## wpiea2024063-print-pdf

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---

### Data sources and sample
- Proprietary micro data from Homebase: nearly 9 million workers at 1 million firms; median firm in the data has fewer than 7 employees, paying an average hourly wage of around $12, with almost exclusively casual or part-time employees.
- BLS Business Employment Dynamics: net and gross job flows, quarterly during 1992Q1-2022Q3, used for Figure 1.
- Indeed job postings: final dataset includes 141,706,597 job postings, 421 occupations, 2,867,705 companies, and 576 counties over January 2019-December 2022.
  - Yearly job postings: 2019: 27,691,685; 2020: 25,900,182; 2021: 43,214,041; 2022: 44,900,736.
- Local government procurement data from USASpending used for instrumental variable analysis (contract-level Department of Defense procurement spending aggregated to county-month).

### Measurement: local labor market tightness
- Tightness measure: vacancy-to-unemployment ratio (vacancies from Indeed aggregated by county-month; unemployment from BLS Local Area Unemployment Statistics).
- Indeed dataset coverage: 142 million job postings in the final dataset (text notes 142 million and Table 1 reports 141,706,597).
- Comparisons: national aggregate series scaled to Jan 2019 = 100 for Indeed vs JOLTs openings; correlation between Indeed postings and JOLTs openings at the state-month level as high as 0.96.

### Methodological novelty: dynamic composition correction
- Problem: composition of aggregate data (even at county-month level) may change systematically in response to shocks, biasing impulse responses for wages and hours.
- Approach: use Homebase granularity to construct county-month measures of employment, hours, and wages which correct precisely for dynamic composition bias by fixing the sample of worker-firm observations at each horizon.
- Capability:
  - Differentiate between existing workers, new joiners, and quitters.
  - Fix employee composition at horizon 0 and trace impacts for the same group over the impulse response horizon.
- Aggregation measures (notation preserved):
  - Sample average: w̄^h_{c,t} = (∑_{j∈E_{c,t+h}} l_{j,t} w_{j,t}) / (∑_{j∈E_{c,t+h}} l_{j,t})
  - Entry-corrected: w̃^h_{c,t} = (∑_{j∈E_{c,t}} l_{j,t} w_{j,t}) / (∑_{j∈E_{c,t}} l_{j,t})
  - Double-corrected: ŵ^h_{c,t} = (∑_{j∈⋂_{k=1}^H E_{c,t+k}} l_{j,t} w_{j,t}) / (∑_{j∈⋂_{k=1}^H E_{c,t+k}} l_{j,t})
- Importance: without the composition correction, impulse responses imply much smaller reductions in hours and almost twice as large wage increases for small firms.

### Main empirical findings (all firms and overview)
- Consistent with the jobs ladder theory: tighter local labor markets (higher vacancy-to-unemployment ratio) lead small firms to:
  - Reduce employment.
  - Reduce hours per worker.
  - Increase wages.
- Persistence and significance:
  - These employment, hours, and wage effects persist for at least a year and are statistically significant.
- Firm and match dynamics:
  - Number of firms and worker-firm matches observed decreases following increased local tightness, consistent with higher firm failure rates (alternative explanations possible).
- Composition effects on movers:
  - Those leaving during tightness have lower hours and wages on average than those remaining.
  - Those joining receive higher wages on average.
- Robustness:
  - Results hold across firm size and industry.
  - Results hold before, during, and after the COVID pandemic.
  - Instrumental variable approach using Department of Defense procurement spending yields similar results to baseline.

### Interpretation and identification
- Interpretation: results correspond to local demand shocks.
- Instrumental variable strategy:
  - Use contract-level USASpending data to construct county-month procurement spending by the Department of Defense as an instrument for local aggregate demand shocks.
  - IV results look much the same as baseline OLS results, supporting causal interpretation.

### Relation to literature and contribution
- Builds on literature showing small firms more sensitive to aggregate shocks (e.g., Gertler and Gilchrist 1994; Crouzet and Mehrotra 2020; Moscarini and Postel-Vinay 2012, 2016a).
- Adds to literature on job-to-job transitions and wage dynamics by observing dynamic wage responses within firms and differentiating stayers and joiners.
- Extends payroll-data studies using Homebase by using proprietary wage and job-level information and a longer time period (pre- and post-COVID-19), enabling analysis of employment, wages, hours, and firm survival in response to business cycle and labor market fluctuations.
- Novelty highlights:
  - Precise correction for dynamic employee composition effects using granular Homebase data.
  - Novel IV using USASpending procurement to isolate plausible local aggregate demand shocks.

### Study period and unit of observation
- County-month unit of observation.
- Period of constructed series: January 2018-December 2022 (Indeed sample period starts January 2019 and ends December 2022; outcome variables in Homebase start a year earlier to allow calculation of annual changes).
- Balanced panel: 576 counties with observations in every month from January 2018 to December 2022 (baseline).

---

### Outcomes for small firms: data coverage and sample composition
- Data source: Homebase timecard records with daily employee-level information on hours, wages, and job-level information, linked to establishments and firms; location at 5-digit zip code and industry at 6-digit NAICS.
- Sample period: January 2018 to December 2022.
- Raw coverage: over 80,000 businesses and over 1 million employees in the U.S.
- Industry focus: retail, hospitality, education and health, leisure and other in-person services—useful for low-wage, low-skill in-person services.
- Limitations:
  - Not representative of aggregate employment.
  - Lacks information on tips, benefits and overtime payments.
  - Sample coverage grows slightly over time (2020 an exception).

- Whole sample counts (taken from source):
  - 576 Counties; 10,560,009 Workers; 1,317,643 Firms; Avg. firm size 8.0; Workers pc 0.09; Firms pc 0.011
  - Counties in Table 4 have a combined population of around 256 million.

- Industry composition (selected exact entries):
  - Full-Service Restaurants: 2,804,779 Workers; 26.6 Percent; 267,698 Firms; 20.3 Percent; Avg. firm size 9.5
  - Unknown: 1,470,023 Workers; 13.9 Percent; 173,672 Firms; 13.2 Percent; Avg. firm size 7.4
  - Other: 1,279,922 Workers; 12.1 Percent; 209,718 Firms; 15.9 Percent; Avg. firm size 5.4
  - Limited-Service Restaurants: 1,116,434 Workers; 10.6 Percent; 122,187 Firms; 9.3 Percent; Avg. firm size 8.2
  - Snack and Nonalcoholic Beverage Bars: 769,221 Workers; 7.3 Percent; 86,510 Firms; 6.6 Percent; Avg. firm size 8.1
  - Drinking Places (Alcoholic Beverages): 453,363 Workers; 4.3 Percent; 46,121 Firms; 3.5 Percent; Avg. firm size 8.6
  - Whole sample: 10,560,009 Workers; 100.0 Percent; 1,317,643 Firms; 100.0 Percent; Avg. firm size 7.2

- Key distributions (percentiles preserved exactly):
  - Avg. firm size percentiles by year (selected):
    - 2019: 5% 3.9; 10% 4.4; 25% 5.5; 50% 6.6; 75% 8.0; 90% 9.5; 95% 10.9
    - 2020: 5% 3.6; 10% 4.2; 25% 5.0; 50% 6.0; 75% 7.2; 90% 8.6; 95% 9.8
    - 2021: 5% 4.1; 10% 4.7; 25% 5.5; 50% 6.5; 75% 7.6; 90% 9.1; 95% 10.0
    - 2022: 5% 4.4; 10% 4.9; 25% 5.9; 50% 6.9; 75% 8.1; 90% 9.4; 95% 10.4
  - Avg. hourly wage (USD) percentiles by year:
    - 2019: 5% 8.24; 10% 8.68; 25% 9.49; 50% 10.47; 75% 11.73; 90% 13.02; 95% 13.66
    - 2020: 5% 8.83; 10% 9.35; 25% 10.25; 50% 11.28; 75% 12.77; 90% 14.23; 95% 15.06
    - 2021: 5% 9.28; 10% 9.86; 25% 10.90; 50% 12.00; 75% 13.58; 90% 15.04; 95% 15.67
    - 2022: 5% 10.25; 10% 10.80; 25% 11.83; 50% 12.98; 75% 14.55; 90% 15.93; 95% 16.58
  - Avg. weekly hours percentiles by year:
    - 2019: 5% 18.6; 10% 19.9; 25% 22.0; 50% 24.0; 75% 26.0; 90% 28.1; 95% 29.6
    - 2020: 5% 19.2; 10% 20.5; 25% 22.5; 50% 24.5; 75% 26.7; 90% 28.9; 95% 30.5
    - 2021: 5% 20.0; 10% 21.2; 25% 23.1; 50% 25.0; 75% 27.0; 90% 28.8; 95% 30.0
    - 2022: 5% 20.8; 10% 22.0; 25% 24.0; 50% 26.2; 75% 28.6; 90% 31.0; 95% 32.6
  - Proxy v/u ratio percentiles by year:
    - 2019: 5% 0.17; 10% 0.23; 25% 0.32; 50% 0.44; 75% 0.61; 90% 0.83; 95% 0.99
    - 2020: 5% 0.06; 10% 0.08; 25% 0.14; 50% 0.24; 75% 0.38; 90% 0.55; 95% 0.67
    - 2021: 5% 0.21; 10% 0.27; 25% 0.39; 50% 0.55; 75% 0.78; 90% 1.08; 95% 1.30
    - 2022: 5% 0.35; 10% 0.43; 25% 0.59; 50% 0.80; 75% 1.12; 90% 1.49; 95% 1.74
  - Unemployment rate (percent) percentiles by year:
    - 2019: 5% 2.3; 10% 2.5; 25% 2.9; 50% 3.4; 75% 4.2; 90% 5.1; 95% 5.7
    - 2020: 5% 3.0; 10% 3.5; 25% 4.6; 50% 6.6; 75% 9.9; 90% 13.3; 95% 15.5
    - 2021: 5% 2.5; 10% 2.9; 25% 3.7; 50% 4.7; 75% 6.0; 90% 7.4; 95% 8.4
    - 2022: 5% 2.1; 10% 2.3; 25% 2.8; 50% 3.4; 75% 4.1; 90% 5.1; 95% 5.8

### Workforce and job characteristics (summary)
- Firms in the dataset are overwhelmingly very small; the median firm has fewer than 7 employees.
- Typical pay: average hourly wage around $12.
- Workers are almost exclusively casual or part-time, with highly intermittent hours.
- Implication: firms studied have highly volatile businesses and offer jobs that are low paid and unreliable.
- Homebase employment and earning trends show a strong correlation with CPS and CES national trends and with CES at the month-state level.

### Estimation approach and treatment of composition bias
- Primary method: ordinary least squares estimation of local projections (Jordà (2005)) to trace impulse responses over horizons h = 1,...,H with specification:
  - y^h_{c,t} − y^0_{c,t} = α^h_t + η^h_c + β^h θ_{c,t} + ∑_{k=1}^K γ^h_k θ_{c,t−k} + ∑_{m=0}^M δ^h_m y_{c,t−m} + u^h_{c,t}
- Composition bias challenges identified:
  - (i) Dynamic composition bias: sample composition changes endogenously over horizon h.
  - (ii) Static composition bias: sample at h = 0 differs across time periods t in ways correlated with θ_{c,t}.
  - (iii) Endogeneity of vacancy-to-unemployment ratio (source of the shock).
- Solutions:
  - Dynamic composition: construct aggregate county-level measures by comparing exactly the same people (or firms) at each horizon h (double-corrected measures).
  - Static composition: include time fixed effects and lagged dependent and independent variables; condition on covariates for marginal impulse responses.
  - Endogeneity: instrumental variables estimates using DoD procurement spending.

---

### Headline results (OLS) — numerical and qualitative summary
- Panel setup: baseline uses three lags of dependent and independent variables (K = M = 3); observations weighted by county population; counties with population < 100,000 omitted; only CDC urban-rural categories 1-4 included.
- Labor market tightness:
  - On impact, labor market tightness increases one percentage point.
  - The effect decays relatively quickly and is statistically indistinguishable from zero after 6 months.
- Labor inputs (response to a one percentage point increase in labor market tightness):
  - Number of employees per firm: after 6 months, has fallen by about 0.1 percent.
  - Average hours per employee: after 6 months, has fallen by around 0.04 percent.
  - Dependent variables in panels 2 and 3 are double-corrected by firm and worker respectively, ruling out composition-change explanations based on differential dropout of larger firms or higher-hours workers.
- Wages:
  - Wages appear to increase following the tightening shock, but quantitative and statistical significance is less clear.
  - The six-month elasticity to a one percent tightening in local labor markets is only around one quarter of one percent.
  - Time fixed effects are included, so these can be interpreted as real wage increases when discounted by national price indices.
- Firm and worker attrition:
  - Panels 5 and 6 suggest that on average, 0.02 percent more firms (and workers) exit the sample following a one percent increase in labor market tightness.
  - Panels use entry-correction by firm and worker respectively; show fraction at period t+h that were observed at period t.
  - Interpretation caveat: increased exits could reflect firm failure and worker unemployment, or firms in distress cutting costs (including on payroll software). Homebase pricing ranges from free up to $80 per month.
- Composition and wage-growth interpretation:
  - Uncorrected samples imply different stories: for hours, uncorrected and entry-corrected show much smaller response than double-corrected (departing workers worked fewer hours).
  - For wages, uncorrected sample shows strong growth driven by entrants; wage growth following tightness appears driven by new entrants (job-ladder dynamics) rather than bargaining of stayers.
- Double-corrected measures tend to have tighter standard errors, especially for wages.

### Robustness (overview)
- Robustness exercises at horizon h = 6 include alternate econometric specifications, alternate sample restrictions, firm-size splits, industry subsamples, and temporal subsamples.
- Alternate specifications (variants include Indep. lags, Long lags, No lags, No TFEs, Placebo) yield very similar results to baseline: employment and hours fall; wages increase (less clear statistical significance for attrition).
- Sample restrictions (Unweighted, No min. pop., Urban, Inc. rural, All counties): wages estimated increases larger in most urban counties; estimated wage increases lowest when all restrictions relaxed.
- Firm-size and industry subsamples: results broadly consistent across firm size categories (1–10 employees, 11–50 employees, >51 employees) and across industries covering ~53 percent of workers, with larger uncertainty for less-representative groups.
- Temporal subsamples (Pre-COVID, Mid-COVID, Post-COVID) produce qualitatively similar results with larger uncertainty.

---

### Instrument construction, DoD procurement data, and IV results
- Instrument motivation: isolate variation in county-month labor market tightness stemming from local aggregate demand shocks using DoD procurement spending from USASpending.gov.
- Implementation: assume spending happens evenly over contract lifetime; divide total obligation by contract duration to proxy monthly/daily outlays.
- DoD procurement scope and summary:
  - Time period aggregated: January 2019 to December 2022.
  - Total number of DoD procurement contracts open during 2019-2022: close to 15 million.
  - Contract size distribution: over three quarters of transactions feature a total expenditure of less than $2,500.
  - Spending concentration: bulk comprised of very large contracts (examples cited in source).
  - Contract duration: over three quarters completed within two months; less than five percent have duration more than 1 year.
- Annual cross-sectional summary (Table 8 exact values):
  - Outstanding contracts by year: 2019: 3,796,762; 2020: 3,608,416; 2021: 3,835,155; 2022: 3,538,846.
  - Spending USD bns by year: 2019: 310; 2020: 326; 2021: 352; 2022: 372.
  - Total obligations USD bns by year: 2019: 334; 2020: 350; 2021: 345; 2022: 320.
  - New contracts (number) by year: 2019: 3,362,758; 2020: 3,188,298; 2021: 3,454,846; 2022: 3,168,839.
  - New contracts (Spending USD bns) by year: 2019: 79; 2020: 83; 2021: 85; 2022: 87.
  - New contracts (Total obligations USD bns) by year: 2019: 159; 2020: 174; 2021: 166; 2022: 149.
- Coverage (Table 9 exact values):
  - Number of recipients by year: 2019: 42,670; 2020: 40,733; 2021: 38,106; 2022: 36,739.
  - Number of counties: 2019: 491; 2020: 491; 2021: 489; 2022: 489.
  - Number of states: 2019–2022: 50,50,50,50.
  - Number of sectors: 2019: 964; 2020: 959; 2021: 910; 2022: 926.
- First-stage statistics (Table 11 exact values):
  - Number of observations: 19873 / 19873 / 11160
  - Instrument F stat: 369 / 369 / 276
  - p value: 0.000 / 0.000 / 0.000
  - Sum of coefficients: 0.042 / 0.042 / 0.022
  - standard error: (0.024) / (0.024) / (0.028)
- Interpretation of first stage:
  - F statistics are large with p-values smaller than 0.001, indicating instrument relevance.
  - Sum of coefficients on lagged instruments is positive, implying positive local government spending shocks are associated with tighter local labor markets.
- Exclusion restriction assessment:
  - Comparison of DoD expenditure share with share of workers in Homebase industries shows almost no overlap, implying DoD purchases are not directly assigned to Homebase industries.
- IV headline findings (qualitative and rescaling note):
  - IV qualitative results broadly consistent with OLS: number of employees per firm falls; average hours per worker falls; firm survival rates fall; employee match rates fall; hourly wages rise (statistical significance weak).
  - Dynamics: shock to labor markets has a hump-shaped response and is more persistent than average increases in labor market tightness.
  - Rescaling IV impulse responses so cumulative labor market impulse matches OLS makes other response differences largely disappear, suggesting IV identifies essentially the same shock as OLS but with larger magnitude.
- IV robustness:
  - IV estimates robust to same factors as OLS (specification, sample restrictions, firm size).
  - Instrument strength falls when instrumented with fewer lags.

### Key substantive conclusions and policy relevance
- Data: proprietary Homebase microdata covering nearly 9 million workers at 1 million firms.
- Principal empirical findings:
  - Small firms reduce employment and hours per worker following an increase in local labor market tightness.
  - Small firms increase wages following an increase in local labor market tightness.
  - Effects persist for at least a year and are statistically significant.
  - Number of firms and worker-firm matches observed decreases, consistent with higher firm failure rates or other compositional changes.
- Methodological contribution:
  - Dynamic sample double-correction and entry-correction control for composition bias; without these corrections impulse responses would suggest much smaller reductions in hours and larger wage increases.
  - Evidence suggests wage growth is driven by new entrants rather than job stayers, consistent with a job-ladder model.
- Policy relevance:
  - Tight labor markets can negatively affect small firms through reduced employment and hours and through higher wages, with implications for monetary and labor-market policy focused on demand shocks.

*Source: wpiea2024063-print-pdf*

### 0. All firms

### 0. All firms

### Data sources and sample
- Proprietary micro data from Homebase: nearly 9 million workers at 1 million firms; median firm in the data has fewer than 7 employees, paying an average hourly wage of around $12, with almost exclusively casual or part-time employees.
- BLS Business Employment Dynamics: net and gross job flows, quarterly during 1992Q1-2022Q3, used for Figure 1 (net job growth standard deviation by firm size).
- Indeed job postings: final dataset includes 141,706,597 job postings, 421 occupations, 2,867,705 companies, and 576 counties over January 2019-December 2022.
  - Yearly job postings: 2019: 27,691,685; 2020: 25,900,182; 2021: 43,214,041; 2022: 44,900,736.
- Local government procurement data from USASpending used for instrumental variable analysis (contract-level Department of Defense procurement spending aggregated to county-month).

### Measurement: local labor market tightness
- Tightness measure: vacancy-to-unemployment ratio (vacancies from Indeed aggregated by county-month; unemployment from BLS Local Area Unemployment Statistics).
- Indeed dataset coverage: 142 million job postings in the final dataset (text notes 142 million and Table 1 reports 141,706,597).
- Figure comparisons:
  - National aggregate series scaled to Jan 2019 = 100 for Indeed vs JOLTs openings (Figure 2a).
  - Correlation between Indeed postings and JOLTs openings at the state-month level: as high as 0.96 (Figure 2b).

### Methodological novelty: dynamic composition correction
- Problem addressed: composition of aggregate data (even at county-month level) may change systematically in response to shocks, biasing impulse responses for wages and hours.
- Approach: use granularity of Homebase data to construct county-month measures of employment, hours, and wages which correct precisely for dynamic composition bias by fixing the sample of worker-firm observations at each horizon.
- Capability: differentiate between existing workers, new joiners, and quitters; fix employee composition at horizon 0 and trace impacts for the same group over the impulse response horizon.
- Importance: without the composition correction, impulse responses imply much smaller reductions in hours and almost twice as large wage increases for small firms.

### Main empirical findings
- Consistent with the jobs ladder theory: tighter local labor markets (higher vacancy-to-unemployment ratio) lead small firms to:
  - Reduce employment.
  - Reduce hours per worker.
  - Increase wages.
- Persistence and statistical significance:
  - These employment, hours, and wage effects persist for at least a year and are statistically significant.
- Firm and match dynamics:
  - Number of firms and worker-firm matches observed decreases following increased local tightness, consistent with higher firm failure rates (alternative explanations possible).
- Composition effects on movers:
  - Those leaving during tightness have lower hours and wages on average than those remaining.
  - Those joining receive higher wages on average.
- Robustness:
  - Results hold across firm size and industry.
  - Results hold before, during, and after the COVID pandemic.
  - Instrumental variable approach using Department of Defense procurement spending yields similar results to baseline.

### Interpretation and identification
- Interpretation: results correspond to local demand shocks.
- Instrumental variable strategy:
  - Use contract-level USASpending data to construct county-month procurement spending by the Department of Defense as an instrument for local aggregate demand shocks.
  - IV results look much the same as baseline OLS results, supporting causal interpretation.

### Relation to literature and contribution
- Builds on literature showing small firms more sensitive to aggregate shocks (e.g., Gertler and Gilchrist 1994; Crouzet and Mehrotra 2020; Moscarini and Postel-Vinay 2012, 2016a).
- Adds to literature on job-to-job transitions and wage dynamics (Moscarini and Postel-Vinay 2016b, 2017, 2023; Karahan et al., 2017) by observing dynamic wage responses within firms and differentiating stayers and joiners.
- Extends payroll-data studies using Homebase by using proprietary wage and job-level information and a longer time period (pre- and post-COVID-19), enabling analysis of employment, wages, hours, and firm survival in response to business cycle and labor market fluctuations.
- Novelty highlights:
  - Precise correction for dynamic employee composition effects using granular Homebase data.
  - Novel IV using USASpending procurement to isolate plausible local aggregate demand shocks.

### Study period and units
- County-month unit of observation.
- Period of observation for constructed series: January 2018-December 2022 (Indeed sample period starts January 2019 and ends December 2022; outcome variables in Homebase start a year earlier to allow calculation of annual changes).

*Source: wpiea2024063-print-pdf - 0. All firms*

### 2.2    Outcomes for small firms

### 2.2    Outcomes for small firms

### Data source and coverage
- Data source: Homebase timecard records with daily employee-level information on hours, wages, and job-level information (manager or non-manager), linked to establishments and firms; location at 5-digit zip code and industry at 6-digit NAICS.
- Sample period: January 2018 to December 2022.
- Raw coverage: over 80,000 businesses and over 1 million employees in the U.S.
- Industry focus: retail, hospitality, education and health, leisure and other in-person services—particularly useful for low-wage, low-skill in-person services.
- Limitations noted:
  - Not representative of aggregate employment.
  - Lacks information on tips, benefits and overtime payments.
  - Sample coverage grows slightly over time (2020 an exception).

### Summary counts and sample composition (from Table 2 and Table 4)
- By year (Workers; Firms; Avg. firm size; Workers pc (%); Firms pc (%)):
  - 2019: 7,562,267 Workers; 647,276 Firms; Avg. firm size 8.1; Workers pc 0.07; Firms pc 0.009
  - 2020: 7,562,099 Workers; 6,326,275? [Note: preserve only values as they appear; Table 2 rows are:
    - 2019: 7,562,267 Workers; 647,276 Firms; 8.1; 0.07; 0.009
    - 2020: 7,562,099 Workers; 326,326? (original table shows 2nd row garbled).]
- Whole sample: 576 Counties; 10,560,009 Workers; 1,317,643 Firms; Avg. firm size 8.0; Workers pc 0.09; Firms pc 0.011
- NB: The counties in Table 4 have a combined population of around 256 million.

(Note: The source provides detailed state-level counts in Table 4. The whole-sample totals above are taken exactly from the source.)

### Industry composition (selected entries from Table 3; Workers, Percent, Firms, Percent, Avg. firm size)
- Full-Service Restaurants: 2,804,779 Workers; 26.6 Percent; 267,698 Firms; 20.3 Percent; Avg. firm size 9.5
- Unknown: 1,470,023 Workers; 13.9 Percent; 173,672 Firms; 13.2 Percent; Avg. firm size 7.4
- Other: 1,279,922 Workers; 12.1 Percent; 209,718 Firms; 15.9 Percent; Avg. firm size 5.4
- Limited-Service Restaurants: 1,116,434 Workers; 10.6 Percent; 122,187 Firms; 9.3 Percent; Avg. firm size 8.2
- Snack and Nonalcoholic Beverage Bars: 769,221 Workers; 7.3 Percent; 86,510 Firms; 6.6 Percent; Avg. firm size 8.1
- Drinking Places (Alcoholic Beverages): 453,363 Workers; 4.3 Percent; 46,121 Firms; 3.5 Percent; Avg. firm size 8.6
- Whole sample: 10,560,009 Workers; 100.0 Percent; 1,317,643 Firms; 100.0 Percent; Avg. firm size 7.2

### Key series distributions (Table 5)
- Avg. firm size (workers per firm) percentiles by year:
  - 2019: 5% 3.9; 10% 4.4; 25% 5.5; 50% 6.6; 75% 8.0; 90% 9.5; 95% 10.9
  - 2020: 5% 3.6; 10% 4.2; 25% 5.0; 50% 6.0; 75% 7.2; 90% 8.6; 95% 9.8
  - 2021: 5% 4.1; 10% 4.7; 25% 5.5; 50% 6.5; 75% 7.6; 90% 9.1; 95% 10.0
  - 2022: 5% 4.4; 10% 4.9; 25% 5.9; 50% 6.9; 75% 8.1; 90% 9.4; 95% 10.4
- Avg. hourly wage (USD) percentiles by year:
  - 2019: 5% 8.24; 10% 8.68; 25% 9.49; 50% 10.47; 75% 11.73; 90% 13.02; 95% 13.66
  - 2020: 5% 8.83; 10% 9.35; 25% 10.25; 50% 11.28; 75% 12.77; 90% 14.23; 95% 15.06
  - 2021: 5% 9.28; 10% 9.86; 25% 10.90; 50% 12.00; 75% 13.58; 90% 15.04; 95% 15.67
  - 2022: 5% 10.25; 10% 10.80; 25% 11.83; 50% 12.98; 75% 14.55; 90% 15.93; 95% 16.58
- Avg. weekly hours percentiles by year:
  - 2019: 5% 18.6; 10% 19.9; 25% 22.0; 50% 24.0; 75% 26.0; 90% 28.1; 95% 29.6
  - 2020: 5% 19.2; 10% 20.5; 25% 22.5; 50% 24.5; 75% 26.7; 90% 28.9; 95% 30.5
  - 2021: 5% 20.0; 10% 21.2; 25% 23.1; 50% 25.0; 75% 27.0; 90% 28.8; 95% 30.0
  - 2022: 5% 20.8; 10% 22.0; 25% 24.0; 50% 26.2; 75% 28.6; 90% 31.0; 95% 32.6
- Proxy v/u ratio percentiles by year (Indeed vacancies divided by BLS unemployment rate):
  - 2019: 5% 0.17; 10% 0.23; 25% 0.32; 50% 0.44; 75% 0.61; 90% 0.83; 95% 0.99
  - 2020: 5% 0.06; 10% 0.08; 25% 0.14; 50% 0.24; 75% 0.38; 90% 0.55; 95% 0.67
  - 2021: 5% 0.21; 10% 0.27; 25% 0.39; 50% 0.55; 75% 0.78; 90% 1.08; 95% 1.30
  - 2022: 5% 0.35; 10% 0.43; 25% 0.59; 50% 0.80; 75% 1.12; 90% 1.49; 95% 1.74
- Unemployment rate (percent) percentiles by year:
  - 2019: 5% 2.3; 10% 2.5; 25% 2.9; 50% 3.4; 75% 4.2; 90% 5.1; 95% 5.7
  - 2020: 5% 3.0; 10% 3.5; 25% 4.6; 50% 6.6; 75% 9.9; 90% 13.3; 95% 15.5
  - 2021: 5% 2.5; 10% 2.9; 25% 3.7; 50% 4.7; 75% 6.0; 90% 7.4; 95% 8.4
  - 2022: 5% 2.1; 10% 2.3; 25% 2.8; 50% 3.4; 75% 4.1; 90% 5.1; 95% 5.8

### Workforce and job characteristics (summary findings)
- Firms in the dataset are overwhelmingly very small; the median firm has fewer than 7 employees.
- Typical pay: average hourly wage around $12 (source text: "the median firm in our data has fewer than 7 employees, paying an average hourly wage of around$12").
- Workers are almost exclusively casual or part-time, with highly intermittent hours (some work a handful of days one week and none the next).
- Implication: firms studied have highly volatile businesses and offer jobs that are low paid and unreliable.
- Homebase employment and earning trends show a strong correlation with CPS and CES national trends and with CES at the month-state level.

### Estimation approach
- Primary method: ordinary least squares estimation of local projections (Jordà (2005)) to trace impulse responses over horizons h = 1,...,H.
- Regression specification (notation preserved from source):
  - y^h_{c,t} − y^0_{c,t} = α^h_t + η^h_c + β^h θ_{c,t} + ∑_{k=1}^K γ^h_k θ_{c,t−k} + ∑_{m=0}^M δ^h_m y_{c,t−m} + u^h_{c,t}
  - Observations indexed by county c and month t; θ_{c,t} is local labor market tightness; α^h_t are time fixed effects; η^h_c are county fixed effects; lags of dependent and independent variables may be included.

### Composition bias challenges and corrections
- Three main interpretation challenges for impulse responses:
  - (i) Dynamic composition bias: sample composition changes endogenously over horizon h.
  - (ii) Static composition bias: sample at h = 0 differs across time periods t in ways correlated with θ_{c,t}.
  - (iii) Identifying the source of the shock driving θ_{c,t} (endogeneity of vacancy-to-unemployment).
- Dynamic composition bias solutions:
  - Construct aggregate county-level measures by comparing exactly the same people (or firms) at each horizon h after period t to avoid dynamic composition bias without relying solely on controls.
  - Three wage aggregation measures defined (preserving notation and formulas from source):
    - Sample average: w̄^h_{c,t} = (∑_{j∈E_{c,t+h}} l_{j,t} w_{j,t}) / (∑_{j∈E_{c,t+h}} l_{j,t})
    - Entry-corrected: w̃^h_{c,t} = (∑_{j∈E_{c,t}} l_{j,t} w_{j,t}) / (∑_{j∈E_{c,t}} l_{j,t})
    - Double-corrected: ŵ^h_{c,t} = (∑_{j∈⋂_{k=1}^H E_{c,t+k}} l_{j,t} w_{j,t}) / (∑_{j∈⋂_{k=1}^H E_{c,t+k}} l_{j,t})
  - Interpretation of measures:
    - Sample average: benchmark, aggregates over all workers in each period (no composition adjustment).
    - Entry-corrected: fixes sample to workers employed in period t (excludes entrants after t; leavers drop out).
    - Double-corrected: restricts to workers observed over the whole horizon (compares like-with-like and fully addresses dynamic composition for a given impulse horizon).
  - Example illustrating differences provided in Table 6 with workers A, B, C, D across periods and horizons; only double-corrected fully addresses dynamic composition across horizons.
  - Similar corrections apply when unit of observation is the firm (e.g., employees per firm).
- Static composition bias solutions:
  - Include time fixed effects and lagged dependent and independent variables to adjust for sample composition changes correlated with business cycle factors.
  - Condition local projections on other covariates to compute marginal impulse responses at different levels of labor market tightness.
- Source of the shock:
  - Vacancy-to-unemployment ratio is endogenous and driven by macro shocks.
  - One interpretation: residual local fluctuations in labor market tightness at monthly frequency may reflect local demand shocks after accounting for common time effects and lags.
  - The authors plan instrumental variables estimates in Section 4 to more plausibly attribute variation to locally exogenous demand shocks.

*Source: wpiea2024063-print-pdf - 2.2    Outcomes for small firms*

### 3.2    Headline results

### 3.2    Headline results

### Data and empirical design
- Balanced panel of 576 counties with observations in every month from January 2018 to December 2022.
- Baseline specification uses three lags of each of the dependent and independent variables (so K = M = 3).
- Observations weighted by county population; counties with populations smaller than 100,000 omitted.
- Only counties in categories 1-4 of the CDC’s 6-part urban-rural classification are included (i.e., “small metro” and larger).
- Country-month outcomes are calculated from Homebase microdata using:
  - dynamic sample double-correction in panels 2-4, and
  - entry-correction in panels 5 and 6.

### Headline empirical findings (ordinary least squares)
- Labor market tightness:
  - On impact, labor market tightness increases one percentage point.
  - The effect decays relatively quickly and is statistically indistinguishable from zero after 6 months.
- Labor inputs (after a one percentage point increase in labor market tightness):
  - Number of employees per firm: after 6 months, has fallen by about 0.1 percent.
  - Average hours per employee: after 6 months, has fallen by around 0.04 percent.
  - Dependent variables in panels 2 and 3 are double-corrected by firm and worker respectively, which rules out composition-change explanations based on differential dropout of larger firms or higher-hours workers.
  - Interpretation: when labor markets are tight, a given pool of small firms sheds workers and gives a fixed set of workers fewer hours.
- Wages:
  - Wages appear to increase following the tightening shock, but quantitative and statistical significance is less clear.
  - The six-month elasticity to a one percent tightening in local labor markets is only around one quarter of one percent.
  - Time fixed effects are included, so these can be interpreted as real wage increases when discounted by national price indices.
- Firm and worker attrition:
  - Firm failure and worker separation rates increase following tightness shocks.
  - Panels 5 and 6 suggest that on average, 0.02 percent more firms (and workers) exit the sample following a one percent increase in labor market tightness.
  - These panels use entry-correction by firm and worker respectively; they show the fraction of firms (panel 5) and workers (panel 6) at period t+h that were observed at period t.
  - Interpretation caveat: increased exits could reflect firms failing and workers becoming unemployed, or firms in distress cutting costs (including on payroll software). Given Homebase pricing ranges from free (basic version for firms with fewer than 20 employees) up to$80 per month, firm failure and worker unemployment is considered the more likely explanation.
- Composition effects and wage growth:
  - Uncorrected samples can imply different stories: for hours, uncorrected and entry-corrected lines show a much smaller response than double-corrected, consistent with departing workers typically working fewer hours at the time of the shock.
  - For wages, the uncorrected sample shows strong growth driven by entrants; this is consistent with new hires having to be competitive while wages for ongoing employees may remain below-market rates.
  - Conclusion: wage growth following tightness appears driven by new entrants (job-ladder dynamics) rather than better bargaining power of workers within a given job.

### Interpretation of sample-correction differences
- The gap between double- and entry-corrected responses indicates that leavers had fewer hours on average than those remaining.
- The gap between double- and entry-corrected wage responses indicates that leavers have on average lower wages than remaining workers; the full-sample line being even higher implies incoming workers have higher wages than even those who remain throughout.
- Double-corrected measures tend to have tighter standard errors, especially for wages, possibly because long-staying employees exhibit less idiosyncratic variation.

### Economic takeaway
- Tight labor markets—typically associated with strong aggregate demand—are challenging for small firms:
  - They reduce employment and hours at small firms even though costs likely rise.
  - More firms fail and more workers leave jobs in response to local labor market tightening.

---

### Robustness (overview of Section 3.3)
- Four robustness exercises: alternate econometric specifications, alternate sample restrictions, different firm sizes, and different subsamples.
- Results summarized at horizon h = 6 (with h = 1 and h = 12 reported in Appendix A).

Key robustness checks and findings:
- Alternate specifications (Figure 5):
  - Variants include adding lags of the independent variable (Indep. lags adds 3 lags), including long lags (Long lags includes 12 lags of both independent and dependent variables), removing lags (No lags), omitting time fixed effects (No TFEs), and a placebo (white noise independent variable).
  - These variants give generally very similar results to the baseline: employment and hours fall; wages increase (but with less obvious statistical significance for firm and employee attrition).
  - No TFEs specification produces stronger wage effects but weaker firm and employee attrition effects.
  - Placebo specification yields effects indistinguishable from zero.
- Sample restrictions (Figure 6):
  - Variants include removing population weighting (Unweighted), removing minimum county population requirement (No min. pop.), using only most urban counties (Urban uses CDC Urban score 1 or 2), including more rural counties (Inc. rural includes CDC urban score up to 6), and no restrictions (All counties).
  - The most consistent pattern is for wages: estimated wage increases are larger for the most urban counties and lowest when all restrictions are relaxed.
  - Interpretation: labor markets are deepest in larger, more densely populated areas, where firms may have less monopsony power and must raise wages more in tight markets.
- Firm-size subsamples (Figure 7):
  - Results are broadly consistent across firm size categories (1–10 employees, 11–50 employees, >51 employees), though uncertainty is larger for the largest firms due to small sample shares.
- Industry subsamples (Figure 8):
  - The six most common industries cover some 53 percent of workers in the sample; percentages in parentheses show share of sample workers in that industry (e.g., Full-Service Restaurants (27%), Limited-Service Restaurants (11%), Snack and Nonalcoholic Beverage Bars (7%), Drinking Places (Alcoholic Beverages) (4%), Women’s Clothing Stores (2%), General Merch. (2%)).
  - Results generally hold across industries, with larger departures and standard errors for less-representative industries.
- Temporal subsamples (Figure 9, described):
  - Estimates repeated for pre-, during-, and post-COVID-19 pandemic sub-periods produce qualitatively similar results though with larger uncertainty in subsamples.

- Overall robustness conclusion: main conclusions—declines in employment and hours at small firms following local tightness, modest real wage increases driven by entrants, and higher firm and worker exits—are robust across specifications, sample restrictions, firm sizes, industries, and sub-periods.

*Source: wpiea2024063-print-pdf - 3.2    Headline results*

### 4. Hourly wage5. Fraction of active firms6. Fraction of workers employed

### 4. Hourly wage5. Fraction of active firms6. Fraction of workers employed

### Instrument construction and motivation
- Goal: isolate variation in county-month labor market tightness stemming from demand shocks, focusing on local aggregate demand shocks relevant for policy (monetary policymakers).
- Instrument: local procurement spending by the United States Department of Defense (DoD) constructed from transaction-level data on USASpending.gov.
- Rationale: fluctuations in DoD procurement spending are argued to be shocks to local aggregate demand that are largely unrelated to local economic conditions; procurement covers purchases of intermediate goods and services and omits spending that is highly cyclical (e.g., unemployment benefits).
- Implementation detail: assume spending happens evenly over the lifetime of each transaction/contract and divide total obligation by contract duration to proxy monthly/daily outlays.

### DoD procurement data: scope, distribution, and summary statistics
- Time period aggregated: January 2019 to December 2022.
- Total number of DoD procurement contracts open during 2019-2022: close to 15 million.
- Contract size distribution: over three quarters of transactions feature a total expenditure of less than $2,500.
- Spending concentration: bulk of actual spending comprised of very large contracts (examples cited: large medical insurance contract $20bn; F-35 contract almost $11bn with option to increase to $175bn).
- Contract duration: over three quarters of contracts are completed within two months; less than five percent have duration more than 1 year; some extend over more than five years.
- Annual cross-sectional summary (Table 8):
  - Outstanding contracts by year: 2019: 3,796,762; 2020: 3,608,416; 2021: 3,835,155; 2022: 3,538,846.
  - Spending USD bns by year: 2019: 310; 2020: 326; 2021: 352; 2022: 372.
  - Total obligations USD bns by year: 2019: 334; 2020: 350; 2021: 345; 2022: 320.
  - New contracts (number) by year: 2019: 3,362,758; 2020: 3,188,298; 2021: 3,454,846; 2022: 3,168,839.
  - New contracts (Spending USD bns) by year: 2019: 79; 2020: 83; 2021: 85; 2022: 87.
  - New contracts (Total obligations USD bns) by year: 2019: 159; 2020: 174; 2021: 166; 2022: 149.
- Coverage (Table 9):
  - Number of recipients by year: 2019: 42,670; 2020: 40,733; 2021: 38,106; 2022: 36,739.
  - Number of counties: 2019: 491; 2020: 491; 2021: 489; 2022: 489.
  - Number of states: 2019–2022: 50,50,50,50.
  - Number of sectors: 2019: 964; 2020: 959; 2021: 910; 2022: 926.
- Cross-sectional percentiles (Table 7 excerpts):
  - By contract, Total obligation (USD) percentiles: 25 %: 1,615; 50 %: 8,023? (note: source lists "1615082,34743,700668,23513,564,612140,948,525" — preserve format as presented)
  - By transaction, Monthly spending (USD) percentiles: 25 %: 964; 50 %: 2,317? (source lists "964231,70225,272176,3801,543,26110,814,371" — preserve format as presented)
- Industry concentration (Table 10): top industries by obligation and percent share include:
  - Aircraft Manufacturing: 334.02 bn, 21.0
  - Engineering Services: 146.09 bn, 9.0
  - Ship Building and Repairing: 136.09 bn, 9.0
  - Guided Missile and Space Vehicle Manufacturing: 108.07 bn, 7.0
  - Research and Development in the Physical, Engineering, and Life Sciences (except Nanotechnology and Biotechnology): 76.05 bn, 5.0
  - Unknown: 73.05 bn, 5.0
  - Other top entries through “Whole sample”: 1,570.0, 100.0

### First-stage statistics and validity checks
- First-stage estimation: instrument county-month labor market tightness with 12 lags of log DoD contract procurement spending.
- Table 11 summary (full-sample average / entry-corrected / double-corrected):
  - Number of observations: 19873 / 19873 / 11160
  - Instrument F stat: 369 / 369 / 276
  - p value: 0.000 / 0.000 / 0.000
  - Sum of coefficients: 0.042 / 0.042 / 0.022
  - standard error: (0.024) / (0.024) / (0.028)
- Interpretation:
  - F statistics are large with p-values smaller than 0.001, indicating instrument relevance.
  - Sum of coefficients on lagged instruments is positive, implying positive local government spending shocks are associated with tighter local labor markets.
- Assessment of exclusion restriction:
  - Comparison of DoD expenditure share with share of workers in Homebase industries (Figure 12) shows almost no overlap, implying DoD purchases are not directly assigned to the industries of Homebase firms (which provide services such as catering and retail rather than defense hardware).
  - The instrument thus behaves more like a general local demand shock than a sector-specific purchase shock.

### Instrumental variables results (headline IV findings)
- Main IV specification: responses of outcome variables to a one percent increase in labor market tightness; instrument uses 12 lags of local DoD procurement spending; observations weighted by county-level populations.
- Qualitative IV results are broadly consistent with OLS:
  - Number of employees per firm: falls.
  - Average hours per worker: falls.
  - Firm survival rates (fraction of active firms): fall.
  - Employee match rates (fraction of workers employed at given firms): fall.
  - Hourly wages: rise, though statistical significance for wages is not strong.
- Dynamics:
  - Shock to labor markets has a hump-shaped response and is more persistent than average increases in labor market tightness.
  - Rescaling IV impulse responses so cumulative labor market impulse matches OLS makes other response differences largely disappear, suggesting IV identifies essentially the same shock as OLS but with larger magnitude.

### Robustness
- IV estimates are robust to the same factors as OLS, including specification, firm size, and other sample restrictions (details in Appendix B).
- Instrument strength falls when instrumented with fewer lags, indicating variable lags in the relationship between federal spending and local labor market tightness.

### Key substantive conclusions and implications
- Data: proprietary Homebase microdata covering nearly 9 million workers at 1 million firms.
- Principal empirical findings:
  - Small firms reduce employment and hours per worker following an increase in local labor market tightness.
  - Small firms increase wages following an increase in local labor market tightness.
  - Effects persist for at least a year and are statistically significant.
  - Number of firms and worker-firm matches observed decreases, consistent with higher firm failure rates or other compositional changes.
- Methodological contribution:
  - Dynamic sample double-correction and entry-correction are used to control for composition bias; without these corrections impulse responses would suggest much smaller reductions in hours and larger wage increases.
  - Evidence suggests wage growth is driven by new entrants rather than job stayers, consistent with a job-ladder model and not with traditional bargaining-stayer models of wage setting.
- Policy relevance:
  - Results highlight that tight labor markets can negatively affect small firms through reduced employment and hours and through higher wages, with implications for monetary and labor-market policy focused on demand shocks.

*Source: wpiea2024063-print-pdf (IMF Working Paper content provided in the source PDF).*

### References

### References

### Bibliographic list (selected entries as listed)
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- Auerbach, A., Y. Gorodnichenko, and D. Murphy, “Local Fiscal Multipliers and Fiscal Spillovers in the USA,” IMF Economic Review, 2020, 68(1), 195–229.
- Autor, D., A. Dube, and A. McGrew, “The Unexpected Compression: Competition at Work in the Low Wage Labor Market,” NBER Working Paper, 2023, (31010).
- Bartik, W.A., M. Bertrand, F. Li, and J. Rothstein, “Measuring the Labor Market at the Onset of the COVID-19 Crisis,” NBER Working Paper, 2020, (27613).
- Blanchard, Olivier, Alex Domash, and Lawrence Summers, “Bad News for the Fed from the Beveridge Space,” Peterson Institute for International Economics Policy Brief, 2022, 22(7).
- CEA, “Investing in America Means Investing in America’s Small Businesses,” Technical Report 2023.
- Chen, Sophia and Do Lee, “The Post-Pandemic Paycheck: Wage and Earning Dynamics from Micro Data,” IMF Working Paper, 2024.
- Chetty, R., J. Friedman, N. Hendren, and M. Stepner, “The Economic Impacts of COVID-19: Evidence from a New Public Database Built using Private Sector Data,” Quarterly Journal of Economics, 2023, forthcoming.
- Christiano, Larence J, Martin S Eichenbaum, and Mathias Trabandt, “Unemployment and Business Cycles,” Econometrica, 2016, 84(4), 1523–1569.
- Galí, Jordi, Frank Smets, and Rafael Wouters, “Unemployment in an Estimated New Keynesian Model,” NBER Macroeconomics Annual, 2011, 26(1), 329–360.
- Kydland, Finn E and Edward C Prescott, “Time to Build and Aggregate Fluctuations,” Econometrica, 1982, 50, 1345–1370.
- Mortensen, Dale T, “Markets with Search Friction and the DMP Model,” The American Economic Review, 2011, 101(4), 1073–1091.
- Pissarides, Christopher A, Equilibrium unemployment theory, MIT press, 2000.
- Ramey, Valerie A, “Can government purchases stimulate the economy?,” Journal of Economic Literature, 2011, 49(3), 673–685.
- Shimer, Robert, “The Cyclical Behavior of Equilibrium Unemployment and Vacancies,” The American Economic Review, 2005, 95(1), 25–49.
- (Additional references follow in the original list as provided.)

### Appendix A — Further robustness checks (figures and captions)
- Figures present robustness of OLS estimates for responses of outcome variables to a one percent increase in labor market tightness at horizons:
  - h = 1 (Figures 14–15): panels include outcomes for "Labor market tightness", "Number of employees/firm", "Average hours/worker", "Hourly wage", "Fraction of active firms", "Fraction of workers employed".
    - Specification variants: Baseline, No lags, No TFEs, Indep. lags (adds 3 lags of the independent variable), Long lags (includes 12 lags of both the independent and dependent variables), Placebo (replaces the independent variable with a white noise process with the same standard deviation as the unemployment-vacancy ratio in the data).
    - Sample and weighting variants: Unweighted (removes population weighting), No min. pop. (removes the minimum county population requirement), Urban (uses only counties with a CDC Urban score of 1 or 2), Inc. rural (includes counties with CDC urban score up to 6), All counties (no restriction).
    - Confidence intervals: 95 percent confidence intervals computed using robust standard errors double-clustered at the county and month.
    - Country-month outcomes: calculated from Homebase microdata using dynamic sample double-correction in panels 2–4 and entry-correction in panels 5 and 6.
    - Observations: weighted by county-level populations (except where Unweighted is specified).
- h = 12 (Figures 16–17): analogous robustness checks reported for horizon h = 12 with same specification and sample variants, same clustering and Homebase microdata corrections.

### Appendix B — Instrumental Variables (figures and captions)
- Figure 18: Headline results — Instrumental variables, rescaled.
  - Shows responses of outcome variables to a one percent increase in labor market tightness.
  - Instrument: 12 lags of local Department of Defense procurement spending.
  - Dotted lines: 95 percent confidence intervals computed using robust standard errors double-clustered at the county and month.
  - Country-month outcomes: calculated from Homebase microdata using dynamic sample double-correction in panels 2–4 and entry-correction in panels 5 and 6.
  - Observations: weighted by county-level populations.
  - Note: Instrumental variables estimates are rescaled by a constant so that the cumulative labor market tightness responses are identical. Grey circles represent the OLS results.
- Robustness of IV estimates (Figures 19–22):
  - Figure 19: Alternate specifications at horizon h = 6. Specification variants: Baseline, No lags, No TFEs, Indep. lags (adds 3 lags), Long lags (12 lags), Placebo (white noise with same standard deviation as the unemployment-vacancy ratio).
  - Figure 20: Alternate sample restrictions at horizon h = 6. Sample variants: Unweighted, No min. pop., Urban, Inc. rural, All counties.
  - Figure 21: Firm size heterogeneity at horizon h = 6. Firm size categories: 1−10 employees, 11−50 employees, >51 employees.
  - Figure 22: Alternate sample periods at horizon h = 6. Periods defined as Pre-COVID = Jan 2019-Feb 2020, Mid-COVID = Mar 2020-Jun 2021, Post-COVID = Jul 2021-Nov 2022.
  - All IV figures report 95 percent confidence intervals computed using robust standard errors double-clustered at the county and month; country-month outcomes are constructed from Homebase microdata with the same corrections as above; observations are weighted by county-level populations.

*The Dynamic Effects of Local Labor Market Shocks on Small Firms in The United States — Working Paper No. WP/2024/063*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024063-print-pdf.pdf_