## wpiea2024222-print-pdf - Section 3 summarizes our methodology and presents the empirical findings. Section 4 concludes.

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---

### Data — overview, advantages, limitations, and benchmarking
- Sample period: January 2019 to December 2021.
- Primary administrative dataset: Homebase (employees at businesses using Homebase scheduling/time clock software).
  - Coverage: over 80,000 businesses and more than 1 million employees across the U.S.
  - Frequency: daily records aggregated to monthly for analysis.
  - Information: wages and hours for individual employees; job-level details including job duration and type; managerial vs nonmanagerial classification; establishment location and industry.
  - Sample restriction: firms that reported positive hours between January 2020 and March 2020.
  - Outlier treatment: observations where hours worked or average hourly wages exceed the top 1 percent of the overall sample are excluded.
- Advantages:
  - Broad coverage of private businesses, including extensive representation of small firms—contrast with Compustat (only publicly traded firms).
  - Worker-level wage and hours information enabling analysis of earnings components and compositional biases.
  - High-frequency geographic granularity (monthly, small geographical units).
- Limitations:
  - No information on tips, benefits, or overtime payments.
  - Skewed toward small businesses in leisure, hospitality, and retail; may not fully represent aggregate employment.
- Benchmarking and validation against official statistics:
  - Cumulative growth in average earnings from January 2020 to December 2021:
    - Homebase: 13.5 percent
    - CPS: 12.2 percent
    - CES: 13.4 percent
  - Month-state level correlations (Homebase vs CES for 2020-2021):
    - Hourly wages: 0.51
    - Employment: 0.69
  - Noted anomaly: CES shows unusually high growth in Q1 2020 relative to Homebase and CPS due to compositional changes (job losses disproportionately large among lower-wage workers).
  - Additional official data sources used: CES, CPS, BLS UNEMP and JTSJOL, QWI, QCEW.
- PPP data and bank matching:
  - Source: SBA PPP loan approvals (loan amounts, lender names, borrower addresses).
  - Bank matching: lender names matched to commercial and savings banks in Call Reports as of Q1 2020 using a probabilistic record linkage algorithm (Stata’s reclink2 package).
  - When lender name matches multiple banks with same legal name, match assigned to bank with branch closest to borrower using Summary of Deposits data as of Q2 2019.
  - Adjusted for mergers between Q2 2019 and Q1 2020 using National Information Center bank mergers file.
  - Matching results:
    - 95.4 percent of banks matched
    - 96.4 percent of PPP loan amounts matched
  - For matched banks, lender financial characteristics from Call Reports used, including number and amount of small business loans outstanding.

### Stylized facts — summary of empirical findings
- Method: Panel of Homebase workers; counties ranked by average earnings growth between March 2020 and December 2019; counties grouped into three categories: below the 10th percentile, between the 10th and 90th percentiles, and above the 90th percentile. Each series indexed to its December 2019 value.

- Fact 1: Earnings growth diverged across counties
  - April 2020 (immediate COVID-19 lockdown impact):
    - Bottom decile counties: average earnings were 20 percent below their December 2019 level.
    - Top decile counties: average earnings were 20 percent above their December 2019 level.
  - December 2020 levels (indexed to December 2019):
    - Bottom decile counties: 68.9 percent
    - Top decile counties: 115.5 percent
  - December 2021 levels (indexed to December 2019):
    - Bottom decile counties: 110.8 percent
    - Top decile counties: 156.9 percent
  - Comparative cumulative growth statement:
    - Cumulative growth from 2020 to 2021 was over 46.07 percent higher in the top decile counties compared to the bottom decile counties.
  - Validation with QCEW: QCEW county-level average weekly wages for the service-providing sector show top decile counties experienced significantly faster wage growth than bottom decile counties (ranking based on growth Q1 2020 vs Q4 2019).

- Fact 2: Earnings grew faster for lower-paid and nonmanagerial workers
  - Manager vs nonmanager classification: “manager” if identified as “manager” or “general manager” in Homebase.
  - January–February 2020: managerial and nonmanagerial earnings nearly identical (both series indexed to 100 for same month in 2019).
  - March–April 2020 dynamics:
    - Managerial earnings: 8.9 percent drop in March 2020, recovered in April; trend relatively flat thereafter with end-2021 similar to Jan–Feb 2020.
    - Nonmanagerial earnings: dropped to 52.5 percent of the 2019 level in April 2020, then reversed with high growth in mid-2020 and throughout 2021.
  - December 2021 levels (indexed to 2019):
    - Nonmanagers: 133.3 percent of the 2019 level.
  - Cumulative differences during 2020–2021:
    - Nonmanagers had 29.7 percentage points higher cumulative earnings growth than managers.
    - Nonmanagers experienced 27.4 percentage points higher cumulative growth in hours and 1.5 percentage points higher growth in hourly wage compared to managers.
  - Observed compositional effects:
    - Both managers and nonmanagers showed an uptick in average hourly wage in April 2020, indicating larger job losses among lower-paid workers within each group.
  - Validation with CES:
    - CES average hourly wage for production and nonsupervisory employees diverged from overall trend after 2021, reaching 3 percentage points above the 2019 level by end of 2022 relative to the overall series.

- Fact 3: Earnings grew faster for workers in small firms
  - Firm-size bins (Homebase): 19 or fewer employees; 20 to 49 employees; 50 to 249 employees; 250 or more employees.
  - April 2020: workers in firms of all sizes experienced similar earnings declines.
  - Recovery and divergence through December 2021:
    - Firms with 19 or fewer employees: average earnings rose to 131.3 percent of their 2019 level.
    - Firms with 250 or more employees: average earnings rose to 115.1 percent of their 2019 level.
  - Drivers: faster increases in both wages and hours worked at smaller firms.
  - Validation with QCEW (private-sector average weekly earnings by firm size, first quarter of each year, indexed to same quarter in 2019):
    - 2023 levels relative to 2019:
      - Firms with fewer than 20 employees: 130.7 percent of the 2019 level.
      - Firms with more than 250 employees: 120.9 percent of the 2019 level.
    - Cumulative difference in 2023: 9.8 percent between smallest and largest firm-size bins.

### 3.1 The role of labor market strength — specification, identification, and results
- Empirical specification and sample:
  - Panel of Homebase workers from January 2020 to December 2021.
  - Final sample: 3.1 million observations across 3,110 counties.
  - Weighting: each observation weighted by its industry’s pre-pandemic share of the labor force in 2019; weights fixed at pre-pandemic level.
  - Cluster standard errors by county and month.
  - Main outcomes (Y): nominal total earnings and its components: average hourly wage and hours worked.
- Baseline regression:
  - ∆Y_i,j,k,c,t = α_0 + α_1 Post_t × Shock_c + β′ Z_i,j,k,c,t + e_i,j,k,c,t
  - ∆Y denotes growth rate in Y from January 2020 to month t measured as log difference.
  - Post_t: dummy equal to one from April 2020 to December 2021.
  - Shock_c: county-specific measure of labor market strength (standardized to unit standard deviation).
  - Controls Z_i,c,t include worker fixed effects, state×industry×month fixed effects, lags of the labor market shock (March, February, January 2020), and county-level controls (log median household income; COVID-19 cases and deaths per capita; average tier 1 capital and core deposit ratios of local banks).
- Dynamic specification:
  - ∆Y_i,j,k,c,t = α_0 + α′_1 [I_t × Shock_c] + β′ Z_i,j,k,c,t + e_i,j,k,c,t
  - I_t: vector of monthly time dummies from February 2020 to December 2021 (January 2020 reference).
- Identification:
  - Primary measure: vacancy-to-unemployment ratio (baseline).
  - Robustness measures: quit rate and unemployment rate.
  - Bartik shock construction using county 2-digit NAICS employment shares for 2017-2018 and national changes in industry-level vacancy-to-unemployment ratio between April 2019 and April 2020; public administration excluded.
  - Direct county-level vacancy-to-unemployment measure: unemployment from BLS Local Area Unemployment Statistics; vacancies from proprietary Indeed data (142 million job postings; covering 421 occupations (ISCO-08), 2.9 million companies, and 576 counties); Indeed correlation with JOLTS up to 0.96 at state-month level.
  - Identification strategy relies on quasi-random assignment of industry demand shocks; inclusion of state×industry×month fixed effects and county-level controls mitigate confounding.
- Key estimated elasticities using the Bartik shock (one-standard-deviation increase in labor market strength):
  - hourly wage: 6 percent increase.
  - hours worked: 12 percent increase.
  - total earnings: 18 percent increase.
- Decomposition of total earnings growth:
  - Hourly wage accounts for approximately one-third of the total earnings increase.
  - Hours worked explain about two-thirds of the total earnings increase.
- Time path from dynamic estimates (April 2020 responses and persistence):
  - April 2020, one-standard-deviation Bartik shock associated with:
    - hourly wage: approximately a 9.7 percent increase.
    - hours worked: approximately a 14.6 percent increase.
    - total earnings: approximately a 23.4 percent increase.
  - Second half of 2020 tapering to around:
    - hourly wage: 15.5 percent.
    - hours worked: 10.1 percent.
    - total earnings: 5.9 percent.
  - By end of 2021, effects decline to about:
    - hourly wage: 9.8 percent.
    - hours worked: 7.2 percent.
    - total earnings: 3.0 percent.
- Persistence interpretation:
  - No pre-pandemic trends detected for February and March 2020 relative to January 2020.
  - Impact is persistent but declines over time; sustained response in total earnings largely driven by persistence in hours worked.
  - By end-2021, effect on hours remains substantial and statistically significant at the 1 percent level, while impact on hourly wages approaches close to zero.

### 3.2 The role of PPP — program, identification, empirical findings, and mechanisms
- PPP program overview:
  - Eligibility: Businesses with 500 or fewer employees (exception: accommodations and food services, NAICS code 72, where threshold applied per physical location).
  - Maximum loan amount: the lesser of 2.5 times the average monthly payroll costs or $10 million; average payroll costs calculated based on prior year’s payroll, excluding compensation exceeding $100,000 per individual.
  - Interest rate: 1 percent; maturity period: 2 years.
  - Forgiveness rules: funds to be used for payroll costs, mortgage interest, rent, and utility payments within an eight-week period, with at least 75 percent allocated to payroll; up to 25 percent of the PPP loan could be used for nonpayroll costs.
  - Disbursement chronology and totals:
    - First round began on April 3, 2020; initial $349 billion fully allocated by April 16.
    - Second bill passed on April 24 adding $320 billion; applications accepted starting April 27.
    - In first two weeks of second round, 60 percent of the funds were disbursed; by early July more than $130 billion remained available.
    - Program stopped accepting applications on August 8, with $525 billion disbursed in total.
  - Institutional delivery: PPP applications managed through the banking system overseen by the SBA; bank-level supply-side constraints produced heterogeneous access across regions.
- Identification strategy using bank-driven PPP supply variation:
  - Bank-level PPP performance measure:
    - PPPE_b = (SharePPP − ShareSBL) / (SharePPP + ShareSBL) × 0.5
      - SharePPP: bank b’s PPP loans as a share of all PPP loans (number of loans).
      - ShareSBL: bank b’s small business loans (SBL) as a share of all SBL in Q4 2020 (number of loans).
  - Predicted PPPE_b obtained by regressing PPPE_b on predetermined supply-side covariates (bank labor intensity, pre-existing SBA lender dummy, bank’s SBA loans as share of SBA loans, dummy for active enforcement actions at PPP launch, dummy for Wells Fargo Bank).
  - County PPP exposure, PPPE_c, is weighted average of bank predicted PPPE_b using branch-share weights (Summary of Deposits).
  - Evidence of orthogonality: correlation between PPPE_c and Shock_c is 0.04.
- Empirical specifications:
  - Main cross-sectional interaction:
    - ∆Y_{i,j,k,c,t} = α_0 + α_1 Post_t × Shock_c + α_2 Post_t × PPPE_c + α_3 Post_t × Shock_c × PPPE_c + β′ Z_{i,j,k,c,t} + e_{i,j,k,c,t}
    - Z includes county banking sector conditions (average tier 1 capital and core deposit ratios).
  - Dynamic monthly specification includes I_t × Shock_c, I_t × PPPE_c, and I_t × Shock_c × PPPE_c interactions.
- Main empirical findings on PPP exposure (preferred Bartik columns 4–6):
  - A one-standard-deviation increase in PPP exposure leads to:
    - 13 percent rise in hourly wage.
    - 19 percent rise in hours.
    - 32 percent rise in total earnings.
  - PPP exposure modestly amplifies the effects of the Bartik shock:
    - A one-standard-deviation increase in PPP exposure increases the Bartik shock’s marginal effect by less than one-sixth.
  - Relative contributions to total earnings:
    - Wage contributes about one-third of total earnings increase.
    - Hours contribute about two-thirds of total earnings increase.
- Time path:
  - Large PPP exposure response between April and June 2020 (aligns with peak disbursement in first two rounds).
  - Effects taper off toward end of 2020; by May 2021 effects are no longer statistically significant.
  - Slight uptick in December 2020 and January 2021.
  - Indirect effect (α_3) follows similar trajectory but with magnitude less than one-tenth of α_2.
- Mechanisms:
  - Direct channel: loan forgiveness requirements incentivized recipients to maintain employment and compensation levels.
  - Indirect channel: covering nonpayroll costs (up to 25 percent) relieved financial pressure and prevented reductions in employment and wages.
- Robustness and complementary evidence:
  - Granja et al. (2022) supports supply-side interpretation: heterogeneity in bank processing capacity affected first-round access; relationship diminished in second round.
  - Orthogonality checks: PPPE_c correlation with Shock_c is 0.04.
  - Controls include local banking sector conditions.

### Robustness checks, heterogeneity, and supplementary specifications
- Controlling for contemporaneous labor market strength:
  - Shock_{c,Y earMt} defined for Year ∈ (2020,2021) as contemporaneous analog to initial shock (Equation 9).
  - Table A2 shows estimated coefficient of the initial shock close to baseline when controlling for contemporaneous shocks.
  - Preferred measures with contemporaneous control:
    - A one-standard-deviation increase in labor market strength results in a 5.7 percent increase in hourly wages, compared to 6.4 percent in baseline.
    - Effect on hours worked nearly identical to baseline.
    - Resulting impact on total earnings is 16.5 percent, slightly lower than the 18 percent baseline.
- Alternative shock measures (Table A1):
  - Using quits-based Bartik shock:
    - Post_t × Shock_c = 0.1213*** (Hourly Wages)
    - Post_t × Shock_c = 0.1460*** (Hours)
    - Post_t × Shock_c = 0.2631*** (Total Earnings)
  - Using unemployment-based Bartik shock:
    - Post_t × Shock_c = -0.0422*** (Hourly Wages)
    - Post_t × Shock_c = -0.0468** (Hours)
    - Post_t × Shock_c = -0.0834*** (Total Earnings)
- Key heterogeneity coefficients (Bartik specifications unless noted):
  - Managerial vs nonmanagerial (Table 4):
    - Post_t × Shock_c × Non-Manager_j for Total Earnings: 0.0650*** (0.0010)
  - High- vs low-wage workers (Table 5):
    - Post_t × Shock_c × Low-Wage_j for Total Earnings: 0.1208*** (0.0077)
  - Job-switchers vs stayers (Table 6):
    - Post_t × Shock_c × Job-Switcher_j for Total Earnings: 0.0078*** (0.0020)
  - Firm size (Table 7):
    - Post_t × Shock_c × Small_i for Total Earnings: 0.0830*** (0.0015)

### Key quantitative results and statistics (preserved exactly)
- Sample and measurement:
  - Worker-level observations: 3,134,354 for Hourly Wages, Hours, Total Earnings, and growth measures.
  - Worker-level means and dispersion:
    - Hourly Wages_{i,j,k,c,t}: Obs 3,134,354; Mean 9.576; St. Dev. 6.978; Min 0.000; Median 10.500; Max 50.000
    - Hours_{i,j,k,c,t}: Obs 3,134,354; Mean 18.815; St. Dev. 15.561; Min 0.000; Median 17.413; Max 87.442
    - Total Earnings_{i,j,k,c,t}: Obs 3,134,354; Mean 242.381; St. Dev. 247.696; Min 0.000; Median 179.526; Max 4,372.125
    - ∆Hourly Wages_{i,j,k,c,t}: Obs 3,134,354; Mean 0.011; St. Dev. 0.710; Min -2.773; Median 0.000; Max 2.708
    - ∆Hours_{i,j,k,c,t}: Obs 3,134,354; Mean 0.071; St. Dev. 0.843; Min -3.231; Median 0.000; Max 3.321
    - ∆Total Earnings_{i,j,k,c,t}: Obs 3,134,354; Mean 0.074; St. Dev. 1.485; Min -5.766; Median 0.000; Max 5.735
  - Worker characteristics (means):
    - Non-Manager_j: 0.884
    - Job-Switcher_j: 0.404
    - Low-Wage_j: 0.765
    - Small_i (employer <50 employees): 0.578
- County-level shock statistics (Panel B):
  - Shock_c (OLS): Obs 3,110; Mean -0.045; St. Dev. 0.007; Min -0.117; Median -0.045; Max 0.014
  - Shock_{c,t} (OLS): Obs 40,430; Mean 0.025; St. Dev. 0.013; Min -0.025; Median 0.025; Max 0.132
  - Shock_c (Bartik): Obs 3,110; Mean -0.551; St. Dev. 0.072; Min -1.241; Median -0.546; Max 0.195
  - Shock_{c,t} (Bartik): Obs 40,430; Mean 0.662; St. Dev. 0.267; Min -0.184; Median 0.645; Max 2.058
  - PPPE_c (PPP exposure): Obs 3,110; Mean -0.161; St. Dev. 0.252; Min -0.500; Median -0.181; Max 0.500
  - Log median household income: Obs 3,110; Mean 10.700; St. Dev. 0.225; Min 9.867; Median 10.677; Max 12.538
  - COVID cases per capita: Obs 3,110; Mean 0.795; St. Dev. 0.147; Min 0.318; Median 0.804; Max 1.102
  - COVID deaths per capita: Obs 3,110; Mean 0.012; St. Dev. 0.003; Min 0.004; Median 0.013; Max 0.017
  - Average tier 1 capital ratio: Obs 3,110; Mean 7.965; St. Dev. 0.508; Min 5.874; Median 7.991; Max 9.109
  - Average core deposit ratio: Obs 3,110; Mean 1.185; St. Dev. 0.161; Min 0.673; Median 1.159; Max 3.371
- Baseline regression estimates (Table 2; standardized shocks):
  - OLS specification (columns 1-3) Post_t × Shock_c:
    - Hourly Wages: 0.1142*** (0.0173)
    - Hours: 0.1743*** (0.0244)
    - Total Earnings: 0.2830*** (0.0402)
  - Bartik specification (columns 4-6) Post_t × Shock_c:
    - Hourly Wages: 0.0643*** (0.0161)
    - Hours: 0.1187*** (0.0225)
    - Total Earnings: 0.1806*** (0.0370)
- PPP exposure interaction results (Table 3; standardized variables, Bartik columns 4-6):
  - Post_t × PPPE_c:
    - Hourly Wages: 0.1345*** (0.0431)
    - Hours: 0.1904*** (0.0614)
    - Total Earnings: 0.3208*** (0.1001)
  - Post_t × Shock_c × PPPE_c:
    - Hourly Wages: 0.0102*** (0.0032)
    - Hours: 0.0142*** (0.0045)
    - Total Earnings: 0.0240*** (0.0074)

### Conclusion — main takeaways and policy relevance
- Aggregate and distributional patterns:
  - Counties with smaller labor market shocks at the onset of COVID-19 saw faster earnings growth afterward.
  - Gains were disproportionately larger for lower-paid, nonmanagerial workers and workers in smaller firms.
  - Drivers of gains: higher hourly wages and increased working hours.
  - Counties that received more labor market support through the PPP experienced differing growth patterns.
- Theoretical alignment:
  - Trends align with job-ladder models where labor market competition drives up earnings as workers move upward.
- Inequality implications:
  - Increasing earnings disparities across geographic regions were observed.
  - Within counties with stronger labor markets, wage inequality among workers decreases.
  - Results point to evolving patterns of wage and spatial inequality and asynchronous labor market conditions across regions.
- Policy relevance and future research:
  - Trends offer insights for post-pandemic stabilization policies and directions for future research on distributional consequences and spatial labor market dynamics.

*Source: wpiea2024222-print-pdf (Section 3 data and stylized facts).*

### Section 3 summarizes our methodology and presents the empirical findings. Section 4 concludes.

### wpiea2024222-print-pdf - Section 3 summarizes our methodology and presents the empirical findings. Section 4 concludes.

### Data — overview
- Sample period: January 2019 to December 2021.
- Primary administrative dataset: Homebase (employees at businesses using Homebase scheduling/time clock software).
  - Coverage: over 80,000 businesses and more than 1 million employees across the U.S.
  - Frequency: daily records aggregated to monthly for analysis.
  - Information: wages and hours for individual employees; job-level details including job duration and type; managerial vs nonmanagerial classification; establishment location and industry.
  - Sample restriction: firms that reported positive hours between January 2020 and March 2020.
  - Outlier treatment: observations where hours worked or average hourly wages exceed the top 1 percent of the overall sample are excluded.

### Data — advantages and limitations of Homebase
- Advantages:
  - Broad coverage of private businesses, including extensive representation of small firms—contrast with Compustat (only publicly traded firms).
  - Worker-level wage and hours information enabling analysis of earnings components and compositional biases.
  - High-frequency geographic granularity (monthly, small geographical units).
- Limitations:
  - No information on tips, benefits, or overtime payments.
  - Skewed toward small businesses in leisure, hospitality, and retail; may not fully represent aggregate employment.

### Benchmarking and validation against official statistics
- Aggregate alignment (Homebase vs CPS and CES):
  - Cumulative growth in average earnings from January 2020 to December 2021:
    - Homebase: 13.5 percent
    - CPS: 12.2 percent
    - CES: 13.4 percent
  - Month-state level correlations (Homebase vs CES for 2020-2021):
    - Hourly wages: 0.51
    - Employment: 0.69
  - Noted anomaly: CES shows unusually high growth in Q1 2020 relative to Homebase and CPS due to compositional changes (job losses disproportionately large among lower-wage workers).
- Additional official data sources used for complementary analyses:
  - Current Employment Statistics (CES) — time series and state-level average hourly wages.
  - Current Population Survey (CPS) — quarterly median usual weekly nominal earnings; labor force statistics time series.
  - BLS series: UNEMP (aggregate unemployment rate), JTSJOL (total nonfarm job openings).
  - Labor market vacancy-to-unemployment ratio: ratio of JTSJOL to UNEMPLOY.
  - Quarterly Workforce Indicators (QWI) — industry-county employment.
  - Quarterly Census of Employment and Wages (QCEW) — county-level average weekly wages for service-providing sector.
- PPP data and bank matching:
  - Source: SBA PPP loan approvals (loan amounts, lender names, borrower addresses).
  - Bank matching: lender names matched to commercial and savings banks in Call Reports as of Q1 2020 using a probabilistic record linkage algorithm (Stata’s reclink2 package).
  - When lender name matches multiple banks with same legal name, match assigned to bank with branch closest to borrower using Summary of Deposits data as of Q2 2019.
  - Adjusted for mergers between Q2 2019 and Q1 2020 using National Information Center bank mergers file.
  - Matching results:
    - 95.4 percent of banks matched
    - 96.4 percent of PPP loan amounts matched
  - For matched banks, lender financial characteristics from Call Reports used, including number and amount of small business loans outstanding.

### Stylized facts — summary and empirical findings
- Method: Panel of Homebase workers; counties ranked by average earnings growth between March 2020 and December 2019; counties grouped into three categories: below the 10th percentile, between the 10th and 90th percentiles, and above the 90th percentile. Each series indexed to its December 2019 value.

- Fact 1: Earnings growth diverged across counties
  - April 2020 (immediate COVID-19 lockdown impact):
    - Bottom decile counties: average earnings were 20 percent below their December 2019 level.
    - Top decile counties: average earnings were 20 percent above their December 2019 level.
  - December 2020 levels (indexed to December 2019):
    - Bottom decile counties: 68.9 percent
    - Top decile counties: 115.5 percent
  - December 2021 levels (indexed to December 2019):
    - Bottom decile counties: 110.8 percent
    - Top decile counties: 156.9 percent
  - Comparative cumulative growth statement:
    - Cumulative growth from 2020 to 2021 was over 46.07 percent higher in the top decile counties compared to the bottom decile counties.
  - Validation with QCEW:
    - QCEW county-level average weekly wages for the service-providing sector show top decile counties experienced significantly faster wage growth than bottom decile counties (ranking based on growth Q1 2020 vs Q4 2019).

- Fact 2: Earnings grew faster for lower-paid and nonmanagerial workers
  - Manager vs nonmanager classification: “manager” if identified as “manager” or “general manager” in Homebase.
  - January–February 2020: managerial and nonmanagerial earnings nearly identical (both series indexed to 100 for same month in 2019).
  - March–April 2020 dynamics:
    - Managerial earnings: 8.9 percent drop in March 2020, recovered in April; trend relatively flat thereafter with end-2021 similar to Jan–Feb 2020.
    - Nonmanagerial earnings: dropped to 52.5 percent of the 2019 level in April 2020, then reversed with high growth in mid-2020 and throughout 2021.
  - December 2021 levels (indexed to 2019):
    - Nonmanagers: 133.3 percent of the 2019 level.
  - Cumulative differences during 2020–2021:
    - Nonmanagers had 29.7 percentage points higher cumulative earnings growth than managers.
    - Nonmanagers experienced 27.4 percentage points higher cumulative growth in hours and 1.5 percentage points higher growth in hourly wage compared to managers.
  - Observed compositional effects:
    - Both managers and nonmanagers showed an uptick in average hourly wage in April 2020, indicating larger job losses among lower-paid workers within each group.
  - Validation with CES:
    - CES average hourly wage for production and nonsupervisory employees diverged from overall trend after 2021, reaching 3 percentage points above the 2019 level by end of 2022 relative to the overall series.

- Fact 3: Earnings grew faster for workers in small firms
  - Firm-size bins (Homebase): 19 or fewer employees; 20 to 49 employees; 50 to 249 employees; 250 or more employees.
  - April 2020: workers in firms of all sizes experienced similar earnings declines.
  - Recovery and divergence through December 2021:
    - Firms with 19 or fewer employees: average earnings rose to 131.3 percent of their 2019 level.
    - Firms with 250 or more employees: average earnings rose to 115.1 percent of their 2019 level.
  - Drivers: faster increases in both wages and hours worked at smaller firms.
  - Validation with QCEW (private-sector average weekly earnings by firm size, first quarter of each year, indexed to same quarter in 2019):
    - 2023 levels relative to 2019:
      - Firms with fewer than 20 employees: 130.7 percent of the 2019 level.
      - Firms with more than 250 employees: 120.9 percent of the 2019 level.
    - Cumulative difference in 2023: 9.8 percent between smallest and largest firm-size bins.

*Source: wpiea2024222-print-pdf (Section 3 data and stylized facts).*

### 3.1    The role of labor market strength

### 3.1    The role of labor market strength

### 3.1.1    Empirical specification
- Objective: understand post-pandemic worker earnings and assess how local labor market strength affects earnings growth using cross-county variation.
- Data and sample:
  - Panel of Homebase workers from January 2020 to December 2021.
  - Final sample: 3.1 million observations across 3,110 counties.
  - Weighting: each observation weighted by its industry’s pre-pandemic share of the labor force in 2019; weights fixed at pre-pandemic level.
  - Cluster standard errors by county and month.
- Main outcomes (Y): nominal total earnings and its components: average hourly wage and hours worked.
- Baseline regression (equation 1):
  - ∆Y_i,j,k,c,t = α_0 + α_1 Post_t × Shock_c + β′ Z_i,j,k,c,t + e_i,j,k,c,t
  - ∆Y denotes growth rate in Y from January 2020 to month t measured as log difference.
  - Post_t: dummy equal to one from April 2020 to December 2021.
  - Shock_c: county-specific measure of labor market strength (standardized to unit standard deviation).
  - Z_i,c,t: controls (specified below).
- Dynamic specification (equation 2):
  - ∆Y_i,j,k,c,t = α_0 + α′_1 [I_t × Shock_c] + β′ Z_i,j,k,c,t + e_i,j,k,c,t
  - I_t: vector of monthly time dummies from February 2020 to December 2021 (January 2020 reference).
  - Estimates cumulative impact of Shock_c over time via I_t × Shock_c interactions.
- Addressing sample composition changes:
  - Restrict sample to workers present in database for at least two years between 2019 and 2021, including temporary layoffs (defined as employed at start, zero earnings during middle, returned by end).
  - Also control for worker fixed effects to rely on within-worker variation and mitigate compositional bias.
- Controls included in Z_i,c,t: worker fixed effects, state×industry×month fixed effects, lags of the labor market shock (March, February, January 2020), and county-level controls (log median household income; COVID-19 cases and deaths per capita; average tier 1 capital and core deposit ratios of local banks).

### 3.1.2    Identification
- Primary measure of labor market strength: vacancy-to-unemployment ratio (baseline).
- Robustness measures: quit rate and unemployment rate.
- Rationale: vacancy-to-unemployment ratio derives from search models (Blanchard and Diamond (1989)); preferred for post-pandemic period due to upward shift in the Beveridge curve.
- Construction of Bartik shock (Shock_c) using shift-share method:
  - Uses county 2-digit NAICS employment shares for 2017-2018 (φ_c,k,2017−2018) and national changes in industry-level vacancy-to-unemployment ratio between April 2019 and April 2020.
  - Shock_c defined as change in projected labor market conditions between April 2019 and April 2020:
    - Shock_c = (∆\ln(V)_c,April 2020 − ∆\ln(V)_c,April 2019) − (∆\ln(U)_c,April 2020 − ∆\ln(U)_c,April 2019)
    - ∆\ln(V)_c,April 2020 = Σ_{k=1}^K φ_c,k,2017−2018 * (ln(V_k,April 2020) − ln(V_k,January 2020))
    - ∆\ln(V)_c,April 2019 = Σ_{k=1}^K φ_c,k,2017−2018 * (ln(V_k,April 2019) − ln(V_k,January 2019))
    - Similar definition for ∆\ln(U)_c,t.
  - Excludes public administration from industries.
- Industry and geographic variation:
  - Service industries, particularly contact-intensive sectors, experienced large negative shocks (e.g., accommodation and food services among the most negative).
  - Information, finance, and insurance saw positive shocks.
  - Construction and manufacturing had substantial negative shocks.
  - County-level shocks vary substantially; greater impacts in Northeast and Midwest, with variation within regions and states; urban centers generally experience higher exposure but rural areas vary.
- Identification strategy relies on quasi-random assignment of industry demand shocks per Borusyak et al. (2022).
  - Address potential threats from differential pre-trends: Figure A8 shows nearly identical earnings trends from early 2019 across counties by Bartik shock deciles.
  - Inclusion of state×industry×month fixed effects mitigates time-varying demand shocks at state-industry level.
  - County-level controls mitigate correlation with local conditions (income, public health, banking).
  - Use of detailed 2-digit industry shocks supports law of large numbers for quasi-random assignment.
- Direct county-level vacancy-to-unemployment measure:
  - Unemployment: BLS Local Area Unemployment Statistics.
  - Vacancies: proprietary Indeed data (142 million job postings; covering 421 occupations (ISCO-08), 2.9 million companies, and 576 counties); aggregated to county-month level.
  - Indeed data correlation with JOLTS at state-month level up to 0.96.
  - Preference for Bartik measure over direct measure due to potential measurement error and local conditions confounding in direct measure; direct measure used for robustness.

### 3.1.3    Results
- Table 2 summary: Columns 1–3 use direct measure; columns 4–6 use Bartik shock. Both measures show significant positive effects of local labor market strength on hourly wage, hours worked, and total earnings.
- Key estimated elasticities using the Bartik shock (one-standard-deviation increase in labor market strength):
  - hourly wage: 6 percent increase.
  - hours worked: 12 percent increase.
  - total earnings: 18 percent increase.
- Decomposition of total earnings growth:
  - Hourly wage accounts for approximately one-third of the total earnings increase.
  - Hours worked explain about two-thirds of the total earnings increase.
- Time path from equation (2) (Figure 5) — April 2020 initial responses and persistence:
  - April 2020, one-standard-deviation Bartik shock associated with:
    - hourly wage: approximately a 9.7 percent increase.
    - hours worked: approximately a 14.6 percent increase.
    - total earnings: approximately a 23.4 percent increase.
  - Second half of 2020 tapering to around:
    - hourly wage: 15.5 percent.
    - hours worked: 10.1 percent.
    - total earnings: 5.9 percent.
  - By end of 2021, effects decline to about:
    - hourly wage: 9.8 percent.
    - hours worked: 7.2 percent.
    - total earnings: 3.0 percent.
- Persistence pattern and interpretation:
  - No pre-pandemic trends detected for February and March 2020 relative to January 2020, supporting identification.
  - Impact is persistent but declines over time; sharp initial response in April 2020 followed by gradual decrease.
  - Sustained response in total earnings is largely driven by persistence in hours worked.
  - By end-2021, effect on hours remains substantial and statistically significant at the 1 percent level, while impact on hourly wages approaches close to zero, indicating lasting total earnings increases stem from maintained higher hours rather than sustained wage growth.

*Source: wpiea2024222-print-pdf - 3.1    The role of labor market strength*

### 3.2    The role of PPP

### 3.2    The role of PPP

### Overview of the PPP program and institutional context
- The Paycheck Protection Program (PPP) was introduced as part of the CARES Act to counter the sharp decline in economic activity and widespread closure of small businesses at the onset of the COVID-19 pandemic.
- Eligibility and loan terms:
  - Businesses with 500 or fewer employees (exception: accommodations and food services, NAICS code 72, where the employment threshold applied per physical location).
  - Maximum loan amount was the lesser of 2.5 times the average monthly payroll costs or $10 million. The average payroll costs were calculated based on the prior year’s payroll, excluding compensation exceeding $100,000 per individual.
  - The loan carried a 1 percent interest rate and a maturity period of 2 years.
- Forgiveness rules (SBA):
  - Funds had to be used for payroll costs, mortgage interest, rent, and utility payments within an eight-week period, with at least 75 percent of the loan allocated to payroll.
  - Businesses were required to maintain both their employee headcount and compensation levels (with an exception allowing restoration of employment and compensation levels if layoffs or wage reductions occurred between February 15 and April 26, 2020).
  - Up to 25 percent of the PPP loan could be used for nonpayroll costs.

- Disbursement chronology and totals:
  - First round began on April 3, 2020; initial $349 billion fully allocated by April 16.
  - Second bill passed on April 24 adding $320 billion; applications accepted starting April 27.
  - In first two weeks of second round, 60 percent of the funds were disbursed; by early July more than $130 billion remained available.
  - Program stopped accepting applications on August 8, with $525 billion disbursed in total.

- Institutional delivery:
  - PPP applications were managed through the banking system while overseen by the SBA.
  - Bank-level supply-side constraints (limited staffing, lack of portal credentials, active supervisory enforcement actions) produced heterogeneous access to PPP funds across regions.
  - Result: areas exposed to banks that underperformed in the first round received relatively less PPP funding; this supply-side heterogeneity diminished in the second round as bottlenecks eased.

### Identification strategy using variation in PPP supply
- Motivation: exploit geographic variation in PPP supply driven by differential bank performance that is plausibly orthogonal to local demand.
- Construction of bank-level PPP performance measure:
  - PPPE_b = (SharePPP − ShareSBL) / (SharePPP + ShareSBL) × 0.5
    - SharePPP is bank b’s PPP loans as a share of all PPP loans (number of loans).
    - ShareSBL is bank b’s small business loans (SBL) as a share of all SBL in Q4 2020 (number of loans).
  - Intuition: PPPE_b measures a bank’s PPP distribution performance relative to its SBL market share.
- Predicted bank performance:
  - Predicted PPPE_b is obtained by regressing bank-level PPPE_b on predetermined supply-side covariates (e.g., bank labor intensity, pre-existing SBA lender dummy, bank’s SBA loans as share of SBA loans, dummy for active enforcement actions at PPP launch, dummy for Wells Fargo Bank) to capture performance explained by supply-side constraints.
- Mapping to counties and PPP exposure:
  - County PPP exposure, PPPE_c, is the weighted average of bank predicted PPPE_b, with weights equal to the share of the number of branches of each bank in the county or within 10 miles of the county center (Summary of Deposits data).
- Evidence that supply-side variation is orthogonal to initial pandemic severity:
  - Granja et al. (2022) find no consistent relationship between PPP allocation and unemployment claims; correlation between PPPE_c and Shock_c is 0.04.

### Empirical specifications
- Main cross-sectional interaction specification (establishment i, worker j, 4-digit NAICS industry k, county c, month t):
  - ∆Y_{i,j,k,c,t} = α_0 + α_1 Post_t × Shock_c + α_2 Post_t × PPPE_c + α_3 Post_t × Shock_c × PPPE_c + β′ Z_{i,j,k,c,t} + e_{i,j,k,c,t}
    - Y is nominal total earnings, average hourly wage, or hours worked.
    - ∆Y is the growth rate in Y from January 2020 to month t measured as log difference.
    - Z includes controls specified in Section 3, importantly local banking sector conditions (average tier 1 capital and core deposit ratios of all banks in the county).
- Dynamic monthly specification:
  - ∆Y_{i,j,k,c,t} = α_0 + α′_1 [I_t × Shock_c] + α′_2 [I_t × PPPE_c] + α′_3 [I_t × Shock_c × PPPE_c] + β′ Z_{i,j,k,c,t} + e_{i,j,k,c,t}
    - I_t is a vector of monthly time dummies from February 2020 to December 2021 (January 2020 reference).

### Main empirical findings on PPP exposure and labor-market outcomes
- Table 3 summary (comparison across specifications):
  - Columns 1–3 use direct labor market strength measure; columns 4–6 use the preferred Bartik shock.
  - PPP exposure shows significant positive effects in preferred estimates (columns 4–6):
    - A one-standard-deviation increase in PPP exposure leads to:
      - 13 percent rise in hourly wage.
      - 19 percent rise in hours.
      - 32 percent rise in total earnings.
  - PPP exposure modestly amplifies the effects of the Bartik shock:
    - A one-standard-deviation increase in PPP exposure increases the Bartik shock’s marginal effect by less than one-sixth.
  - Relative contributions to total earnings:
    - Wage contributes about one-third of total earnings increase.
    - Hours contribute about two-thirds of total earnings increase.
- Time path of effects (Figure 5 narrative):
  - Large PPP exposure response between April and June 2020 (aligns with peak disbursement in first two rounds).
  - Effects taper off toward end of 2020; by May 2021 effects are no longer statistically significant.
  - Slight uptick in December 2020 and January 2021 (possible explanations: delayed loan forgiveness decisions, year-end fiscal adjustments, or new hires to meet forgiveness criteria).
  - Indirect effect (α_3) follows similar trajectory but with magnitude less than one-tenth of α_2.

### Mechanisms and interpretation
- Two primary channels through which PPP can affect wages and hours:
  - Direct channel: loan forgiveness requirements incentivized recipients to maintain employment and compensation levels (direct effect on labor demand).
  - Indirect channel: by covering nonpayroll costs (up to 25 percent of loan), PPP could relieve financial pressure and prevent reductions in employment and wages.
- The research design leverages supply-driven variation to isolate PPP effects on local labor demand and examine mediation through local labor market conditions (e.g., vacancy-to-unemployment ratio).

### Robustness and complementary evidence
- Granja et al. (2022) evidence supports supply-side interpretation:
  - Heterogeneity in bank processing capacity affected first-round access; relationship between exposure to constrained banks and PPP share diminished in second round as bottlenecks eased.
- Orthogonality checks:
  - PPPE_c has low correlation (0.04) with initial local pandemic shock Shock_c, suggesting variation in PPP exposure is not driven by local demand shocks.
- Controls:
  - Regressions include local banking sector conditions (average tier 1 capital and core deposit ratios) to account for potential correlation between local bank health and PPP distribution.

*Source: IMF Working Paper — section 3.2 "The role of PPP" (wpiea2024222-print-pdf)*

### 4.  While we do not attempt to empirically distinguish the effects from the initial shock and evolving

### wpiea2024222-print-pdf - 4.  While we do not attempt to empirically distinguish the effects from the initial shock and evolving

### Controlling for contemporaneous labor market strength
- Definition:
  - The contemporaneous shock Shock_{c,Y earMt} is defined as:
    - Shock_{c,Y earMt} = (∆\ln(V)_{c,Y earMt} − ∆\ln(V)_{c,2019Mt}) − (∆\ln(U)_{c,Y earMt} − ∆\ln(U)_{c,2019Mt}) for Year ∈ (2020,2021). (Equation 9)
  - Distinction:
    - Shock_{c,t} (contemporaneous shock) is distinguished from Shock_{c} (initial shock) as defined in equation 3.
- Robustness results:
  - Table A2 (with contemporaneous control) shows the estimated coefficient of the initial shock is very close to baseline (Table 2).
  - Using preferred measures (columns 4-6):
    - A one-standard-deviation increase in labor market strength results in a 5.7 percent increase in hourly wages, compared to 6.4 percent in the baseline.
    - The effect on hours worked is nearly identical to baseline.
    - The resulting impact on total earnings is 16.5 percent, slightly lower than the 18 percent observed in the baseline.

### Main findings on post-pandemic U.S. labor market dynamics (Conclusion)
- Aggregate and distributional patterns:
  - Counties with smaller labor market shocks at the onset of COVID-19 saw faster earnings growth afterward.
  - Gains were disproportionately larger for:
    - Lower-paid, nonmanagerial workers.
    - Workers in smaller firms.
  - Drivers of gains:
    - Higher hourly wages.
    - Increased working hours.
  - Counties that received more labor market support through the PPP experienced differing growth patterns (a divergence in growth).
- Theoretical alignment:
  - Trends align with job-ladder models where labor market competition drives up earnings as workers move upward.
  - Microdata evidence allows testing and confirmation of these predictions through variation across areas and workers.
- Inequality implications:
  - Increasing earnings disparities across geographic regions were observed.
  - Within counties with stronger labor markets, wage inequality among workers decreases.
  - Overall, results point to evolving patterns of wage and spatial inequality and asynchronous labor market conditions across regions.
- Policy relevance and future research:
  - Trends offer valuable insights for post-pandemic stabilization policies.
  - Findings present promising directions for future research on distributional consequences and spatial labor market dynamics.

### Key quantitative results and statistics (preserving source figures exactly)
- Sample and measurement:
  - Worker-level observations: 3,134,354 for Hourly Wages, Hours, Total Earnings, and growth measures.
  - Worker-level means and dispersion:
    - Hourly Wages_{i,j,k,c,t}: Obs 3,134,354; Mean 9.576; St. Dev. 6.978; Min 0.000; Median 10.500; Max 50.000
    - Hours_{i,j,k,c,t}: Obs 3,134,354; Mean 18.815; St. Dev. 15.561; Min 0.000; Median 17.413; Max 87.442
    - Total Earnings_{i,j,k,c,t}: Obs 3,134,354; Mean 242.381; St. Dev. 247.696; Min 0.000; Median 179.526; Max 4,372.125
    - ∆Hourly Wages_{i,j,k,c,t}: Obs 3,134,354; Mean 0.011; St. Dev. 0.710; Min -2.773; Median 0.000; Max 2.708
    - ∆Hours_{i,j,k,c,t}: Obs 3,134,354; Mean 0.071; St. Dev. 0.843; Min -3.231; Median 0.000; Max 3.321
    - ∆Total Earnings_{i,j,k,c,t}: Obs 3,134,354; Mean 0.074; St. Dev. 1.485; Min -5.766; Median 0.000; Max 5.735
  - Worker characteristics (means):
    - Non-Manager_j: 0.884
    - Job-Switcher_j: 0.404
    - Low-Wage_j: 0.765
    - Small_i (employer <50 employees): 0.578
- County-level shock statistics (Panel B):
  - Shock_c (OLS): Obs 3,110; Mean -0.045; St. Dev. 0.007; Min -0.117; Median -0.045; Max 0.014
  - Shock_{c,t} (OLS): Obs 40,430; Mean 0.025; St. Dev. 0.013; Min -0.025; Median 0.025; Max 0.132
  - Shock_c (Bartik): Obs 3,110; Mean -0.551; St. Dev. 0.072; Min -1.241; Median -0.546; Max 0.195
  - Shock_{c,t} (Bartik): Obs 40,430; Mean 0.662; St. Dev. 0.267; Min -0.184; Median 0.645; Max 2.058
  - PPPE_c (PPP exposure): Obs 3,110; Mean -0.161; St. Dev. 0.252; Min -0.500; Median -0.181; Max 0.500
  - Log median household income: Obs 3,110; Mean 10.700; St. Dev. 0.225; Min 9.867; Median 10.677; Max 12.538
  - COVID cases per capita: Obs 3,110; Mean 0.795; St. Dev. 0.147; Min 0.318; Median 0.804; Max 1.102
  - COVID deaths per capita: Obs 3,110; Mean 0.012; St. Dev. 0.003; Min 0.004; Median 0.013; Max 0.017
  - Average tier 1 capital ratio: Obs 3,110; Mean 7.965; St. Dev. 0.508; Min 5.874; Median 7.991; Max 9.109
  - Average core deposit ratio: Obs 3,110; Mean 1.185; St. Dev. 0.161; Min 0.673; Median 1.159; Max 3.371
- Baseline regression estimates (Table 2; standardized shocks):
  - OLS specification (columns 1-3):
    - Post_t × Shock_c:
      - Hourly Wages: 0.1142*** (0.0173)
      - Hours: 0.1743*** (0.0244)
      - Total Earnings: 0.2830*** (0.0402)
  - Bartik specification (columns 4-6):
    - Post_t × Shock_c:
      - Hourly Wages: 0.0643*** (0.0161)
      - Hours: 0.1187*** (0.0225)
      - Total Earnings: 0.1806*** (0.0370)
- PPP exposure interaction results (Table 3; standardized variables):
  - Post_t × PPPE_c (Bartik columns 4-6):
    - Hourly Wages: 0.1345*** (0.0431)
    - Hours: 0.1904*** (0.0614)
    - Total Earnings: 0.3208*** (0.1001)
  - Post_t × Shock_c × PPPE_c (Bartik columns 4-6):
    - Hourly Wages: 0.0102*** (0.0032)
    - Hours: 0.0142*** (0.0045)
    - Total Earnings: 0.0240*** (0.0074)
- Heterogeneity highlights (selected coefficients, Bartik specs unless noted):
  - Managerial vs nonmanagerial (Table 4):
    - Post_t × Shock_c × Non-Manager_j for Total Earnings: 0.0650*** (0.0010)
  - High- vs low-wage workers (Table 5):
    - Post_t × Shock_c × Low-Wage_j for Total Earnings: 0.1208*** (0.0077)
  - Job-switchers vs stayers (Table 6):
    - Post_t × Shock_c × Job-Switcher_j for Total Earnings: 0.0078*** (0.0020)
  - Firm size (Table 7):
    - Post_t × Shock_c × Small_i for Total Earnings: 0.0830*** (0.0015)
- Specification details common across regressions:
  - Outcome Y denotes nominal average hourly wage, hours worked, or total earnings.
  - ∆Y_{i,j,k,c,t} denotes growth rate from January 2020 to month t measured as log difference.
  - Post_t is a dummy equal to one for t ≥ April 2020 (or quarterly analogs).
  - Shock_c is either direct measure or Bartik shock to local labor market strength; standardized to unit standard deviation.
  - PPPE_c denotes exposure to PPP lending; standardized to unit standard deviation.
  - Controls Z_{i,j,k,c,t} include worker fixed effects, state-industry-month fixed effects, lags of the labor market shock (March 2020, February 2020, January 2020), and county-level controls (log median household income, COVID-19 cases and deaths per capita, average tier 1 capital and core deposit ratios).
  - Weighting: each observation weighted by its industry’s pre-pandemic share of the labor force in 2019.
  - Standard errors clustered by county and time.
  - Statistical significance: ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

*Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024222-print-pdf.pdf*

### 2021. Initial labor market shocks (Bartik),Shock

### 2021. Initial labor market shocks (Bartik),Shock

### Regression specification and controls
- Main regression (Figure A10; county-quarter panel for accommodation and food services, Q1 2020 to Q4 2021):
  - ∆Y_{k,c,t} = α_0 + α′_1 [I_t × Shock_c] + α′_2 [I_t × PPPE_c] + α′_3 [I_t × Shock_c × PPPE_c] + β′ Z_{k,c,t} + e_{k,c,t}
  - Y: nominal average weekly wages (earnings); ∆Y is log difference from Q1 2020 to t.
  - I_t: vector of quarter dummies Q2 2020 to Q4 2021.
  - Shock_c: Initial labor market shocks (Bartik) standardized to unit standard deviation.
  - PPPE_c: exposure to PPP lending standardized to unit standard deviation.
  - Z_{k,c,t} contains county fixed effects, state-industry-quarter fixed effects, lags of the labor market shock measured as of March 2020, February 2020, and January 2020, and county-level controls including log median household income, COVID-19 cases and deaths per capita, and average tier 1 capital and core deposit ratios of all banks within the county.
  - Observations are weighted by industry’s share of the labor force in 2019.
  - Standard errors clustered by county and time; vertical whiskers plot 90 percent confidence intervals.

- Worker-level regressions (Tables A1 and A2; Homebase panel, January 2020 to December 2021):
  - ∆Y_{i,j,k,c,t} = α_0 + α_1 Post_t × Shock_c + β′ Z_{i,j,k,c,t} + e_{i,j,k,c,t} (Table A1)
  - ∆Y_{i,j,k,c,t} = α_0 + α_1 Post_t × Shock_c + α_2 Shock_{c,t} + α_3 Shock_{c,t−1} + β′ Z_{i,j,k,c,t} + e_{i,j,k,c,t} (Table A2)
  - Y: nominal average hourly wage, hours worked, or total earnings; ∆Y is log difference from January 2020 to month t.
  - Post_t: dummy equal to one for t ≥ April 2020.
  - Shock_Q_c (Quits) uses JOLTS quits rate in place of vacancy-to-unemployment ratio; Shock_U_c (Unemployment) uses Labor Force Statistics unemployment rate.
  - Labor market shocks standardized to unit standard deviation.
  - Z_{i,j,k,c,t} includes worker fixed effects, state-industry-month fixed effects, lags of the labor market shock (March, February, January 2020), and county-level controls (log median household income, COVID-19 cases and deaths per capita, average tier 1 capital and core deposit ratios).
  - Observations weighted by industry’s pre-pandemic share of the labor force in 2019.
  - Standard errors clustered by county and time.
  - ***, **, and * indicate statistical significance at the 1, 5, and 10 percent, respectively.

### Key empirical findings (county and worker panels)
- Figure A10 (county-level accommodation and food services earnings):
  - Regression includes α_1 (Local labor market strength), α_2 (PPP exposure), and α_3 (Local labor market strength × PPP exposure) as quarter-varying coefficients plotted for 2020q1–2021q4 (coefficients and confidence intervals plotted; exact plotted values not tabulated in text).

- Table A1: Alternative measures of local labor market strength (Post_t × Shock_c coefficients)
  - Columns (1)–(3): Hourly Wages, Hours, Total Earnings (Measure = Quits; Specification = Bartik)
    - Post_t × Shock_c = 0.1213*** (Hourly Wages)
    - Post_t × Shock_c = 0.1460*** (Hours)
    - Post_t × Shock_c = 0.2631*** (Total Earnings)
  - Columns (4)–(6): Hourly Wages, Hours, Total Earnings (Measure = Unemployment; Specification = Bartik)
    - Post_t × Shock_c = -0.0422*** (Hourly Wages)
    - Post_t × Shock_c = -0.0468** (Hours)
    - Post_t × Shock_c = -0.0834*** (Total Earnings)
  - Observations = 3,134,354 (for each column)
  - R^2 values reported:
    - Columns (1)–(3): R^2 = 0.49, 0.48, 0.49 respectively (noted as "0.490.480.49" in table layout)
    - Columns (4)–(6): R^2 = 0.49, 0.48, 0.49 respectively (noted similarly)
  - Controls: Yes; Worker FE: Yes; State-Industry-Time FE: Yes.

- Table A2: Robustness to contemporaneous shocks (Post_t × Shock_c coefficients with contemporaneous shocks included)
  - Columns (1)–(3): Hourly Wages, Hours, Total Earnings (Specification = OLS)
    - Post_t × Shock_c = 0.1067*** (Hourly Wages)
    - Post_t × Shock_c = 0.1671*** (Hours)
    - Post_t × Shock_c = 0.2687*** (Total Earnings)
  - Columns (4)–(6): Hourly Wages, Hours, Total Earnings (Specification = Bartik; includes Shock_{c,t} and Shock_{c,t−1})
    - Post_t × Shock_c = 0.0565*** (Hourly Wages)
    - Post_t × Shock_c = 0.1107*** (Hours)
    - Post_t × Shock_c = 0.1652*** (Total Earnings)
  - Observations = 3,134,354 (for each column)
  - R^2 values reported:
    - Columns (1)–(3): R^2 = 0.51, 0.50, 0.50 respectively (noted as "0.510.500.50")
    - Columns (4)–(6): R^2 = 0.51, 0.49, 0.50 respectively (noted as "0.510.490.50")
  - Controls: Yes; Worker FE: Yes; State-Industry-Time FE: Yes.

### Interpretation and synthesis of quantitative results
- Using the Bartik initial labor market shock measure:
  - Positive and statistically significant Post_t × Shock_c coefficients are estimated when the shock is constructed from vacancy-to-unemployment (Bartik) or quits measures (e.g., 0.1213***, 0.1460***, 0.2631*** in Table A1 columns (1)–(3)), indicating stronger pre-pandemic local labor market strength is associated with larger post-pandemic growth in hourly wages, hours, and total earnings for the Homebase sample.
  - When the shock is constructed from unemployment rates (Shock_U_c), coefficients switch sign and are negative and statistically significant (e.g., -0.0422***, -0.0468**, -0.0834***), indicating the direction of estimated effects depends on the shock definition.
- Results are robust to inclusion of contemporaneous shocks (Table A2):
  - Post_t × Shock_c remains positive and statistically significant across specifications, though magnitudes are attenuated when controlling for contemporaneous Shock_{c,t} and Shock_{c,t−1} (compare 0.2687*** in Table A2 column (3) to 0.1652*** in column (6)).

### Methodological notes relevant to interpretation
- All shock measures standardized to unit standard deviation.
- Extensive fixed effects and lag controls included (county or worker fixed effects; state-industry-quarter/month fixed effects; lags of labor market shock measured as of March 2020, February 2020, and January 2020).
- County-level controls include log median household income, COVID-19 cases and deaths per capita, average tier 1 capital and core deposit ratios of banks within the county.
- Weighting: observations weighted by industry’s share of the labor force in 2019 (county panel) or industry’s pre-pandemic share of the labor force in 2019 (worker panel).
- Standard errors clustered by county and time.

*Divergence in Post-Pandemic Earnings Growth: Evidence from Micro Data Working Paper No. WP/2024/222*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024222-print-pdf.pdf_