• No results found

C: the heterogeneous nonrational model with a lockdown

VIII. Conclusions

Second, the government’s containment policy forces agents to cut back consumption to at most 86.9% of pre-epidemic consumption at the pandemic’s peak. Three factors determine the strictness of this policy. First, the lockdown’s strictness follows the number of infected agents in the economy but with a decreasing marginal effect. Furthermore, as the number of susceptible agents decreases, the optimal lockdown strictness increases. This relationship results from a negative externality of the number of susceptible agents on social welfare. Finally, as the end of the pandemic comes closer, the optimal lockdown becomes less strict since the foregone utility of dying to the virus becomes smaller over time.

Third, by forcing agents to cut back economic activity, the containment policy leads to a slower propagation of the virus. As a result, the infection peak is later and lower, fewer agents recover from the virus at the end of the pandemic, and fewer agents die. In the simulations, a lockdown saves the lives of four thousand Dutch citizens. Though, instead of a 2.2% aggregate consumption loss in the first year of the pandemic without intervention, aggregate consumption is 10.2% lower in the first year of the pandemic.

Fourth, the young cut back consumption by 3.75% at the pandemic’s peak with no lockdown and the old by 5.45%. With a lockdown, both cut back consumption by 15.35% at the pandemic’s peak.

Furthermore, the number of deceased agents decreases in all age groups but the youngest. The difference is largest in the oldest group. Moreover, during the pandemic, the young lose utility because of the lockdown while the old gain utility. The utility loss of the young is slim and temporary, but the utility gain of the old is slim and permanent.

So, do the young have a point? Even taking long COVID into account, my findings indicate that they are the losers of the lockdown. Other research projects, e.g., Acemoglu et al. (2020) who look into age-targeted policies, propose Pareto efficient containment policies. Further research may investigate optimal Pareto efficient containment policies in the context of long COVID.

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Appendix A

This appendix contains the technical details of the simulations. The code is written in Python and is available online3. The code runs the model for 14483 agents for 120 periods. I set both as high as possible while keeping the run time of the model manageable. I chose 14483 because the Dutch population counted 14483 thousand citizens aged sixteen and above in 2019, before the pandemic.

Furthermore, I chose to run the model for 120 weeks to ensure that the number of infected agents reaches zero by the end of the simulation.

Because of the stochastic nature of population health dynamics, randomness influences the results. Therefore, the code runs the model multiple times. Specifically, it runs the homogeneous nonrational model twelve times and the heterogeneous nonrational model eight times to keep the total run time manageable. After running the model twelve or eight times, the code takes averages of all variables. The figures found in section six present these averages.

Furthermore, Figure 12 is based on code added to the model later than the rest of the model.

Because of time constraints, Figure 12 is based on a simulation with dynamics similar to the main simulation but uses only five runs of the model.

Finally, the results in section seven are based on three runs of the model.

Appendix B

This appendix elaborates on the results in Eichenbaum et al. (2020) regarding aggregate labor dynamics in the perfect foresight model.

As explained in section three, the perfect foresight model, the homogeneous nonrational model, and the heterogeneous nonrational model underestimate aggregate labor since infected agents - and agents with long COVID in the heterogeneous nonrational model - maintain the pre-epidemic amount of labor hours but consume less than before the pandemic owing to their decreased productivity. As a result, aggregate hours fall less than aggregate consumption. The results Eichenbaum et al. (2020) present in their paper regarding the perfect foresight model indicate that aggregate labor dynamics are identical to aggregate consumption dynamics, however.

Figure 19 presents the aggregate consumption and aggregate labor panels Eichenbaum et al.

(2020) present in Figure 1 of their paper.

Figure 20 presents consumption and labor by type, which Eichenbaum et al. (2020) present in Figure 2 of their paper.

The red lines in Figure 19 show that aggregate labor dynamics are identical to aggregate consumption dynamics. The black lines and the red lines in Figure 20 show that consumption and labor dynamics are identical for recovered and susceptible agents. The blue lines show that infected agents consume less than recovered agents but work as many hours. As a result, the decline in aggregate hours must be smaller than the decline in aggregate consumption. Hence, Figures 19 and 20 are inconsistent.

Figure 19: Aggregate consumption and labor in the perfect foresight model, according to Eichenbaum et al.

(2020).

Figure 20: Consumption and labor by type in the perfect foresight model.

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