  - Interaction MP easing_t × LMP_i,c,t−1 coefficients: 13.913 ∗∗∗; 3.400 ∗; 5.439 ∗∗∗; 5.442 ∗∗; 7.624 ∗∗∗; 8.722 ∗∗; 7.895 ∗∗ (standard errors (3.111), (1.789), (1.834), (2.330), (2.398), (3.389), (3.839))
  - Observations by column: 15,092,441; 15,070,026; 15,070,026; 15,070,026; 15,070,026; 12,851,844; 12,851,727
  - Number of Firms: 377,669; 355,254; 355,254; 355,254; 355,254; 199,839; 199,839
  - Notes: Standard errors double clustered at firm and CZ. *** p<0.01, ** p<0.05, * p<0.1.

- Table 5: Cumulative Labor Demand Effect of Monetary Policy, One Year Horizon (sum of 4 quarters ∑_{h=0}^3 Log Vacancies_{i,c,t+h})
  - MP easing_t coefficients: -0.198; 0.746 ∗∗∗; 0.940 ∗∗∗ (standard errors (0.164), (0.131), (0.133))
  - LMP_i,c,t−1 coefficients: 80.868 ∗∗∗; 46.129 ∗∗∗; 48.791 ∗∗∗; 69.003 ∗∗∗; 72.139 ∗∗∗; 75.894 ∗∗∗; 78.076 ∗∗∗ (standard errors (6.709), (4.358), (4.492), (5.465), (5.613), (5.916), (5.729))
  - Interaction MP easing_t × LMP_i,c,t−1: 72.928 ∗∗∗; 30.573 ∗∗∗; 18.408 ∗∗; 38.610 ∗∗∗; 27.042 ∗∗∗; 34.824 ∗∗∗; 35.245 ∗∗∗ (standard errors (12.821), (7.398), (7.529), (9.688), (9.843), (12.230), (13.644))
  - Observations and firm counts match Table 4. Notes: Effects reflect one-year cumulative impact. *** p<0.01, ** p<0.05, * p<0.1.

- Table 6: Labor Demand Effect of Monetary Policy across Vacancy Types (Log Vacancies_{i,c,t,j})
  - LMP_i,c,t−1 coefficients by specification: 18.036 ∗∗∗; 19.173 ∗∗∗; 18.391 ∗∗∗; 21.736 ∗∗∗ (standard errors (1.282), (1.337), (1.311), (1.523))
  - Type_j coefficients: -0.148 ∗∗∗; -0.243 ∗∗∗ (standard errors (0.018), (0.014))
  - Interaction MP easing_t × LMP_i,c,t−1: 6.430 ∗∗; 7.785 ∗∗∗; 7.495 ∗∗∗; 8.701 ∗∗ (standard errors (2.868), (2.843), (2.703), (3.631))
  - Higher-order interactions reported, including triple interaction MP easing_t × LMP_i,c,t−1 × Type_j: -2.938 ∗; -3.576 (standard errors (1.623), (2.400))
  - Observations: 17,342,560; 17,342,560; 16,277,587; 16,277,587
  - Vacancy Types analyzed include college and software skill requirements. Standard errors double clustered at firm and CZ.

- Table 7: Cumulative Labor Demand Effect across Vacancy Types, One Year Horizon (∑_{h=0}^3 Log Vacancies_{i,c,t+h,j})
  - LMP_i,c,t−1 coefficients: 60.537 ∗∗∗; 70.127 ∗∗∗; 57.072 ∗∗∗; 77.867 ∗∗∗ (standard errors (4.516), (5.117), (4.418), (5.653))
  - Type_j coefficients: -0.705 ∗∗∗; -1.173 ∗∗∗ (standard errors (0.067), (0.049))
  - Interaction MP easing_t × LMP_i,c,t−1: 27.150 ∗∗; 38.581 ∗∗∗; 23.695 ∗∗; 39.483 ∗∗∗ (standard errors (10.664), (11.387), (10.184), (12.935))
  - LMP_i,c,t−1 × Type_j: -19.180 ∗∗∗; -41.591 ∗∗∗ (standard errors (3.412), (3.610))
  - MP easing_t × LMP_i,c,t−1 × Type_j: -22.864 ∗∗∗; -31.576 ∗∗∗ (standard errors (5.582), (7.925))
  - Observations: 30,184,882 across columns. Vacancy Types: college, software.

- Table 8: Wage Effect of Monetary Policy (Log Wages_{i,c,t})
  - MP easing_t coefficients: 0.001; 0.146 ∗∗∗; 0.148 ∗∗∗ (standard errors (0.038), (0.023), (0.024))
  - LMP_i,c,t−1 coefficients vary across specifications: 0.277 ∗∗; -0.084; -0.011; 0.056; 0.112 ∗; 0.354 ∗∗∗; 0.390 ∗∗∗ (standard errors (0.137), (0.085), (0.093), (0.061), (0.065), (0.077), (0.081))
  - Interaction MP easing_t × LMP_i,c,t−1 estimates: 0.191; -0.579 ∗∗; 0.009; -0.495 ∗; 0.090; 0.433; 0.363 (standard errors (0.389), (0.271), (0.271), (0.279), (0.277), (0.349), (0.482))
  - Observations by column: 3,611,431; 3,546,366; 3,546,366; 3,546,366; 3,546,366; 2,716,562; 2,715,673
  - Number of Firms reported in columns: 281,380; 216,315; 216,315; 216,315; 216,315; 97,858; 97,856
  - Notes: Log Wages defined relative to CZ-time average wage. MP easing_t is the negative of Jarociński and Karadi(2020) shock.

*Italic: Source — wpiea2022128-print-pdf - References*

### section 3. Standard errors are double clustered at the firm and commuting zone level. *** p<0.01, ** p<0.05, *

### section 3. Standard errors are double clustered at the firm and commuting zone level. *** p<0.01, ** p<0.05, * p<0.1.

### Wage response to monetary policy (Table 9; Figure 13)
- Regression reported: ∑_{h=0}^{3} Log Wage Measure_{i,c,t+h} = α + β MP easing_{t} × LMP_{i,c,t−1} + θ X_{i,c,t} + γ_{i,t} + γ_{c,t} + ε_{i,c,t}.
- Key coefficient patterns (as reported in Table 9):
  - MP easing_{t}: -0.076; 0.118 ∗∗; 0.121 ∗∗. (Standard errors reported: (0.075); (0.051); (0.051))
  - LMP_{i,c,t−1}: 1.155 ∗∗∗; 0.039; 0.142; 0.376 ∗∗; 0.460 ∗∗; 0.905 ∗∗∗; 0.905 ∗∗∗. (Standard errors: (0.399); (0.227); (0.237); (0.187); (0.201); (0.235); (0.251))
  - MP easing_{t} × LMP_{i,c,t−1}: 1.547 ∗; 0.321; 0.952; 0.509; 1.145 ∗; 1.680 ∗∗∗; 0.941. (Standard errors: (0.871); (0.626); (0.637); (0.633); (0.641); (0.572); (0.748))
- Estimation details:
  - Sum includes 4 quarters (one-year horizon).
  - Log Wages_{i,c,t} defined as log wage of vacancies posted by firm i in commuting zone c in quarter t, relative to the commuting zone-time average wage.
  - MP easing_{t} is the negative of the monetary policy shock by Jarociński and Karadi (2020); positive = monetary policy easing.
  - LMP_{i,c,t−1} is the cumulative vacancy share of firm i in commuting zone c at quarter t−1.
  - Standard errors double clustered at firm and commuting zone levels.
- Empirical implication:
  - Monetary policy easing is associated with differential wage responses depending on firm-level LMP; interaction terms are generally positive (some statistically significant), indicating stronger wage effects for firms with higher LMP.

### Wage Phillips relationship by labor market power (Table 10; Figure 14)
- Regression reported: Wage Growth_{c,t} = α + θ Unemployment Rate_{c,t} + δ 1{LMP_{c,t}} + β Unemployment Rate_{c,t} × 1{LMP_{c,t}} + γ_{c} + γ_{t} + ε_{c,t}.
- Key coefficients (Table 10):
  - Unemployment Rate_{c,t}: -1.546 ∗∗∗; -1.735 ∗∗∗; -2.745 ∗∗∗; -5.301 ∗∗∗. (Standard errors: (0.291); (0.391); (0.394); (0.811))
  - 1LMP_{c,t} (dummy for HHI above median): -0.090 ∗∗∗; -0.091 ∗∗∗; -0.078; -0.102 ∗∗. (Standard errors: (0.031); (0.031); (0.052); (0.050))
  - Unemployment Rate_{c,t} × 1LMP_{c,t}: 1.840 ∗∗∗; 1.619 ∗∗∗; 2.810 ∗∗∗; 2.485 ∗∗∗. (Standard errors: (0.529); (0.529); (0.747); (0.728))
- Estimation details:
  - Wage Growth_{c,t} is annual wage growth of posted vacancies from Burning Glass Technology at the commuting zone-year level.
  - Unemployment Rate_{c,t} from BLS at commuting zone year-level.
  - 1{LMP_{c,t}} = 1 if commuting zone HHI based on vacancy postings is above median.
  - Standard errors clustered at commuting zone level.
- Empirical implication:
  - The negative slope of the Phillips curve (wage growth vs. unemployment) is attenuated in regions with higher labor market power; the positive and significant interaction coefficients indicate that higher LMP weakens the negative relationship between unemployment and wage growth.

### Labor demand response of vacancies to monetary policy (Tables 4, A1–A5; Figures 6–12, A2–A3)
- Core specification (used across tables/figures):
  - Log Vacancies_{i,c,t} = α + β MP easing_{t} × LMP_{i,c,t−1} + θ X_{i,c,t} + γ_{i,t} + γ_{c,t} + ε_{i,c,t}.
  - MP easing_{t} positive = monetary policy easing (Jarociński and Karadi (2020) or alternative shocks).
  - LMP_{i,c,t−1} = cumulative vacancy share of firm i in commuting zone c at t−1 (or industry-level alternative LMP_alt).
  - Standard errors double clustered at firm and commuting zone levels (unless otherwise noted).
- Representative coefficients and robustness:
  - Table A1 (robustness to choice of monetary policy shock), column (1): MP easing_{t} × LMP_{i,c,t−1} = 1.415 ∗∗∗ (0.405) using Nakamura and Steinsson (2018) shock in that specification. Other columns show similar positive and significant interaction estimates across alternative shocks.
  - Table A2 (alternative industry-level LMP_alt):
    - MP easing_{t}: 0.447 ∗∗∗; 0.830 ∗∗∗; 0.894 ∗∗∗. (SEs: (0.050); (0.040); (0.042))
    - LMP Industry_{i,c,t}: 0.657 ∗∗∗; -0.098 ∗∗; -0.047; 0.979 ∗∗∗; 1.076 ∗∗∗; 1.202 ∗∗∗; 1.223 ∗∗∗. (SEs reported per column)
    - MP easing_{t} × LMP Industry_{i,c,t}: 0.807 ∗∗∗; 0.110; 0.206; 0.520 ∗∗∗; 0.582 ∗∗∗; 0.607 ∗∗∗; 0.868 ∗∗∗. (SEs reported per column)
  - Table A3 (excluding Public Administration):
    - MP easing_{t}: 0.330 ∗∗∗; 0.625 ∗∗∗; 0.672 ∗∗∗. (SEs: (0.036); (0.031); (0.035))
    - LMP_{i,c,t−1}: large positive coefficients (e.g., 24.517 ∗∗∗; 15.485 ∗∗∗; 15.952 ∗∗∗; … up to 24.005 ∗∗∗). (SEs reported per column)
    - MP easing_{t} × LMP_{i,c,t−1}: positive and often significant (e.g., 15.005 ∗∗∗; 3.556 ∗; 5.611 ∗∗∗; … up to 9.181 ∗∗). (SEs reported per column)
  - Table A4 (with aggregate controls including 4 lags of GDP growth, inflation and unemployment rate):
    - MP easing_{t}: 0.064 ∗∗; 0.429 ∗∗∗; 0.432 ∗∗∗. (SEs: (0.031); (0.029); (0.031))
    - LMP_{i,c,t−1}: 38.060 ∗∗∗; 21.163 ∗∗∗; 21.580 ∗∗∗; … up to 35.724 ∗∗∗. (SEs reported)
    - MP easing_{t} × LMP_{i,c,t−1}: 35.809 ∗∗∗; 12.253 ∗∗∗; 12.309 ∗∗∗; … up to 17.615 ∗∗∗. (SEs reported)
  - Table A5 (dynamic labor demand effects across horizons 0–7 quarters):
    - MP easing_{t}: reported positive and significant at many horizons (e.g., 0.696 ∗∗∗; 1.965 ∗∗∗; 1.820 ∗∗∗; 0.940 ∗∗∗; 1.185 ∗∗∗; 0.682 ∗∗∗; 0.615 ∗∗; 0.853 ∗∗∗). (Standard errors shown as (0.035) and (0.000) in alternating formatting in table.)
    - LMP_{i,c,t−1}: large positive growth across horizons (examples: 20.318 ∗∗∗; 22.713 ∗∗∗; 39.246 ∗∗∗; 44.025 ∗∗∗; … up to 137.411 ∗∗∗). (SEs reported per horizon)
    - MP easing_{t} × LMP_{i,c,t−1}: positive and often significant across horizons (examples: 5.442 ∗∗; 7.895 ∗∗; 37.053 ∗∗∗; 41.740 ∗∗∗; … up to 71.901 ∗∗∗). (SEs reported per horizon)
    - Total Effect summaries (from Table A5):
      - Total Effect, Low LMP (listed across horizons): 0.7; 2.3; 2.1; 1.3; 1.6; 1.1; 1.1; 1.4 with accompanying parentheses values (0.0), (0.1), (0.1), (0.1), (0.2), (0.2), (0.3), (0.3).
      - Total Effect, High LMP (listed across horizons): 0.9; 3.3; 3.0; 2.4; 2.9; 2.7; 3.0; 3.5 with accompanying parentheses values (0.1), (0.2), (0.3), (0.4), (0.4), (0.5), (0.6), (0.7).
- Empirical implications:
  - Monetary policy easing raises vacancy postings, and the effect is larger for firms with greater labor market power (positive MP easing × LMP interaction coefficients across multiple specifications and shocks).
  - Results are robust to alternative shock measures, exclusion of Public Administration, inclusion of aggregate controls, and alternative LMP definitions at the industry level.
  - Dynamic evidence shows persistent and often increasing interaction effects across horizons up to multiple quarters.

### Heterogeneity by vacancy characteristics and firm market power (Figures 3–11, 9–10)
- Vacancy-type heterogeneity:
  - Figures 3, 9, 10 document differences in the vacancy-share–wage relationship and vacancy responses depending on whether vacancies require a college degree.
  - Figure 9 reports ˆβ_H and ˆβ_H+ˆω_H from regressions including MP easing_{t} × LMP_{i,c,t−1} × VacancyType, separating vacancies that require college degree (Vacancy Type = 1) from those that do not.
- Labor market power geography and sectoral concentration:
  - Figure 4 maps the share of vacancies controlled by high-LMP firms (top 5% of vacancy-share distribution) across U.S. commuting zones.
  - Figure 5 shows the share of firms with high labor market power within each industry.
- Firm-size / market-power heterogeneity:
  - Figures 6–8 and 10 illustrate that the vacancy response to a 10 bps easing of monetary policy is larger for firms at higher percentiles of the LMP distribution (Low = 5th percentile; Median = 50th; High = 95th).
  - Confidence intervals in Figures 7–8 indicate statistical significance of the differential responses; standard errors double clustered at firm and commuting zone levels.

### Employment and vacancy dynamics (Figures 11–12)
- Employment sensitivity to vacancies:
  - Figure 11 plots a binscatter between firm-level log change in employment (Compustat) and Log Vacancies (BGT). Regression form: ΔEmployment_{i,t} = α_{i} + α_{t} + β_{1} Log Vacancies_{i,t} + ε_{i,t}.
- Interaction of LMP and monetary policy on employment:
  - Figure 12 shows ˆβ_H from ∑_{H} ΔEmployment_{i,t+h} = α_H + β_H MP easing_{t} × LMP_{i,t−1} + θ_H X_{i,t} + γ_{i,H} + γ_{t+H} + ε_{i,t+H}.
  - LMP_{i,t−1} is defined as 1 if the firm is in the top 5% of labor market power in at least one commuting zone.
  - Standard errors clustered at the firm level; shaded areas represent 95% confidence intervals.

### Additional figures and robustness visualizations (Appendix)
- Figure A1: plots monetary policy shocks (Jarociński and Karadi (2020)) in percentage points, with positive values reflecting monetary policy easing; components: Monetary Policy vs. Central Bank Information.
- Figure A2: vacancy response using industry-level alternative LMP (LMP_alt_{i,c,t−1}); bars for Low (5th), Median (50th), High (95th) LMP.
- Figure A3: cumulative one-year-ahead vacancy responses for Low/Median/High LMP.
- Figure A4: dynamic wage interaction coefficients (ˆβ_H) across horizons with standard errors double clustered at firm and commuting zone levels.

*Source: wpiea2022128-print-pdf - section 3. Standard errors are double clustered at the firm and commuting zone level. *** p<0.01, ** p<0.05, * p<0.1.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022128-print-pdf.pdf_