Lally’s paper on a cost-benefit analysis of Covid vaccine “mandates”

Earlier in the week I did a post that included economist (and former Victoria University academic) Martin Lally’s sketch outline of an approach to thinking about applying cost-benefit analysis techniques to Covid vaccine “mandates”. In that post I included a few suggestions, questions, and thoughts on aspects of Lally’s note and the wider issue of coercion in a Covid context.

Since then, Lally has extended his note into a fuller short paper. I offered to make it more widely available here


Here is his Abstract


Covid-19 vaccine mandates for the general population must trade off the rights of those who object to being vaccinated against the costs that the unvaccinated impose upon the vaccinated, most particularly the increased risk to vaccinated people of death by covid-19.  This paper provides a methodology for doing so.  It is then applied to the case of New Zealand.  It reveals that even if the adverse impact of penalties on vaccine objectors (at least some of whom may have rational grounds for objecting) is as small as a reduction in their quality of life of 1% per year for a period of five years and the existence of unvaccinated people is entirely responsible for covid-19 infections amongst the vaccinated, the number of additional deaths amongst the vaccinated resulting from not adopting a vaccine mandate is too few to justify a policy of mandating.  However, unlike the general population, health workers come into frequent and close contact with large numbers of sick people, who are prime targets for covid-19, and therefore the vaccine mandate may be justified for these workers.

The paper largely speaks for itself. Lally lays out his assumptions (and sources) quite clearly, so anyone who disagrees can identify where (specifically) their disagreement arises and what alternative assumptions/approaches they would use.. As per the Abstract, he concludes that cost-benefit analysis does not support vaccine “mandates” in general, but one of the extensions of the earlier note is to explore the specific case of health care workers where his numbers suggest a cost-benefit analysis for compulsion may stack up. There is also a section at the end exploring the risks and incentives facing the young and the old faced with the offer of the vaccine.

To me, the most interesting part of the paper was his attempt to estimate how many lives (among the vaccinated) would need to be saved by coercing part of the population to be vaccinated to make such a policy pass a cost-benefit assessment. On his numbers (you can read the reasoning in the paper)

So, vaccine mandating would be warranted only if failure to do so leads to a pool of unvaccinated people who thereby induce at least 5,200 additional deaths from covid-19 amongst the vaccinated. 

And how likely is that?

I now consider whether at least 5,200 additional such deaths amongst the vaccinated could occur.  The worst case scenario for the 90% of the over 12s who vaccinate without mandating (4.2m*0.9 = 3.8m) is that they are all infected as a result of the existence of the unvaccinated people who might be induced into vaccinating.  In the absence of an effective vaccine, the proportion dying is the Infection Fatality Rate (IFR).  Recent surveys suggest figures of 0.3 – 0.4% for Europe and the Americas (Ioannidis, 2021, page 10), and 0.70% for Europe and 0.58% for the Americas (Meyerowitz-Katz and Merone, 2021, Figure 2).  The midpoint is about 0.5%, which implies 3.8m*0.005 = 19,000 dead.  However, this IFR relates to the entire population rather than only those over 12, and the latter IFR would be higher because the IFR is monotonically increasing with age.  Correction for this raises the IFR for the over 12s to about 0.60%.[1]  This implies 3.8m*0.006 = 23,000.  The vaccines reduce the risk of death by 85% to 88% on average over the first six months but rapidly wanes beyond that point (Nordstrom et al, 2021, Table 2 and Table 5).  If a booster is used at that point, the average reduction in the death rate would then be at least 85%.  This implies 23,000*(1 – 0.85) = 3,400 deaths amongst the vaccinated. 

This is the worst case.  It is inconceivable that all of the 3.8m vaccinated would be infected.  Amongst those infected, it is inconceivable that all would be infected as a result of the pool of unvaccinated people, i.e., some of the vaccinated would be infected even if there were no unvaccinated people because the vaccine does not eliminate the risk of its recipients transmitting the virus and therefore vaccinated people could be infected by other vaccinated people.  In fact, all of the vaccinated might become infected even if the unvaccinated pool did not exist, through the virus transmitting through the vaccinated.  Amongst those vaccinated who were infected as a result of the unvaccinated pool, some would be infected as a result of the vaccine objectors who will not succumb to the penalties, and a mandating policy cannot eliminate this group.  Taking account of all three of these points, the additional covid-19 deaths amongst the vaccinated in the absence of vaccine mandating would be significantly less than 3,400.

[1] Steyn et al (2021, page 14) cites age-related IFR data from Verity et al (2020, Table 1) and matches it to the New Zealand population proportions by age groups, which implies an IFR of 0.95%.  The same data can be used to estimate the IFR for the 12+ group, at 1.13%.  Both figures are unreliable because they are based upon IFR data from March 2020 from only one paper (Verity et al, 2020) rather than from recent surveys of the literature (as with Ioannidis, 2021 and Meyerowitz-Katz and Merone, 2021).  However, the increase of 19% (0.95% to 1.13%) can be applied to the preferred IFR estimate for the entire population of 0.5%, to yield 0.6% for the 12+ group.

It is quite simple, but illuminating, reasoning.

My point in running this post, and hosting Lally’s paper, is not to endorse all his reasoning or his conclusions. But it seemed like an interesting attempt to look at the issues rigorously – in a way that there is no sign officials and ministers have – which deserved to be available to a wider audience.

24 thoughts on “Lally’s paper on a cost-benefit analysis of Covid vaccine “mandates”

  1. Michael, thanks for posting this.

    I am particularly interested in the risk / reward for vaccination by age group that was generated by Martin perhaps as an afterthought. While vaccination makes sense for the 80 year old, the author clearly indicates that there is little benefit in being vaccinated for the 20 year old, given their covid-19 risk profile showing the likelihood of death being one in 500,000.

    Interestingly, Medsafe data shows that there is a serious vaccine injury, ie blood clotting, strokes, heart attacks etc, for approximately one in every 5,600 vaccination events.

    Furthermore, the risk of death following vaccination, again according to Medsafe is approximately one in 67,500. However this data is reported by age, and is only one in about one in 2.3m for a 20 year old.

    Medsafe will have the age based data for serious vaccine injury but have chosen not to publish it.

    What I would love to see Martin produce is a risk / reward analysis of age related death from vaccination vs covid infection, and also one relating to serious injury from vaccination. Two things come to mind, the first is this would produce an age at which everyone younger has little to no benefit resulting from vaccination, and everyone older would potentially benefit, albeit for a period measured in months after which time a booster shot is required.

    Having a booster shot exposes the vaccinated person to the risk of death and injury following vaccination all over again. I wonder how many booster shots it would take to seriously reduce the risk reward profile of vaccination to the extent that even older people would be better off without it.

    The second thought is that voluntary adverse event reporting systems like the one operated by Medsafe are notorious for under reporting. Some suggestions are that as few as 10% – 20% of adverse events are ever reported. What difference would factoring in say a 25% or a 50% under reporting profile make to the results?

    It would require an OIA request to obtain vaccine injury by age data, but the resulting risk / reward / by age report would make very interesting reading indeed.

    Liked by 1 person

    • Brendan, that thought entered my mind soon after generating the results that I did, and it is on my “To Do” list. Nevertheless, the risks to a healthy 20 year old from being vaccinated are likely very very low just as the benefits are, so the principal purpose in such a person being vaccinated is as a gift to those among their fellow citizens who are at much higher risk of death from covid (in the form of the 20 year old being less likely to act as a transmitter of the virus if vaccinated). I note this point in the paper. One can understand why public health authorities are not telling us this, Martin

      Liked by 1 person

      • Hi Martin, I look forward to seeing your paper.

        Just to pick up on your comment “the 20 year old being less likely to act as a transmitter of the virus if vaccinated” This appears to be a popular myth promulgated by the MSM in order to promote vaccination uptake through guilt as well as fear.

        The respected medical journal Lancet states that: “fully vaccinated individuals with breakthrough infections have peak viral load similar to unvaccinated cases and can efficiently transmit infection in household settings, including to fully vaccinated contacts.”

        I’m very concerned that as the virus spreads in New Zealand, we run the risk of the unvaccinated being unjustifiably scapegoated. If we are being honest about the data, vaccination provides limited personal protection from hospitalisation and death for a period measured in months, but limited to no protection from infection, viral load and subsequent transmission.

        Liked by 1 person

      • Brendan, the Lancet seems to be equating (in virus transmission terms) fully vaccinated people that have “breakthrough infections” with unvaccinated people that have “breakthrough infections”. However, a fully vaccinated person is presumably much less likely to be in this category than an unvaccinated person, and hence the possible social benefit from people getting vaccinated, Martin


      • Hi Martin

        I don’t know why you would presume a fully vaccinated person is less likely to contract the virus, given what we now know about infection rates in highly vaccinated countries.

        The UK Government have taken their responsibility to perform careful monitoring of the vaccine’s effectiveness seriously. Their recent week 42 report linked below shows that for those aged between 30 and 80 years, per 100,000 of the population, the double vaccinated are up to twice as likely to be infected with Covid-19 than the unvaccinated. Page 13, table 2.

        Click to access Vaccine-surveillance-report-week-42.pdf

        There is the usual disclaimer about the reliability of the information underneath the table, but if this data is substantially correct then in the months to come, everyone will be most at risk of infection from the double vaccinated, not the unvaccinated.

        There is a lot we don’t know about the medium to long term effects of this mRNA vaccine on the immune system. Now it appears that the FDA have asked a Federal judge to make the public wait until the year 2076 to disclose all of the data and information it relied upon to license Pfizer’s COVID-19 vaccine.

        Happy days.

        Liked by 1 person

    • This is flat out misinformation in that it claims the adverse reports are caused by the vaccine when almost all of them are not. It’s curious, Michael, that you choose not to point that out.


      • I don’t generally read any anti-vax stuff, but I also don’t censor commenters unless they are vulgar, blasphemous or personally insulting to other comnenters etc.

        But, as I say, any specific issues with Martin’s paper? Serious question. I thought his first go round overstated the costs, and he responded to that observation by using what seems to me more plausible numbers in the fuller paper.


      • Dear Judge Holden, the blame for ‘misinformation’ relating to adverse event reporting appears to lie with Medsafe, whose most recent report states there have been 1,290 serious adverse events following vaccination. That is approximately one serious adverse event including stroke, heart attack and blood clots for every 5,500 injections.

        Perhaps you should take up your concerns with them?


      • An adverse event following vaccination is not an adverse event caused by vaccination, which is what anti vax misinformation paddlers claim. It’s simple Brendan.


  2. Without reading Martin’s paper, it appears from your summary to assume a high rate of voluntary vaccination in deriving a low marginal benefit from mandating. But if everyone believed the risk of death or serious debilitation were low there would be far less voluntary vaccination and, consequentially, higher rates of death and illness among the larger unvaccinated population.

    In addition, even if one agrees mandating vaccines is unjustified, should we allow discrimination against unvaccinated people because they are a much greater threat to vaccinated people, both directly and indirectly through their excess consumption of health services?


    • On the first point, Martin (reasonably enough) treats illness/death among the unvaccinated as irrelevant to this calculation, since they have presumably concluded that the expected value of the risk is less to them than the “cost” of being vaccinated. The unvaccinated become relevant only to the extent treating them crowds out medical care for others (but if I recall, Martin notes the possibility of deprioritising the unvaccinated in the allocation of Covid medical care).

      Can’t speak for Martin, but I suspect he would not outlaw private discrimination, but might have problems with the govt compelling discrimination. Personally, as someone who is vaccinated I’m quite unbothered by who I mix with, as I assume (a) most people will eventually get the virus, and (b) as a reasonably healthy vaccinated person the expected downside of getting it is quite low. There are of course some who are more vulnerable.

      Liked by 1 person

    • We achieved a high level of vaccination before mandates were even announced, so we got to a high point voluntarily. As for discrimination against the unvaccinated for the reasons you give, my paper concludes that those costs that the unvaccinated inflict on the vaccinated are too small relative to any reasonable allowance for the adverse effect of the discrimination on the unvaccinated. It is also worth noting that the biggest example of avoidable excess consumption of public health services comes from people who ingest the wrong things or the right things to excess, Martin

      (MHR: Martin suggested I make it clear that this reply was to Lefthander’s comment, and not to my reply that appears immediately above).


      • There is clear evidence that it is actually the unvaccinated who are at risk from the vaccinated. Presumably if you are vaccinated you are protected? If not, what is the point? Many of the vaccinated will be assuming they are bulletproof and will act accordingly. There is every reason to believe they will be the superspreaders of covid in the months to come. The unvaccinated will be used as a convenient scapegoats by those in charge and those who don’t understand how this virus works.
        This is a massive experiment. This new technology was never properly tested or approved. No matter what Medsafe say. So much about the testing was dodgy it’s hard to know where to begin. Medsafe accepted the data from Pfizer at face value, probably the most corrupt corporation on the planet.
        I would ask you to have a read of this analysis regarding the pending booster shots coming our way in a few months.


      • Rob, even the proponents of vaccines do not assert that they are 100% effective; Prof Hendy and his team use an effectiveness figure of 94% and I used the more conservative figure of 85% in my analysis. So, the unvaccinated increase the risk to the vaccinated. Thus, there is a trade-off between the right to say no to the vaccine and the risk the unvaccinated pose. However, as you say, it is a massive experiment. My reading of the history of pharmaceuticals is that they have usually been beneficial but there have been failures, and thalidomide is a striking example, Martin


  3. Dear Michael

    Hello from the UK. A very interesting discussion. However, the matter is simpler.

    Vaccines are completely pointless and always have been. These are my reasons.

    Covid 19 it is the ‘flu, the internal toxicosis of the body, partly due to metabolism of food and partly due to the many poisons in our environment which can and do enter our bodies in the air, food and water.

    Covid 19 was renamed last year by way of re-branding to sell more drugs that big pharma make.
    I used to think that vaccines were of some use until, at 60 years of age last year, I researched properly. I changed my mind.

    No vaccine ever has been of use, it was only made to appear so by advertising incessantly that they were of some use in preventing a specific illness or limiting the extent of that illness.

    Whether a vaccine causes harm or sometimes death depends on the toxicity of the vaccine and the immune status of the individual. And of course vaccines have caused a lot of harm and sometimes deaths over the decades.

    And I have had my fair share of vaccines, certainly polio, tetanus and a BCG. The last mentioned may well have been the cause of what was diagnosed as measles when I was 15 years old.

    I put the following link on my website if you or anyone is interested. Please note I do use humour to lighten the mood and to help make the points.

    This has a link at the bottom to my Covid 19 Summary and the other issues including who is behind it all.

    Kind regards

    Baldmichael Theresoluteprotector’sson

    Please excuse the nom-de-plume, this is as much for fun as a riddle for people to solve if they wish.


    • Michael, are you comfortable with the copious amount of anti vax misinformation your readers appear to subscribe to? This is just the most egregious example, which you either tolerate or outright endorse.

      Martin’s “analysis ” is a superb example of nonsense CBA. Plug in any numbers you like in to get the result you want, and it all sounds so coolly rational. Laughable.


      • As I’ve noted repeatedly I’m keen as many people as possible are vaccinated. But favouring vaccination and imposing punitive regimes on those who choose not to be, or who refuse to show govt papers to go about normal life, is quite another matter.

        On Martin’s analysis, he lays out his assumptions etc clearly. Where specifically do you disagree? The point of cost- benefit analysis isn’t usually to get a right answer, but to impose some discipline on setting down assumptions and understanding sensitivities.


      • Martin sets out to demonstrate his already fixed view that mandating is poor policy and so his analysis is tainted. He overcounts the objectors, overstates the costs (although to be fair to him, he just makes these up), ignores the positive effects of the mandate in improving vaccination rates and therefore doesn’t allow for the positive effects on the health system created by reduced crowding out, deaths and illness. It’s as bad if not worse than his attempt to demonstrate proof for his concluded view that the first lockdown didn’t stack up. It looks like objective analysis, but it’s the opposite.


      • I’ll leave Martin to engage on the substance if he wants, but whatever his priors the point on the exercise was (i presume) to identify specific assumptions, incl authorities where possible. He seems to have done that, and if you have specific areas of disagreement – and it seems you may – perhaps you might elaborate those.


      • Michael, I concur with your comments. My paper provides a framework for analysing the costs and benefits of vaccine mandates. The parameter values used are debatable. If anyone disagrees with the parameter estimates, I invite them to offer their estimates (along with an explanation as to how they reached those estimates), and then insert them into the model to see if the conclusion changes. Alternatively or in addition, they might disagree with the framework, in which case they should present their framework, insert their parameter estimates into it, and then present the conclusion, Martin


      • Ok. It’s likely that there is a net positive qaly impact on the vaccine hesitant from mandating as most of them will become vaccinated as a consequence and reap the health rewards (both real and psychological). The only unknown is the extent of the upside for the already vaccinated population, which is likely to be significant for the reasons outlined my me above. Primarily, access to public health services will be maintained as the system is unlikely to be overwhelmed by unvaccinated COVID sufferers.


      • Dear Judge

        Thank you for your reply. However, your comment is very silly. You have not specified what anti-vax misinformation you are referring to.

        If you could kindly supply me with what you consider to be misinformation then I can come back to you.

        Kind regards



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