UNIVERSITY OF WAIKATO
Hamilton
New Zealand

The Rollout of COVID-19 Booster Vaccines is AssociatedWith Rising Excess Mortality in New Zealand
John Gibson

Working Paper in Economics 11/22
June 2022

John Gibson
School of Accounting, Financeand Economics
University of Waikato
Private Bag 3105
Hamilton, 3240
New ZealandTel: +64 (7) 838 4289
Email: jkgibson@waikato.ac.nz

Abstract

The rollout of booster doses of COVID-19 vaccines to the general population is controversial.
The ratio of vaccine risk to benefits likely has swung more towards risk than during the original
randomized trials, due to dose-dependent adverse events and to fixation of immune responses
on a variant no longer circulating, yet the evidence underpinning mass use of boosters is weaker
than was the evidence for the original vaccine rollout. In light of an unsatisfactory risk-evidence
situation, aggregate weekly data on excess mortality in New Zealand are used here to study the
impacts of rolling out booster doses. Instrumental variables estimates using a plausible sourceof exogenous variation in the rate of booster dose rollout indicate 16 excess deaths per 100,000
booster doses, totaling over 400 excess deaths from New Zealand’s booster rollout to date. The
value of statistical life of these excess deaths is over $1.6 billion. The age groups most likely
to use boosters had 7–10 percentage point rises in excess mortality rates as boosters were rolled
out while the age group that is mostly too young for boosters saw no rise in excess mortality.

Keywords
COVID-19
excess mortality
instrumental variables
vaccines
New Zealand
JEL Classification
D61
I18

1

I.

Introduction

The rollout of booster doses of COVID-19 vaccines to the general population has been
controversial in many countries. In September 2021 an advisory panel of outside experts to the
US Food and Drug Administration (FDA) voted 16-2 against widespread use of these boosters
due to lack of safety data and doubts about benefits of mass boosting over targeted approaches(Perrone and Neergaard, 2021). After this vote was ignored and the FDA approved boosters
for the general population the top two officials in FDA’s Office of Vaccines Research andReview resigned and criticized decision-making about mass rollout of boosters (Krause et al,2021). This critique noted that if unnecessary boosting causes significant adverse reactions it
may increase vaccine hesitancy more generally; a concern raised elsewhere that the potentially
low benefits of COVID-19 vaccines relative to the costs borne by vaccinees (such as exposure
to breakthrough infections and to vaccine adverse events) may undermine public confidence inother vaccination efforts (Godlee, 2020; Gibson, 2022a). Even the World Health Organization
argue that a vaccination strategy based on repeated booster doses of the original vaccine
composition is unlikely to be appropriate or sustainable (WHO, 2022).
Notwithstanding these concerns, many countries began booster rollouts in the second
half of 2021, and to date (mid-June, 2022), 2.1 billion booster doses have been given, comparedwith 10 billion original protocol doses. These are especially a feature of rich countries, where
boosters have been one-quarter of all doses given versus just 3% of doses administered in lowincome countries (Mathieu et al, 2021). Aggregate data for one set of rich countries (the OECDmembers) show higher excess mortality when more booster doses are used.1 This accords withhigher all-cause mortality amongst vaccinees in Pfizer’s original randomized trial (Gibson,
2022b)—recalling that booster doses are just the original Pfizer/BioNTech BNT162b2 recipe.
Moreover, if vaccine adverse events are dose-dependent, and if using a booster formulated forthe original Wuhan strain of SARS-CoV-2 fixates the immune system to protect against avariant no longer circulating (Reynolds et al, 2022), the ratio of vaccine risks to benefits swings
more towards risks than at the time of the original randomized trials. Hence, there are calls torelax coercive vaccine policies (Bardosh et al, 2022) and as a safety measure for further booster
vaccinations to be discontinued (Yamamoto, 2022). Several European countries have already
restricted some mRNA vaccines to only those aged over 30 years due to these safety concerns.
Given this shift in the risk-benefit ratio, stronger evidence should underpin mass use ofboosters but in fact the opposite holds; even with caveats about limited scope of the original
trials (Doshi, 2020) and lack of access to their raw data (Doshi et al, 2022) at least the original
vaccine rollout waited for large-scale trials yet booster rollouts (and their extension to younger
age groups) often rely on far weaker, observational, studies. These observational studies may
be biased by assuming selection on observables, by miscategorising treatment groups (and thetreatment periods), and by under-estimating the (residual) numbers unvaccinated causing their
COVID-19 rates to be exaggerated (Neil et al, 2022). This gradual erosion of evidence-based

1
Appendix A shows that monthly average excess mortality p-scores (the percentage by which total deaths differ
from expected deaths) are 4.4 percentage points higher for every 10 doses per 100 people higher is the average
booster rate (the mean booster rate is 28 per 100), for 31 OECD countries between August 2021 and May 2022.

2

medicine, to instead be inverted as medicine-based evidence, is exemplified in a remark madeby Dr Eric Rubin, editor-in-chief of the New England Journal of Medicine, when participating
in an FDA advisory panel that voted to give emergency use authorization to Pfizer’s BNT162b2
vaccine for 5-11 year old children:“We’re never going to learn about how safe this vaccine is unless we start giving it. That’s justthe way it goes. That’s how we found out about rare complications of other vaccines...”(FDA, 2021, p.312)

In light of debates about mass rollout of booster doses of COVID-19 vaccines, evidence
is provided here on the association between booster rollout and rising excess mortality in New
Zealand. Time-series analysis of aggregate data is often considered a weaker form of evidence
but the sort of studies usually thought to give stronger evidence, like large randomized control
trials (RCTs), are either not being done for boosters (Makary, 2022) or have various biases thatlikely inflate apparent vaccine efficacy (Gibson, 2022b). Moreover, aspects of the current study
help bring it closer to the experimental ideal. First, New Zealand persisted with zero-COVID
for longer than most countries other than China, allowing effects of higher doses to be studied
free from other (confounding) effects. Most people in New Zealand who received the original
two doses of Pfizer and then the booster had no prior exposure to SARS-CoV-2. For example,
only by late February 2022 did cumulative cases of COVID-19 in New Zealand exceed 1% of
the population.2 By then, 8.2 million original protocol Pfizer doses and 2.2 million booster
doses had been administered. In other words, about half of the population were both ‘fully
vaccinated’ and ‘boosted’ prior to having any experience of COVID-19.
A second strength of the study is to exploit a plausible source of exogenous variation,with an instrumental variables (IV) strategy, so associations between booster rollout and excess
mortality can be interpreted not just as correlations but also in quasi-experimental causal terms.
The results suggest 16 (95% CI: 5 to 27) excess deaths per 100,000 booster doses, amounting
to over 400 excess deaths in New Zealand given the booster doses administered to date. If thisrate of excess deaths is extrapolated to other countries, it amounts to over 300,000 excess deaths
worldwide. The rise in excess mortality since the booster rollout began occurs in all age groups
except the youngest (under age 30), who mostly are ineligible for boosters. In economic terms,
if an age-adjusted value of statistical life of $4 million is applied, excess mortality associatedwith New Zealand’s booster rollout is valued at over $1.6 billion.3 Even just one percent of thisvalue of lost life ($16 million) would have been more than sufficient to carefully study booster
impacts by randomizing the rollout and could also have funded surveys of vaccine adverse
events rather than relying on the current passive reporting system. Instead, local healthauthorities seemed to outsource decisions to industry-captured overseas regulators.

2

Using cumulative cases per million people from Our World in Data. Omicron arrived on 26 January 2022.
Earlier variants were suppressed by using two-week managed isolation and quarantine for overseas arrivals,
quarantining community cases and their household contacts, and a series of hard lockdowns.
3
Cost-benefit analyses by the NZ Treasury reportedly use a Value of Statistical Life (VSL) of $4.7 million(Coughlan, 2019) which is about $5m in 2022 terms. Age-adjustment is needed because no booster-related risein excess mortality shows up for the 0-29 age group. Using a quality-adjusted life year value of $62,000 (Lally,2021) adds up to almost $1 million for the median person aged 0-29 years, so without them the average VSL forthe remaining ages should be about $4 million.

3

II.

Excess Mortality Estimates

Estimates of excess mortality for a particular era require the expected number of deaths
per period (weekly, in this case). The means from a prior era are often used. For example, Kunget al (2021) compare week-specific mean death rates from 2015-19 to death rates in 2020 whenarguing that there were no apparent adverse effects of lockdowns on mortality in New Zealand.
Expected deaths can also be calculated from regressions, letting factors that change over time
be incorporated (using means ignores such changes). A regression approach is used here:(1)
where j indexes weeks and t years, theare fixed effects for each week of the year, the timeindex T (=1 for 2011, 2 for 2012 and so on) allows for secular trends (such as from rising life
expectancy), the resident population (ResPop) controls for any increase in deaths due to a larger
population, and the vector of shocks is for mass death events not expected to reoccur.
There are three notable features of equation (1). The full span of data from the start of2011 is used because it is inefficient to discard part of a time-series.4 Death rates are not usedbecause their denominator depends on population projections for the latest years (Németh etal, 2021), which are inexact for New Zealand due to migration-induced fluctuations in
population. Instead, quarterly population estimates are a control variable, and in conjunction
with the time-trend allow dynamic forecasting of expected deaths into the booster era. Third,
parameters are estimated through to the end of March 2020 (and then used to predict on an
April-to-March year basis). This timing reflects New Zealand’s late response to COVID-19(Gibson, 2022c), as major interventions (lockdowns and MIQ) did not affect weekly deaths
before April 2020, covers the vaccine rollout period (<1% of doses were prior to April 2021),
and allows for the slow reporting of deaths such that reliable figures end in April 2022.5
Results of equation (1) are given in Appendix B, for all-ages and for the four age-groups
specified in the deaths data: 0-29 years, 30-59 years, 60-79 years, and 80 years plus. In seasonalpatterns, all-ages deaths peak in week 32 (late July), with 153 more (95% CI: 125 to 181) thanin week 7 (mid-February) that has fewest deaths. There are more deaths as population increases
but fewer over time holding population constant. The two shocks (Christchurch earthquake andmosque shooting) are precisely (p<0.02) estimated to purge their effects from the predictions(that is, these shocks are modelled as non-recurrent).
Weekly all-cause, all-ages, deaths are shown in panel A of Figure 1, as a 3-week moving
average (so based on the week ahead, the week behind, and the current week). This slightsmoothing lets patterns be seen clearly without distraction from very short-term volatility. In
addition to actual deaths for 2021-22, the expected number of deaths each week are also shown,
based on the regression analysis discussed above. Expected deaths rise linearly from midFebruary to the end of July, then decline with some unevenness through to December, fluctuate
a little and then reach their annual low of 610 per week in mid-February.
4

Data are from https://www.stats.govt.nz/experimental/covid-19-data-portal. Counts of all deaths (for four age
groups), based on week of death, are given. This is more correct than using date of registration (which is basedon burial or cremation dates).
5
As of mid-June 2022, deaths data are available through late May. However, latest counts are revised upwards
for several weeks thereafter so the most accurate data have a lag of at least eight weeks.

4Figure 1: Excess Mortality and COVID-19 Vaccine Rollout in New ZealandA) Actual and Expected Deaths (Weekly Moving Averages): April 2021 to March 2022
800

Weekly Deaths

750

700

650

600
April

June

AugustOctober

Actual Deaths

DecemberFebruary

Expected Deaths

800

45

700

40

600

35

500

30

400

25

300

20

200

15

100

10

0

5

‐100
April

0

June

AugustExcess deaths (left axis)

October

December

Vaccinated (right axis)

5

February
Boosted (right axis)

People vaccinated, boosted (100,000s)

Excess deaths, cumulative April 2021 to March 2022

B) Cumulative Excess Deaths and COVID-19 Vaccine Rollout: April 2021 to March 2022

Actual deaths largely followed the pattern of expected deaths until November, albeit
with a slightly later and higher (n=780) peak and faster decline. Thereafter deaths deviatedfrom the usual seasonal pattern; fluctuating around 650 per week until late February rather thanfalling to 610 per week as expected. March 2022 saw a sharp rise in deaths by about 100 per
week over their expected number.
The excess deaths are cumulated and shown in Panel B of Figure 1. For the first eightmonths, cumulative totals fluctuated around 0 in a fairly narrow band (rarely exceeding ±100).
However, from December cumulative excess deaths rose from -100 to over +300 by the end of
February, and then rose more sharply, to +800 by the end of March. This figure also shows therollout of original protocol and booster doses. The sustained rise in excess mortality from
December coincides with the booster rollout.
The rise in excess mortality in the last four months of the April-to-March year was
experienced by all ages except the 0-29 years group, who are mostly ineligible for boosters(Table 1). From the pre-booster era to the booster era excess mortality p-scores rose by sevenpercentage points for the 30-59 and 60-79 age groups and by ten percentage points for theoldest age group. In other words, the age groups most likely to use boosters show large rises inexcess mortality after boosters are rolled out.

Table 1: Excess Mortality by Age Group: New Zealand 2021-22
Mean Excess Mortality p-score
Change from pre-booster
Age GroupPre-booster era
Booster era
era to booster era*0 – 296.0

3.8-2.2 [0.782]

30 – 59-4.3

2.7

7.0 [0.017]

60 – 79

0.1

7.3

7.2 [0.003]

80 and above

0.3

10.4

10.1 [0.000]

ALL AGES

-0.2

8.2

8.4 [0.000]

Notes : The p-score is the percentage by which weekly deaths deviate from expected deaths. The prebooster era is April to November 2021, and the booster era is December 2021 through March 2022.
* p-values for the null hypothesis of zero change in [ ].

III.

Booster Impacts

The visual evidence of 400 cumulative excess deaths while boosters went from zero toover two million is suggestive, especially as the age-disaggregated data show no rise in excess
deaths for the one group (0-29 years) mostly ineligible for boosters. Notably there is no similar
temporal association with rollout of the original protocol doses. Also, only the last part of therise in deaths in Figure 1 may be attributed to Omicron; community cases were first seen at theend of January and there is typically a 3-week infection-to-death lag (Gibson, 2022c).
Statistical analyses with cumulative data may face spurious regression problems, as
Hendry (1980) famously showed with cumulative rainfall and the UK price level. Therefore,
the remaining analyses use first-differenced data. Removing common trends gives smaller
correlations; the 0.88 for cumulative excess deaths and booster rollout shown in the figure
becomes 0.37 for their first differences (95% CI: 0.81 to 0.93, and 0.11 to 0.59).

6

Results of six different regressions, for first-differences of the time-series in Panel B of
Figure 1, are reported in Table 2. Three are unconditional (bivariate) relationships while theothers include control variables for original protocol doses (one can only be ‘boosted’ if already‘fully vaccinated’) and for COVID-19 attributed deaths. The first set of regressions use OLS(with Newey-West robust standard errors), the next use distributed lag models, to allow for
effects that accumulate over time (the 28-day lag corresponds to the common interval for
attributing deaths after a positive PCR test to COVID-19), and the third set of regressions use
instrumental variables to enable causal interpretations.
There are 16 excess deaths per 100,000 booster doses (95% CI: 6 to 25) with theunconditional OLS regression (Table 2). This rate rises to 32 using the 28-day lag, and is evenhigher, at 54, with instrumental variables. Thus, the OLS results can be viewed as conservative.
With covariates included the coefficients have a tighter spread, with 12, 17, and 16 excess
deaths per 100,000 booster doses, ceteris paribus, according to the OLS, distributed lag, andinstrumental variables estimates.
Table 2: Estimates of the Relationship Between Booster Rollout and Excess Mortality
MethodNo control variables
With control variables
15.6 (6.0 – 25.2)
12.1 (5.7 – 18.6)
Ordinary Least Squares (OLS)
Distributed Lag (DL)32.1 (20.8 – 43.5)

17.0 (10.0 – 24.0)

Instrumental Variables (IV)53.8 (9.8 – 97.9)

15.6 (4.6 – 26.5)

Notes : Coefficients show estimated excess deaths per 100,000 booster doses. 95% CI in ( ). Full results of
the regressions are reported in Appendix C. N =51 for OLS and IV and N =48 for DL.

The regression results show statistical associations between booster rollout and excess
deaths using observational data not randomized data. Thus, confounding from omitted relevant
variables or reverse causation cannot be ruled out. Instrumental variables estimation allows
quasi-experimental causal interpretations, subject to using valid instruments. In New Zealandthe government frequently emphasized that pace of the vaccine rollout depended on Pfizer forthe timing and quantity of shipments (Hipkins, 2021). This exogenous variation in doses
available also altered timing intervals between doses (shorter when more doses were on hand).
Satisfaction of the instrument relevance condition for vaccine availability shows in the highfirst-stage F-statistic (17.6). The exclusion restriction is that no pathway from available booster
doses to excess mortality exists, except through doses actually given. Crowding-out could be
an alternative pathway if vaccines had been purchased through usual channels; more Pfizer
doses available might mean less spent on other life-saving drugs. Yet the vaccine taskforce was
led by the Ministry of Business, Innovation and Employment (MBIE) rather than by the usual
medicines buying agency (Pharmac), and purchases of Pfizer doses did not reduce Pharmac’sother spending so crowding-out seems unlikely.
An underlying theory of why X causes Y helps to interpret empirical relationships as
causal. Here, dose-dependent adverse events may explain why booster rollout is associatedwith rising excess deaths while rollout of original protocol doses is not. Secondary analysis ofserious adverse events reported in the mRNA vaccine RCTs shows higher risks with Modernathan with Pfizer (Fraiman et al, 2022), perhaps from dosage differences (100mg for Moderna7versus 30mg for Pfizer).6 The use of the Pfizer booster raises the accumulated dosage, which
may then make these vaccine adverse events more likely.
The instrumental variables estimate of 16 (95% CI: 5 to 27) excess deaths per 100,000
booster doses, ceteris paribus, implies over 400 excess deaths in total given the booster doses
administered in New Zealand to date. This estimate should not display omitted variables bias
nor reflect reverse causation, which can also be further ruled out by noting that all-cause deaths
needed for calculating excess mortality are reported with a time lag. Hence, few people could
be aware, in near-real-time, of increased mortality risk that might spur them to get a booster.
IV.

Conclusions

Weekly data on all deaths in New Zealand, from 2011 through the end of March 2022,
are used here to calculate excess mortality during the rollout of COVID-19 vaccines. There isa close relationship between booster rollout and rising excess mortality. This relationship was
not seen with the rollout of the original protocol vaccine doses. The age groups most likely touse boosters had 7–10 percentage point rises in excess mortality rates as boosters were rolled
out while the age group that is mostly too young for boosters saw no rise in excess mortality.
Instrumental variables estimates that exploit a plausible source of exogenous variation in therate of administering booster doses suggest 16 excess deaths per 100,000 booster doses given,amounting to over 400 excess deaths from New Zealand’s booster rollout. Value of statisticallife of these excess deaths is over $1.6 billion. Even a small fraction of this (say, one percent)would have been sufficient to fund robust evidence on the impacts of rolling out COVID-19
booster vaccines.

6

Increased risk (relative to placebo group baselines) of serious adverse events were 151 per 100,000 vaccinatedwith Moderna and 101 per 100,000 vaccinated with Pfizer. These increased risks exceeded the risk reduction for
COVID-19 hospitalization for vaccinees.

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10Appendix A
Evidence from a Monthly Panel of OECD Countries
Data on the number of people vaccinated under original protocols for the COVID-19
vaccines and the number of booster doses given (both per 100 population) were obtained
from Our World in Data (Mathieu et al, 2021) for the 31 countries (including New Zealand)that are members of the OECD and are part of the short-term mortality fluctuations database(Németh et al, 2021). These data were aggregated to monthly averages by country, for theAugust 2021 to May 2022 period, where the beginning of this period aligns with the start ofbooster rollouts to the general population in many of these countries and the end of the period
is set by the availability of excess mortality estimates for a majority of these countries. In thissample, excess mortality p-scores (the percentage by which total deaths differ from expected
deaths) average 11.8, the vaccination rate (for original protocol doses) averages 72.3% andbooster use averages 28.3 doses per 100 people. In other words, deaths are running 12 percent
higher than expected and the interest here is in seeing how the variation around this averagerelates to the use of the COVID-19 vaccines (both boosters and original protocol doses).
While the estimated relationship is a conditional correlation, concern about omitted variables
bias can be mitigated by using two-way fixed effects to control for time-invariant unobservedcountry factors and space-invariant temporal factors that might otherwise confound therelationship. The results of this regression are as follows:

Excess mortality p-scores are 4.4 percentage points higher for every 10 doses per 100 people
higher is the average booster rate (p<0.01), controlling for the proportion of people who had
been fully vaccinated under original protocols (noting that being fully vaccinated is anecessary condition for being boosted). In other words, excess mortality is higher where andwhen booster use is higher.

11Appendix B: Regression Equations Used For Estimating Expected Weekly Deaths
Population (log)Time index
Weekly fixed effects
Week_2
Week_3
Week_4
Week_5
Week_6
Week_7
Week_8
Week_9Week_10
Week_11
Week_12
Week_13
Week_14
Week_15
Week_16
Week_17
Week_18
Week_19
Week_20
Week_21
Week_22
Week_23
Week_24
Week_25
Week_26

All-ages
989.163(212.039)-6.342(3.712)

Age 80 plus
432.633(150.972)-1.931(2.643)

Ages 60-79
360.709(106.027)-1.923(1.856)

Ages 30-59
91.129(58.153)-0.670(1.018)Ages 0-29
104.645(31.110)-1.817(0.545)-10.200(13.665)
6.700(13.665)-18.000(13.665)-19.600(13.665)-8.500(13.665)-20.700(13.665)-20.200(13.665)-12.072(14.047)-17.800(13.665)-11.478(14.041)-6.900(13.665)-6.517(13.665)
3.072(14.056)-5.706(14.056)
12.628(14.056)
14.294(14.056)
12.517(14.056)
32.739(14.056)
33.628(14.056)
33.850(14.056)
56.517(14.056)54.405(14.056)
51.850(14.056)
74.739(14.056)
79.566(14.059)

0.300(9.730)14.400(9.730)3.500(9.730)1.300(9.730)-0.800(9.730)-10.300(9.730)-4.900(9.730)2.630(10.002)-0.200(9.730)11.402(9.997)8.400(9.730)2.718(9.730)
6.827(10.008)
10.160(10.008)
18.938(10.008)
19.494(10.008)
23.160(10.008)
31.160(10.008)
37.938(10.008)33.827(10.008)50.494(10.008)52.716(10.008)44.938(10.008)
61.938(10.008)
69.988(10.010)-3.300(6.833)-3.500(6.833)-15.800(6.833)-15.700(6.833)-5.500(6.833)-3.100(6.833)-10.300(6.833)-7.025(7.024)-4.600(6.833)-13.899(7.021)-8.600(6.833)-1.552(6.833)-2.505(7.028)-6.061(7.028)2.606(7.028)-1.505(7.028)-0.950(7.028)9.495(7.028)3.939(7.028)5.272(7.028)10.939(7.028)8.161(7.028)14.606(7.028)13.383(7.028)10.462(7.030)-4.200(3.748)-1.200(3.748)-2.600(3.748)-1.600(3.748)1.100(3.748)-4.100(3.748)-2.200(3.748)-4.090(3.853)-7.600(3.748)-4.658(3.851)-2.400(3.748)-3.438(3.748)1.390(3.855)-4.054(3.855)-2.721(3.855)-2.165(3.855)-3.832(3.855)-2.832(3.855)-4.610(3.855)-0.054(3.855)-1.721(3.855)-2.054(3.855)-1.943(3.855)
1.835(3.855)-0.091(3.856)-3.000(2.004)-3.000(2.004)-3.100(2.004)-3.600(2.004)-3.300(2.004)-3.200(2.004)-2.800(2.004)-3.587(2.060)-5.400(2.004)-4.323(2.059)-4.300(2.004)-4.263(2.004)-2.639(2.061)-5.750(2.061)-6.195(2.061)-1.528(2.061)-5.861(2.061)-5.084(2.061)-3.639(2.061)-5.195(2.061)-3.195(2.061)-4.417(2.061)-5.750(2.061)-2.417(2.061)-0.792(2.062)

Week_27
Week_28
Week_29
Week_30
Week_31
Week_32
Week_33
Week_34
Week_35
Week_36
Week_37
Week_38
Week_39
Week_40
Week_41
Week_42
Week_43
Week_44
Week_45
Week_46
Week_47
Week_48
Week_49
Week_50
Week_51
Week_52
ShocksChch earthquake
Mosque shooting

80.054(14.105)
100.721(14.105)
103.054(14.105)
122.054(14.105)
119.609(14.105)132.165(14.105)
119.498(14.105)
104.165(14.105)86.721(14.105)
82.054(14.105)
99.054(14.105)
87.832(14.105)
65.165(14.105)49.828(14.216)
61.163(14.223)
26.496(14.223)
20.496(14.223)23.940(14.223)27.496(14.223)
6.496(14.223)3.051(14.223)
7.274(14.223)-10.060(14.223)-14.504(14.223)-1.726(14.223)-7.564(13.549)

71.583(10.043)82.805(10.043)87.805(10.043)103.028(10.043)
97.250(10.043)100.805(10.043)
91.250(10.043)
88.694(10.043)
71.361(10.043)
70.361(10.043)
77.472(10.043)
62.028(10.043)
57.028(10.043)
54.006(10.122)52.131(10.127)31.909(10.127)33.242(10.127)30.909(10.127)
30.576(10.127)
21.465(10.127)
15.687(10.127)
11.465(10.127)
10.020(10.127)2.687(10.127)7.020(10.127)
4.008(9.647)

11.828(7.053)21.495(7.053)22.383(7.053)23.717(7.053)23.828(7.053)31.050(7.053)24.717(7.053)16.828(7.053)16.050(7.053)18.606(7.053)29.050(7.053)18.939(7.053)14.939(7.053)1.994(7.108)15.469(7.112)
4.691(7.112)-2.198(7.112)-3.420(7.112)
1.025(7.112)-5.531(7.112)-4.309(7.112)
3.358(7.112)-15.531(7.112)-4.420(7.112)-2.642(7.112)-6.556(6.775)-0.585(3.868)-1.696(3.868)-4.363(3.868)-2.252(3.868)3.304(3.868)1.748(3.868)6.081(3.868)3.415(3.868)1.081(3.868)-2.919(3.868)-3.585(3.868)9.859(3.868)-2.919(3.868)-2.964(3.899)-4.096(3.901)-4.429(3.901)-5.318(3.901)
0.460(3.901)-1.651(3.901)-6.096(3.901)-3.985(3.901)-2.763(3.901)
0.126(3.901)-9.096(3.901)-5.207(3.901)-2.247(3.716)-2.771(2.068)-1.883(2.068)-2.771(2.068)-2.438(2.068)-4.771(2.068)-1.438(2.068)-2.549(2.068)-4.771(2.068)-1.771(2.068)-3.994(2.068)-3.883(2.068)-2.994(2.068)-3.883(2.068)-3.207(2.085)-2.341(2.086)-5.675(2.086)-5.230(2.086)-4.008(2.086)-2.452(2.086)-3.341(2.086)-4.341(2.086)-4.786(2.086)-4.675(2.086)-3.675(2.086)-0.897(2.086)-2.769(1.987)149.722(32.541)76.782(32.275)-7.302(23.169)-5.019(22.980)

20.250(16.272)
47.986(16.138)80.904(8.925)18.584(8.851)55.872(4.772)
15.231(4.733)

Constant-1,834.061-2,473.826-1,461.046
23.522
2,076.075(4,282.831)(3,049.381)(2,141.572)(1,174.587)(628.258)
R-squared
0.781
0.754
0.580
0.316
0.353
Notes: Estimated using n=483 weekly observations from the beginning of 2011 until the end of March 2020.
Standard errors in ( ). Coefficients from these equations are used to estimate expected deaths from April 2020
onwards.

Appendix C: Full Results of Regressions Relating Excess Mortality to Booster Rollout

Booster doses

Ordinary Least Squares
Bivariate
w/ controls

Distributed Lag Model
Bivariate
w/ controls

Instrumental Variables
Bivariate
w/ controls

15.593**(4.758)47.964(35.886)

53.813*(21.927)

Original doses
COVID-19 deaths
Constant

7.246(9.291)

12.124**(3.217)-5.920(3.570)14.058**(1.289)10.969(5.866)

Lagged variables
Boostert-1
Boostert-2
Boostert-3

0.241(6.579)-37.487(51.547)-100.350(67.151)
122.014*(49.569)-48.145(26.630)
23.427(22.153)
18.062(10.694)
3.676(23.409)-3.720(22.311)-8.082(13.375)
0.772(2.561)-10.666**(3.565)26.391*(10.629)32.141**(5.642)17.011**(3.419)-6.048(3.841)29.520**(9.582)0.863
48

Originalt-1
Originalt-2
Originalt-3
COVID-deathst-1
COVID-deathst-2
COVID-deathst-3
Long-run Impact
Booster doses
Original doses
COVID-19 deaths
R-squared
ObservationsFirst-stage F-test

0.140
51

0.744
51

23.667(14.438)2.078(16.168)
13.024**(2.184)8.864(8.746)0.634
48-12.057(7.322)15.515**(5.446)-4.897*(2.424)14.272**(2.213)7.482(5.656)0.391
51
15.8**

0.739
51
17.6**

Notes: Excess mortality, booster doses, and original doses are first differences of the series shown in Panel B of Figure 1.
Doses are in units of 100,000, deaths in units of ones. The long-run impact for the distributed lag model is the sum of thecontemporaneous and lagged terms. The instrumental variable is the available stock of vaccine doses. Heteroscedasticity
and autocorrelation consistent Newey-West standard errors in ( ); **, * denote statistical significance at 1% and 5% level.