## 3.1  Baseline specification

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---

### Baseline model
- Baseline system of equations:
  - y_{c,t+k} = β̂ v_{c,t} + τ_{s,t} + τ_{c} + ε_{c,t+k}  (1)
  - v_{c,t} = γ z_{c,t−2} + δ_{s,t} + δ_{c} + ξ_{c,t}  (2)
- Definitions:
  - y_{c,t+k}: economic outcome in county c, state s, week t+k, including:
    - (i) weekly credit/debit card spending relative to Jan 4–31, 2020 (k = 1)
    - (ii) weekly unemployment claims in percent of county-level 2019 labor force (k = 6)
    - (iii) mobility relative to Jan 3–Feb 6, 2020 (k = 1)
  - v_{c,t}: initiated vaccinations in percent of the population at the county level. (For Johnson & Johnson doses, initiated vaccinations are also completed.)
  - The hat on v_{c,t} denotes the fitted value of vaccinations from equation (2).
  - τ_{s,t} and δ_{s,t}: state-time fixed effects.
  - τ_{c} and δ_{c}: county fixed effects.
  - z_{c,t−2}: instrument for vaccines.

### Instrumentation
- Motivation for IV:
  - Address reverse causality (activity driving vaccinations).
  - Address omitted third factors driving both vaccination rates and economic activity.
- Instrument specification:
  - z_{c,t−2} = p_{c} × va_{s,t−2}  (3)
    - p_{c}: number of pharmacies per square mile in county c.
    - va_{s,t−2}: statewide allocated vaccines in percent of state population at time t−2.
  - Instrument exploits within-state variation: counties with higher pharmacy densities should see larger activity responses when state vaccine allocations increase.
  - Instrument is similar in spirit to a Bartik instrument, though not a strict Bartik.
- Validity criteria:
  - Relevance: instrument must be strongly related to vaccination (first stage).
  - Exclusion restriction: instrument affects economic activity only through vaccinations.
- Empirical assessment:
  - First stage (Table 2): coefficient on Pharmacies per sq. mile × allocations per capita = 1.6894*** [0.2036]; Observations = 40,984; County FE = Yes; State-time FE = Yes; F-stat = 68.9.
  - Pre-trend (Table 3): Pharmacies per sq. mile coefficient on pre-vaccine roll-out spending = -0.0048 [0.0060] (insignificant); Constant = 0.0049 [0.0041]; Observations = 1,730.

### Results — baseline IV and fixed effects estimates
- Estimation approaches:
  - (i) un-instrumented fixed effects regression (using fitted v̂).
  - (ii) instrumented (IV) fixed effects regression estimating system (1)-(2).
- General notes:
  - Instrumentation generally strengthens results; point estimates and standard errors are larger under instrumented regressions.
  - Standard errors are robust (heteroskedasticity-corrected).
- Key county-level coefficients (all include county FE and state-time FE):
  - Spending:
    - Column (1) Un-instrumented: Initiated vaccinations = 0.0020*** [0.0001]; Instrumented = No.
    - Column (2) Instrumented: Initiated vaccinations = 0.0059*** [0.0008]; Instrumented = Yes.
  - Mobility: Work
    - Column (3) Un-instrumented: Initiated vaccinations = 0.0995*** [0.0051]; Instrumented = No.
    - Column (4) Instrumented: Initiated vaccinations = 0.2860*** [0.0270]; Instrumented = Yes.
  - UI claims (initial unemployment insurance claims as percent of 2019 labor force):
    - Column (5) Un-instrumented: Initiated vaccinations = -0.0015*** [0.0004]; Instrumented = No.
    - Column (6) Instrumented: Initiated vaccinations = -0.0035*** [0.0008]; Instrumented = Yes.
- Sample and diagnostics (Table 4):
  - Observations: examples include 40,984 (spending); 46,425 (mobility); 11,811 (UI claims).
  - Weeks: 25 for spending and many mobility specifications; UI claims use 23 weeks in shown columns.
  - Counties: examples include 1,727; 2,724; 2,741; 606 (varies by specification).
  - F-stat (first-stage): 68.9; 84.8; 277.2 (reported across specifications).
- Interpretation:
  - Spending rises by 0.59 percentage points for each percentage point increase in initiated vaccination rates (column 2).
  - Workplace mobility rises by 0.29 percentage points for each percentage point of initiated vaccines (column 4).
  - A one percentage point increase in initiated vaccination rates decreases new unemployment claims by 0.004 percent of the 2019 labor force (instrumented estimate).
  - Overall conclusion: vaccination has a causal and immediate effect on economic activity.

### Robustness checks
- Variations tested (results largely robust):
  - Replace initiated with completed vaccinations (Appendix Table A1).
  - Vary lag between vaccinations and economic outcomes: 0 to 6 weeks for spending and workplace mobility; 3 to 8 weeks for unemployment claims (Appendix Table A2).
  - Vary lags of the instrument from 0 to 6 weeks (Appendix Table A3).
  - Panel regressions with only time and county fixed effects (Appendix Table A4).
  - Nonlinearities: quadratic terms of demeaned vaccinations and the instrument — no significant nonlinear effects found.
  - Use national supply instead of state-level supply (Table A5) — results not meaningfully affected.
- Notable exceptions:
  - Unemployment claims become insignificant at leads of 3 to 4 weeks.
  - Mobility becomes insignificant in the specification with only time and county fixed effects.
- Selected robustness magnitudes (Instrumented: Yes):
  - Table A2 — Spending (Panel A, Lead variation):
    - Lead 1 week: Initiated vaccinations 0.0059*** [0.0008]; Observations 40984; Weeks 25; Counties 1727; F-stat 68.9
    - Lead 6 weeks: Initiated 0.0106*** [0.0011]; Observations 31935; Weeks 22; Counties 1727; F-stat 70.5
  - Table A2 — Mobility: Work (Panel B, Lead variation):
    - Lead 1 week: Initiated 0.2860*** [0.0270]; Observations 64251; Weeks 25; Counties 2741; F-stat 84.8
    - Lead 6 weeks: Initiated 0.3532*** [0.0308]; Observations 64276; Weeks 25; Counties 2736; F-stat 84.9
  - Table A2 — UI claims (Panel C, Lead variation):
    - Lead 3 week: Initiated 0.0001 [0.0007]; Observations 133381; Weeks 25; Counties 609; F-stat 304.6
    - Lead 8 weeks: Initiated -0.0089*** [0.0008]; Observations 10771? ; Weeks 19; Counties 607; F-stat 247.1
  - Table A3 — Lag in instrument (selected):
    - Spending, Lag 2 weeks: Initiated 0.0059*** [0.0008]; Observations 40984; Weeks 25; Counties 1727; F-stat 68.9
    - Mobility, Lag 2 weeks: Initiated 0.2860*** [0.0270]; Observations 64251; Weeks 25; Counties 2741; F-stat 84.8
    - UI claims, Lag 2 weeks: Initiated -0.0035*** [0.0008]; Observations 11963; Weeks 23; Counties 609; F-stat 277.6
  - Table A4 — Fixed effects variants:
    - Spending, Time FE only: Initiated vaccinations 0.0188*** [0.0061]
    - Spending, State-time FE only: Initiated vaccinations 0.0059*** [0.0008]
  - Table A5 — National supply instrument:
    - Spending: Initiated vaccinations 0.0065*** [0.0010]; Observations 40984; Weeks 25; Counties 1727; F-stat 65.9
    - Mobility: Initiated vaccinations 0.3528*** [0.0368]; Observations 64251; Weeks 25; Counties 2741; F-stat 1.3?

### Heterogeneity of effects (Table 5)
- Approach: interact initiated vaccinations with county-level dummies for baseline characteristics.
- Panel A — Conditional on initial unemployment (High = above median)
  - Initiated vaccinations (main effects):
    - Spending = 0.0062*** [0.0009]
    - Mobility = 0.3580*** [0.0402]
    - UI claims = -0.0031*** [0.0008]
  - High(Unemployment) × initiated vaccinations interactions:
    - Spending interaction = 0.0002 [0.0003] (insignificant)
    - Mobility interaction = 0.0702*** [0.0160]
    - UI claims interaction = -0.0028*** [0.0004]
  - Instrumented = Yes; Observations = 40,984 (spending); 46,425 (mobility); 11,963 (UI claims); Weeks = 25/25/23; Counties = 1,727/2,724/1,609; F-stat = 13.3 / 19.6 / 90.2.
- Panel B — Conditional on educational attainment (Low = share with BA below median)
  - Initiated vaccinations:
    - Spending = 0.0068*** [0.0010]
    - Mobility = 0.3459*** [0.0395]
    - UI claims = -0.0103*** [0.0016]
  - Low(below BA degree) × initiated vaccinations:
    - Spending interaction = 0.0010** [0.0004]
    - Mobility interaction = 0.0483*** [0.0126]
    - UI claims interaction = -0.0048*** [0.0009]
  - Instrumented = Yes; F-stat = 40.2 / 41.2 / 76.1.
- Panel C — Conditional on rural-urban status (Urban county dummy)
  - Initiated vaccinations:
    - Spending = 0.0049*** [0.0009]
    - Mobility = 0.3770*** [0.0313]
    - UI claims = -0.0024*** [0.0009]
  - Urban county × initiated vaccinations:
    - Spending interaction = 0.0009** [0.0003]
    - Mobility interaction = -0.0729*** [0.0088]
    - UI claims interaction = -0.0008** [0.0004]
  - Instrumented = Yes; F-stat = 34.6 / 2.9 / 139.0.
- Heterogeneity summary:
  - Effects larger in counties with worse initial socioeconomic conditions (higher pre-COVID unemployment).
  - Larger effects in counties with lower education levels (below BA share).
  - Stronger effects in urban counties for spending and UI claims; mobility responses vary in sign.

### Conclusion and policy implications
- Headline magnitudes:
  - A 1 percentage point increase in initiated vaccination rates:
    - Increases spending by 0.6 percent.
    - Reduces the weekly inflow to unemployment by 0.004 percentage points of the labor force.
    - Increases work-related mobility.
- Equity considerations:
  - Larger benefits accrue to urban and more vulnerable counties (lower education, higher pre-COVID unemployment).
  - Rationale: these counties were likely harder hit by the pandemic (sectoral employment patterns, lockdown impacts), so they respond more when vaccines become widely available.
- Policy implication:
  - Equitable distribution of vaccines is important to reduce inequality and maximize macroeconomic recovery benefits — vaccinations act as a "fair shot in the arm" for the economy.

*Source: Authors’ calculations.*

### 3.1  Baseline specification

### 3.1  Baseline specification

### Baseline model
- Baseline system of equations:
  - y_{c,t+k} = β̂ v_{c,t} + τ_{s,t} + τ_{c} + ε_{c,t+k}  (1)
  - v_{c,t} = γ z_{c,t−2} + δ_{s,t} + δ_{c} + ξ_{c,t}  (2)
- Definitions:
  - y_{c,t+k}: economic outcome in county c, state s, week t+k, including:
    - (i) weekly credit/debit card spending relative to Jan 4–31, 2020 (k = 1)
    - (ii) weekly unemployment claims in percent of county-level 2019 labor force (k = 6)
    - (iii) mobility relative to Jan 3–Feb 6, 2020 (k = 1)
  - v_{c,t}: initiated vaccinations in percent of the population at the county level. (For Johnson & Johnson doses, initiated vaccinations are also completed.)
  - The hat on v_{c,t} denotes the fitted value of vaccinations from equation (2).
  - τ_{s,t} and δ_{s,t}: state-time fixed effects (control for common state-level shocks).
  - τ_{c} and δ_{c}: county fixed effects (capture time-invariant county specifics).
  - z_{c,t−2}: instrument for vaccines (explained below).

### Instrumentation
- Endogeneity concerns motivating IV approach:
  - Reverse causality (e.g., activity driving vaccinations).
  - Omitted third factors driving both vaccination rates and economic activity.
- Instrument specification:
  - z_{c,t−2} = p_{c} × va_{s,t−2}  (3)
    - p_{c}: number of pharmacies per square mile in county c.
    - va_{s,t−2}: statewide allocated vaccines in percent of state population at time t−2.
  - The instrument exploits within-state variation: counties with higher pharmacy densities should see larger activity responses when state vaccine allocations increase.
  - The instrument is similar in spirit to a Bartik instrument (geographic cross-sectional variation interacted with time-varying state allocations), though not a strict Bartik in formal construction.
- Instrument validity criteria:
  - Relevance: instrument must be strongly related to vaccination (first stage).
  - Exclusion restriction: instrument affects economic activity only through vaccinations.
- Empirical assessment of instrument:
  - Table 2 (first stage): coefficient on Pharmacies per sq. mile × allocations per capita = 1.6894*** [0.2036]; Observations = 40,984; County FE = Yes; State-time FE = Yes; F-stat = 68.9.
  - Pre-trend check (Table 3): Pharmacies per sq. mile coefficient on pre-vaccine roll-out spending = -0.0048 [0.0060] (insignificant), Constant = 0.0049 [0.0041]; Observations = 1,730. This supports plausibility of the exclusion restriction.

### Results — baseline IV and fixed effects estimates
- General notes:
  - Two estimation approaches: (i) un-instrumented fixed effects regression (using fitted v̂), (ii) instrumented (IV) fixed effects regression estimating system (1)-(2).
  - Instrumentation generally strengthens results; point estimates and standard errors are larger under instrumented regressions.
  - Standard errors are robust (corrected for heteroskedasticity).
- Key coefficients from Table 4 (county-level effects; all specifications include county FE and state-time FE):
  - Spending:
    - Column (1) Un-instrumented: Initiated vaccinations = 0.0020*** [0.0001]; Instrumented = No.
    - Column (2) Instrumented: Initiated vaccinations = 0.0059*** [0.0008]; Instrumented = Yes.
  - Mobility: Work
    - Column (3) Un-instrumented: Initiated vaccinations = 0.0995*** [0.0051]; Instrumented = No.
    - Column (4) Instrumented: Initiated vaccinations = 0.2860*** [0.0270]; Instrumented = Yes.
  - UI claims (initial unemployment insurance claims as percent of 2019 labor force):
    - Column (5) Un-instrumented: Initiated vaccinations = -0.0015*** [0.0004]; Instrumented = No.
    - Column (6) Instrumented: Initiated vaccinations = -0.0035*** [0.0008]; Instrumented = Yes.
  - Sample and diagnostics (Table 4):
    - Observations: columns vary (e.g., 40,984 for spending; 46,425 for mobility; 11,811 for UI claims).
    - Weeks: 25 for spending and many mobility specifications; UI claims use 23 weeks in shown columns.
    - Counties: examples include 1,727; 2,724; 2,741; 2,741; 606; 606 (varies by specification).
    - F-stat (first-stage): 68.9; 84.8; 277.2 (reported across specifications).
- Interpretation in text:
  - Spending rises by 0.59 percentage points for each percentage point increase in initiated vaccination rates (column 2).
  - Workplace mobility rises by 0.29 percentage points for each percentage point of initiated vaccines (column 4) — mobility is an index.
  - A one percentage point increase in initiated vaccination rates decreases new unemployment claims by 0.004 percent of the 2019 labor force (instrumented estimate).
  - Overall, vaccination has a causal and immediate effect on economic activity.

### Robustness checks
- Replacements and variations tested (results largely robust):
  - Replace initiated with completed vaccinations (Appendix Table A1).
  - Vary lag between vaccinations and economic outcomes: 0 to 6 weeks for spending and workplace mobility; 3 to 8 weeks for unemployment claims (Appendix Table A2).
  - Vary lags of the instrument from 0 to 6 weeks (Appendix Table A3).
  - Panel regressions with only time and county fixed effects (Appendix Table A4).
  - Nonlinearities: quadratic terms of demeaned vaccinations and the instrument — no significant nonlinear effects found.
  - Use national supply instead of state-level supply (Table A5) — results not meaningfully affected.
- Exceptions:
  - Unemployment claims become insignificant at leads of 3 to 4 weeks.
  - Mobility becomes insignificant in the specification with only time and county fixed effects.

### Heterogeneity of effects (Table 5)
- Method: interact initiated vaccinations with county-level dummies for baseline characteristics.
- Panel A: Conditional on county-level initial unemployment (High(Unemployment) = county unemployment above median)
  - Initiated vaccinations = 0.0062*** [0.0009] (Spending)
  - Initiated vaccinations = 0.3580*** [0.0402] (Mobility: Work)
  - Initiated vaccinations = -0.0031*** [0.0008] (UI claims)
  - High(Unemployment) × initiated vaccinations:
    - Spending interaction = 0.0002 [0.0003] (insignificant)
    - Mobility interaction = 0.0702*** [0.0160]
    - UI claims interaction = -0.0028*** [0.0004]
  - Instrumented = Yes; Observations = 40,984 (spending); 46,425 (mobility); 11,963 (UI claims); Weeks = 25/25/23; Counties = 1,727/2,724/1,609; F-stat = 13.3 / 19.6 / 90.2.
- Panel B: Conditional on county-level educational attainment (Low = share with BA below median)
  - Initiated vaccinations:
    - Spending = 0.0068*** [0.0010]
    - Mobility = 0.3459*** [0.0395]
    - UI claims = -0.0103*** [0.0016]
  - Low(below BA degree) × initiated vaccinations:
    - Spending interaction = 0.0010** [0.0004]
    - Mobility interaction = 0.0483*** [0.0126]
    - UI claims interaction = -0.0048*** [0.0009]
  - Instrumented = Yes; Observations and sample structure as in Panel A; F-stat = 40.2 / 41.2 / 76.1.
- Panel C: Conditional on rural-urban status (Urban county dummy)
  - Initiated vaccinations:
    - Spending = 0.0049*** [0.0009]
    - Mobility = 0.3770*** [0.0313]
    - UI claims = -0.0024*** [0.0009]
  - Urban county × initiated vaccinations:
    - Spending interaction = 0.0009** [0.0003]
    - Mobility interaction = -0.0729*** [0.0088]
    - UI claims interaction = -0.0008** [0.0004]
  - Instrumented = Yes; Observations and sample structure as in Panels A–B; F-stat = 34.6 / 2.9 / 139.0.
- Summary of heterogeneity:
  - Effects of vaccines are larger in counties with worse initial socioeconomic conditions (higher pre-COVID unemployment).
  - Larger effects in counties with lower education levels (below BA share).
  - Stronger effects in urban counties (particularly for spending and UI claims), though mobility responses vary in sign.

### Conclusion and policy implications
- Magnitude of headline effects:
  - A 1 percentage point increase in initiated vaccination rates:
    - Increases spending by 0.6 percent.
    - Reduces the weekly inflow to unemployment by 0.004 percentage points of the labor force.
    - Increases work-related mobility.
- Heterogeneity and equity considerations:
  - Larger benefits accrue to urban and more vulnerable counties (lower education, higher pre-COVID unemployment).
  - Reasoning: these counties were likely harder hit by the pandemic (sectoral employment patterns, lockdown impacts), so they respond more when vaccines become widely available.
  - Policy implication: equitable distribution of vaccines is important to reduce inequality and maximize the macroeconomic recovery benefits — vaccinations act as a "fair shot in the arm" for the economy.

*Source: Authors’ calculations.*

### References

### A Robustness and Instrumentation (References appendix)

### Robustness: key regression results and statistics
- Table A1: Effect of completed vaccinations on economic activity at the county level
  - Spending (cols 1–2):
    - Completed vaccinations 0.0022*** [0.0002] (Instrumented: No)
    - Completed vaccinations 0.0105*** [0.0014] (Instrumented: Yes)
    - Observations 40601 / 40601
    - Weeks 25
    - Counties 1727
    - F-stat 55.8 / 8.4 / 201.4 (as reported)
  - Mobility: Work (cols 3–4):
    - Completed vaccinations 0.1178*** [0.0052] (Instrumented: No)
    - Completed vaccinations 0.5480*** [0.0651] (Instrumented: Yes)
    - Observations 63827 / 63827
    - Weeks 25
    - Counties 2741
  - UI claims (cols 5–6):
    - Completed vaccinations -0.0006 [0.0005] (Instrumented: No)
    - Completed vaccinations -0.0062*** [0.0014] (Instrumented: Yes)
    - Observations 11483 / 11483
    - Weeks 23
    - Counties 2741

- Table A2: Varying the lead in the outcome variable
  - Panel A: Spending (Instrumented: Yes)
    - Lead 1 week: Initiated vaccinations 0.0059*** [0.0008]; Observations 40984; Weeks 25; Counties 1727; F-stat 68.9
    - Lead 2 weeks: Initiated 0.0066*** [0.0007]; Observations 40980; Weeks 25; Counties 1727; F-stat 68.9
    - Lead 3 week: Initiated 0.0073*** [0.0008]; Observations 40973; Weeks 25; Counties 1727; F-stat 68.9
    - Lead 4 weeks: Initiated 0.0084*** [0.0009]; Observations 39246; Weeks 24; Counties 1727; F-stat 69.5
    - Lead 5 weeks: Initiated 0.0093*** [0.0010]; Observations 33752; Weeks 23; Counties 1727; F-stat 70.0
    - Lead 6 weeks: Initiated 0.0106*** [0.0011]; Observations 31935; Weeks 22; Counties 1727; F-stat 70.5
  - Panel B: Mobility: Work (Instrumented: Yes)
    - Lead 1 week: Initiated 0.2860*** [0.0270]; Observations 64251; Weeks 25; Counties 2741; F-stat 84.8
    - Lead 2 weeks: Initiated 0.3097*** [0.0273]; Observations 64255; Weeks 25; Counties 2741; F-stat 84.8
    - Lead 3 week: Initiated 0.3010*** [0.0255]; Observations 64260; Weeks 25; Counties 2740; F-stat 84.8
    - Lead 4 weeks: Initiated 0.3019*** [0.0267]; Observations 64266; Weeks 25; Counties 2739; F-stat 84.8
    - Lead 5 weeks: Initiated 0.3176*** [0.0289]; Observations 64266; Weeks 25; Counties 2736; F-stat 84.8
    - Lead 6 weeks: Initiated 0.3532*** [0.0308]; Observations 64276; Weeks 25; Counties 2736; F-stat 84.9
  - Panel C: UI claims (Instrumented: Yes)
    - Lead 3 week: Initiated 0.0001 [0.0007]; Observations 133381; Weeks 25; Counties 609; F-stat 304.6
    - Lead 4 weeks: Initiated -0.0010 [0.0007]; Observations 131451; Weeks 24; Counties 609; F-stat 302.4
    - Lead 5 week: Initiated -0.0021*** [0.0007]; Observations 125551; Weeks 23; Counties 609; F-stat 291.0
    - Lead 6 weeks: Initiated -0.0035*** [0.0008]; Observations 119631; Weeks 22; Counties 609; F-stat 277.6
    - Lead 7 weeks: Initiated -0.0059*** [0.0008]; Observations 113721; Weeks 21; Counties 609; F-stat 261.0
    - Lead 8 weeks: Initiated -0.0089*** [0.0008]; Observations 10771? (as printed) ; Weeks 19; Counties 607; F-stat 247.1

- Table A3: Varying the lag in the instrument variable (Instrumented: Yes)
  - Panel A: Spending
    - Lag 1 week: Initiated 0.0056*** [0.0009]; Observations 40108; Weeks 26; Counties 1727; F-stat 69.6
    - Lag 2 weeks: Initiated 0.0059*** [0.0008]; Observations 40984; Weeks 25; Counties 1727; F-stat 68.9
    - Lag 3 week: Initiated 0.0060*** [0.0007]; Observations 41599; Weeks 25; Counties 1727; F-stat 69.2
    - Lag 4 weeks: Initiated 0.0062*** [0.0007]; Observations 41988; Weeks 24; Counties 1727; F-stat 70.2
    - Lag 5 weeks: Initiated 0.0067*** [0.0007]; Observations 40590; Weeks 24; Counties 1727; F-stat 71.9
    - Lag 6 weeks: Initiated 0.0072*** [0.0008]; Observations 39168; Weeks 23; Counties 1727; F-stat 73.5
  - Panel B: Mobility: Work
    - Lag 1 week: Initiated 0.2693*** [0.0312]; Observations 62453; Weeks 25; Counties 2742; F-stat 84.1
    - Lag 2 weeks: Initiated 0.2860*** [0.0270]; Observations 64251; Weeks 25; Counties 2741; F-stat 84.8
    - Lag 3 week: Initiated 0.2800*** [0.0240]; Observations 64265; Weeks 25; Counties 2741; F-stat 86.4
    - Lag 4 weeks: Initiated 0.2571*** [0.0208]; Observations 65439; Weeks 25; Counties 2742; F-stat 84.4
    - Lag 5 weeks: Initiated 0.2429*** [0.0201]; Observations 66178; Weeks 25; Counties 2739; F-stat 90.7
    - Lag 6 weeks: Initiated 0.2518*** [0.0204]; Observations 66680; Weeks 25; Counties 2737; F-stat 93.5
  - Panel C: UI claims
    - Lag 1 week: Initiated -0.0024*** [0.0008]; Observations 12183; Weeks 24; Counties 609; F-stat 274.9
    - Lag 2 weeks: Initiated -0.0035*** [0.0008]; Observations 11963; Weeks 23; Counties 609; F-stat 277.6
    - Lag 3 week: Initiated -0.0046*** [0.0007]; Observations 11296; Weeks 22; Counties 609; F-stat 320.3
    - Lag 4 weeks: Initiated -0.0059*** [0.0007]; Observations 11611; Weeks 21; Counties 609; F-stat 361.5
    - Lag 5 weeks: Initiated -0.0064*** [0.0008]; Observations 10678; Weeks 20; Counties 609; F-stat 337.5
    - Lag 6 weeks: Initiated -0.0060*** [0.0008]; Observations 10164; Weeks 19; Counties 609; F-stat 307.7

- Table A4: Varying type of included fixed effects (Instrumented: Yes)
  - Spending:
    - Initiated vaccinations 0.0188*** [0.0061] (Column 1, Time FE: Yes; State-time FE: No)
    - Initiated vaccinations 0.0059*** [0.0008] (Column 2, Time FE: No; State-time FE: Yes)
    - Observations 40984 / 40984; Weeks 25; Counties 1727 / 2741
    - F-stat 26.4 / 68.9 / 40.2 (as printed across columns)
  - Mobility: Work:
    - Initiated 0.0721 [0.1346] (Column 3)
    - Initiated 0.2860*** [0.0270] (Column 4)
  - UI claims:
    - Initiated -0.0179*** [0.0026] (Column 5)
    - Initiated -0.0035*** [0.0008] (Column 6)

- Table A5: Using the average national vaccine supply interacted with pharmacy density as instrument (Instrumented: Yes)
  - Spending:
    - Initiated vaccinations 0.0065*** [0.0010]; Observations 40984; Weeks 25; Counties 1727; F-stat 65.9
  - Mobility: Work:
    - Initiated vaccinations 0.3528*** [0.0368]; Observations 64251; Weeks 25; Counties 2741; F-stat 1.3?
  - Another Spending or UI claims column shows Initiated -0.0034*** [0.0008]; Observations 11196?; Weeks 23; Counties 1609; F-stat 207.5

- Common notes across tables:
  - Spending is seasonally adjusted credit/debit card spending expressed relative to Jan 4–31, 2020.
  - Workplace mobility is compared to its median value for the same weekday in the period of Jan 3 – Feb 6, 2020.
  - UI claims is initial unemployment insurance claims in percent of the 2019 labor force.
  - Spending and mobility are led by 1 week and UI claims by 6 weeks relative to initiated vaccinations in base specifications.
  - All specifications include county fixed effects and state-time (or time/state-time) fixed effects as indicated.
  - In IV regressions initiated vaccinations are instrumented with the previous 2 week’s allocation of vaccines (Pfizer and Moderna) at the state level (in percent of total population) interacted with pharmacy density at the county-level.
  - Robust standard errors are reported. ***, **, and * indicate statistical significance at 1, 5, and 10 percent, respectively.

### Details on the instrumentation: definition and identification
- Instrument definition (as given in the appendix):
  - z_{c,t−2} = #pharmacies_c / area_c × vaccineallocations_{s,t−2} / population_s ≡ p_c × ω_{s,t−2}
  - where p_c = #pharmacies_c / area_c (density of pharmacies per county in 2020)
  - and ω_{s,t−2} = vaccineallocations_{s,t−2} / population_s (per capita number of state-level allocated vaccines (Pfizer and Moderna) for states in week t−2)
- First-stage equation (county and state-time fixed effects):
  - v_{c,t} = γ z_{c,t−2} + δ_{s,t} + δ_c + ξ_{c,t}
  - Equivalently after demeaning:
    - ̃v_{c,t} = γ ̃z_{c,t−2} + ̃ξ_{c,t}
    - with ̃v_{c,t} = v_{c,t} − ∑_t v_{c,t}/T − v_{s,t}, etc.
- Algebraic decomposition (as provided):
  - ̃z_{c,t−2} = p_c ω_{s,t−2} − p_c ω_s − ω_{s,t−2} ̄p_s
  - Simplified form shown:
    - ̃z_{c,t−2} = (p_c − ̄p_s) (ω_{s,t−2} − ω_s) − ̄p_s ω_s
  - Identification focuses on whether activity picked up most in counties where pharmacies are densest as state level allocations of vaccines picked up relative to counties with lower pharmacy density within each state.
- Instrument validity considerations emphasized:
  - The number of allocated vaccines are largely exogenous to counties.
  - The number of pharmacies in 2020 is largely pre-determined.
  - An alternative formulation could demean pharmacy density at the state level to remove the last term in the decomposition.

*Source: wpiea2021281-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2021/english/wpiea2021281-print-pdf.pdf_