VoxEU Column COVID-19

The pandemic endgame

Infection externalities are a key feature of the Covid-19 pandemic, as individuals fail to account for the full consequences of their actions. This column develops a model of infection dynamics and economic choices and studies the resulting optimal policy outcomes. Under a scenario of the pandemic ending deterministically following an effective vaccination campaign, the model suggests that countries whose vaccination campaigns are proceeding quickly should impose a strict lockdown, while countries whose campaigns will not be completed within a few months should not impose a lockdown at all. In contrast, if the appearance of a cure is more ‘stochastic' – for example, if the virus mutates further or the vaccines turn out to be less effective than hoped – optimal policy calls for alternating between lockdowns and ‘inverse lockdowns’, with the latter stimulating social interaction.

A quickly growing literature on the nexus between epidemiology and economics emphasises the prevalence of infection externalities in the Covid-19 pandemic. Although individuals tend to respond with caution to the spread of the virus, they fail to fully internalise the consequences of their actions. The efficient response to the pandemic therefore requires corrective government intervention (e.g. Eichenbaum et al. 2020).1 

So far there is much less agreement on the magnitude of these externalities, their evolution over time, or specific policy recommendations.2 We still lack a transparent framework that unmasks the most basic interrelations and connects them to robust policy implications. This holds especially true with respect to the later stage of the pandemic, which we will hopefully experience soon. How should policymakers play the pandemic endgame?

A transparent and flexible framework

In a recent paper (Gonzalez-Eiras and Niepelt 2020b), we develop a transparent and flexible model of infection dynamics and economic choices that provides some answers. Unlike most contributions to the literature, the model’s epidemiological block is reduced to capture the essence of infection dynamics which we represent with a single endogenous state variable.  This renders the model much easier to analyse, allowing us to embed numerous economic elements and their consequences for policy.

Two findings concern the pandemic endgame. First, when the pandemic ends deterministically – for instance, following an effective vaccination campaign – then policy can markedly differ across countries with different end dates but otherwise identical fundamentals. Second, government interventions might stimulate rather than curb social interaction. We discuss these findings in turn.

Sharp policy discontinuities

Consider first a scenario where the pandemic ends deterministically, for example following vaccination campaigns as they currently get underway in many countries. The model implies that in such a scenario (and holding everything else constant), countries like Israel, whose vaccination campaign is proceeding quickly, should impose a strict lockdown. Other countries whose campaigns do not hold the promise of being finished within a few months’ time should not impose a lockdown at all.

Underlying this striking difference is an optimal policy discontinuity. The further in the future the pandemic’s anticipated end date lies, the stronger social distancing measures would have to be to keep infections in check until the end date arrives. But when that date exceeds a critical value, then keeping infections in check becomes costlier than simply ‘giving up’ or letting the pandemic run its course.

This is particularly relevant for poorer countries. Despite the work by international (donor) organisations, inoculation campaigns in developing countries are unlikely to keep up with those in richer ones. We should therefore expect fewer lockdowns in poorer countries.4

Inverse lockdowns

A sceptic might caution against the view that the pandemic policy environment is deterministic. After all, the virus might further mutate, a completely new strain might appear, the vaccines could turn out to be less effective than hoped, or other difficulties might arise. A more robust approach to managing the pandemic thus envisions the stochastic appearance of a cure – whatever it eventually might be. This is also the approach that most models of optimal policy in a pandemic adopt.

In such a stochastic environment, our analysis yields another surprising finding. Under the optimal policy, a lockdown or similar measures to foster social distancing are followed by their opposite, namely, policies to stimulate activity and promote interaction. In other words, lockdowns are followed by ‘inverse lockdowns’. This reversal result is quite general and follows directly from the presence of ‘dynamic externalities’ – i.e. the fact that individuals do not internalise the effects of their actions on aggregate infection dynamics.

Early on in an epidemic, dynamic externalities are negative as infections push society closer to the pandemic nadir with high costs due to both peak infections and measures to contain them. The optimal policy response thus amounts to slowing infections down. But later in time, the dynamic externalities turn positive. As individuals themselves adopt social distancing measures to avoid the private costs of catching the disease, they disregard the fact that society must undergo a minimum number of infections for the epidemic to come to a halt. At this point, infections exert a positive dynamic externality. When it is sufficiently strong (which is always the case in our analyses, eventually), the optimal policy amounts to an inverse lockdown.

Policy discussions and initiatives on temporary sales tax reductions, employment subsidies, or ‘back-to-work’ bonuses might have been a prelude to broader inverse lockdowns. In fact, our analysis suggests that inverse lockdowns constitute a key policy instrument. Calibrated to match features of the Covid-19 pandemic, our model implies that the welfare gains from optimal policy are substantial – in the order of 5% of life-time consumption – except if inverse lockdowns are not feasible.  In that case the optimal (constrained) policy barely improves welfare relative to laissez faire.


Our analysis considers many other scenarios and identifies additional robust implications. As far as the pandemic endgame is concerned, it leaves policymakers with one key question: Will the pandemic end sooner rather than later? If the answer is yes, strict social distancing is likely to be optimal. Otherwise, it is not and, eventually, inverse lockdowns might constitute the instrument of choice.


Eichenbaum, M S, S Rebelo and M Trabandt (2020), “The macroeconomics of epidemics”, NBER Working Paper 26882.

Gonzalez-Eiras, M and D Niepelt (2020a), “Tractable epidemiological models for economic analysis”, CEPR Discussion Paper 14791.

Gonzalez-Eiras, M and D Niepelt (2020b), “Optimally Controlling an Epidemic”, CEPR Discussion Paper 15541.

Kermack, W O and A G McKendrick (1927), “A contribution to the mathematical theory of epidemics”, Proceedings of the Royal Society, Series A 115(772): 700–721.


1 Eichenbaum et al. (2020) were among the first in the recent wave of work starting in March 2020 who showed that privately optimal behavioural responses, while slowing down infections, are far from sufficient to replicate the optimal societal response. Many other papers, often published in CEPR’s Covid Economics, have since made a similar case.

2 This also reflects an abundance of modelling approaches, based on different assumptions and with different foci, each with its specific advantages.

3 See also Gonzalez-Eiras and Niepelt (2020a). The epidemiological model due to Kermack and McKendrick (1927), which most other theoretical analyses build upon, features two endogenous state variables.

4 This also holds true for other reasons.

5 Our baseline model and a battery of robustness checks and extensions always imply optimal lockdowns in the early phase of the pandemic, for three to four months, with activity reductions by 25% to 40%.

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