Our analysis finds it is optimal to increase the SICP stock over time to a steady state of $829 billion (assuming a 3% discount rate). The first panel of Fig. 2 presents the optimal investment response as a function of the background hazard rate (on the horizontal axis). The lower dashed horizontal line represents the current SICP level in the model, and the current background hazard rate is given by the dashed vertical line at 0.1 (together resulting in an initial hazard rate of 0.05). As the hazard rate is increasing over time, the investment response in the first panel of Fig. 2 can be interpreted as a plan that moves over time from left to right. The optimal strategy involves an immediate, large increase in SICP (vertical arrow) followed by moderate increases as the background hazard increases to a steady state of 0.4 (at the second dashed vertical line)—at which point the SICP stock remains constant at $829 billion (upper dashed horizontal line). The explicit time path is presented in the second panel of Fig. 2, where each unit of time represents one year.
The optimal strategy generates $10.4 trillion in social net benefits—again, the present value of expected economic gains from investment. On average, each dollar spent is expected to generate $12.55 in economic gains. The average expected gains are fairly consistent (e.g., in the range of $9–$15 in benefits per dollar of SICP capital) across a wide range of perturbations in the model's parameters relative to the baseline scenario presented above.
A sensitivity analysis, detailed in the SI, examines steady-state SICP outcomes and expected gains from investment when each model parameter is increased or decreased by 50%. We find that a 1% change in any given parameter generates less than a 1% change in the optimal steady-state SICP stock in all but one case (a healthcare benefits parameter), with most changes being less than 0.2%. The optimal paths to the new steady states in these cases are not substantially different from the baseline scenario unless the steady state has been significantly altered (the primary outliers here being healthcare benefits and SICP effectiveness parameters). We also find that a 1% change in any parameter generates less than a 0.11% change in expected net gains from investment, except for a 0.22% change associated with the healthcare benefits parameter. These small parameter impacts indicate our baseline model results are fairly robust.
Policymakers who fail to invest in public health are leaving substantial sums of money on the table. This is shown in Fig. 3. The horizontal axis indicates target steady-state SICP stocks, while the vertical axis represents the percentage gain in expected economic welfare relative to a benchmark scenario in which society simply holds SICP fixed at current levels.
The curve represents the relation between target stocks and the expected gains from optimal investment in SICP. For the socially optimal steady-state SICP stock of $829 billion, we assume an economically optimal investment strategy was used to obtain this steady state. This target stock yields maximum economic gains, expressed in Fig. 3 as an 87.8% gain in welfare relative to the benchmark scenario (holding the current stock constant). For each alternative (smaller) SICP target, calculating economic gains requires calculating economic values both along a particular path to the target and at the target. We assume society follows the welfare-maximizing strategy until the alternative target is reached, thereafter maintaining this target value into perpetuity. This assumption means any reductions in welfare gains, relative to the socially optimal strategy, stem from stopping prematurely at the wrong target. Welfare gains would be further reduced if, as might be expected, society instead pursued a sub-optimal path to the sub-optimal target. Accordingly, we view the welfare gains presented in Fig. 3 as conservative (high) relative to what might be expected in practice. No economic gains occur where the curve crosses the horizontal axis; this is the baseline scenario in which the target stock equals the current SICP stock.
Figure 3 illustrates that society stands to generate large gains from relatively small increases in the current SICP level. As investment levels continue to increase, the additional gains become smaller although they may still be quite large in absolute terms. For instance, optimal economic gains are only 3.3% larger than those arising the initially proposed American Jobs Plan investments (with $595 billion steady-state SICP), but this roughly translates to a $330 billion gain in expected cost savings. Finally, note that Fig. 3 is qualitatively similar across various assumptions about extant annual investments and damage costs, which were used to calibrate the model. Likewise, the quantitative results here related to the 20% reductions in SICP are also similar across the same assumptions about extant annual investments and damage costs.
Within the optimal investment pattern, SICP levels are chosen to ensure that the marginal rate of return to investing in SICP always equals the depreciation-adjusted social opportunity cost of capital (i.e., the discount rate, reflecting the rate of return from alternative capital investments in the economy, plus the SICP depreciation rate). Our framework is one of joint production in the sense that the single SICP capital stock jointly produces three types of benefits: general healthcare, self-protection, and self-insurance. As such, the overall rate of return generated by the stock of SICP can be examined as a portfolio of three returns, one for each type of benefit that SICP produces. Our notion of a portfolio here differs from standard notions where multiple, distinct investments are made to each generate a rate of return that contributes to an overall return. Here, we have a single investment that simultaneously generates three returns that cannot be tailored individually. The collective return determines the optimal level of SICP investment, but the individual components give insight into which effects are driving the last units of investment.
The first rate of return is a risk-free rate of return due to increased general healthcare capacity that can be broadly used prior to a pandemic. This return does not explicitly reflect pandemic risks, although it does change over time based on overall investment responses made, at least in part, due to outside forces that drive changes in the background hazard rate.
The second is a rate of return from self-protection that reduces the likelihood of a pandemic. Finally, there is a rate of return to self-insurance that reduces the costs associated with any pandemic that does occur. The risk-related returns also depend on the background hazard rate as well as society's risk responses in the form of SICP investments. Each of the risk-related returns provides incentives to expand the stock beyond that needed for general medical care and sufficient to be prepared for a pandemic. The degree to which SICP contributes to each effect can be inferred by examining the portfolio of returns.
The three rates of return are presented in Fig. 4 for different values of background hazard rates, assuming SICP investments are made optimally at each of these background rates. An optimal strategy requires the three rates to always sum to the depreciation-adjusted required rate of return (8% in our analysis: 3% discount rate plus 5% depreciation rate). We find that the risk-free rate of return is positive and small and slowly declines as the background hazard rises. With zero background hazard, the value equals the depreciation-adjusted required rate of return, 0.08. Larger background hazard rates incentivize overinvestment in SICP for the purpose of just general healthcare, reducing the risk-free rate of return slightly.
The self-insurance rate of return is zero when there is no background hazard and jumps to about 2.25% with the first nonzero units of background hazard. The self-insurance rate of return declines relatively faster than the risk-free rate of return as the background hazard is increased. This indicates an overinvestment in SICP for the purpose of just reducing the costs of pandemics that do occur.
Finally, the self-protection rate of return is also zero when there is no background hazard, but is positive and increasing as the background hazard increases. For most hazard rates, this rate of return exceeds the discount rate. This result means that self-protection, i.e., trying to prevent a pandemic, is the driving force of our investment pattern. The relative importance of self-protection increases when either the future is valued less (higher discount rate) or SICP capital depreciates quicker (higher depreciation rate), and increasingly so for increases in the depreciation rate. That prevention is a higher priority than mitigating pandemic costs is consistent with prior work suggesting that prevention of environmental risks is generally a better investment than investments made to mitigate economic damages associated with adverse events. We find this priority on prevention while adopting risk-averse behavior contrasts with Finnoff et al. (2007), who show the necessity of risk neutrality for prioritizing prevention (in cases where the time horizon is not uncertain, so that preferences are set a priori, prior to optimization, in contrast to the present problem).
A more complex model might consider additional types of capital stocks that are each specific to one type of benefit, in which case the portfolio of returns could be more tailored. Our results here suggest that, in such cases, we might expect a greater focus on prevention-specific capital when that is available.
The analysis above is based on a calibrated relation between current estimated SICP investments and associated economic damages from COVID-19. It is generally common knowledge that capital stocks were used inefficiently, reducing the effectiveness of both self-prevention and self-insurance activities, likely due to inefficient Federal and State oversight. We now perform an additional sensitivity analysis to examine the effects of using SICP more effectively in each of these areas. In each case, we assume the baseline results based on historical trends reflect the current, less-effective management reflected in the calibrated model.
First, suppose that, under the optimal strategy, SICP is utilized in such a fashion to be twice as effective in reducing the variable component of economic damages to provide self-insurance. We find the optimal steady-state SICP stock in this case is $744 billion, which is a 10.3% decline: less capital is required if it is used more effectively, although the reduction is comparatively small relative to the effects on damages. The expected economic gains in this case are $10.58 trillion, which is a 2 percent gain relative to the optimum when capital is used less effectively.
Now suppose that, under the optimal strategy, SICP is utilized to be twice as effective in reducing the hazard rate to provide self-protection. We find the optimal steady-state SICP stock in this case is $530.9 billion, which is a 35.9% decline: significantly less capital is required if it is used more effectively. The expected economic gains in this case are $11.2 trillion, which is a 7.7% gain relative to the optimum when capital is used less effectively. These results are consistent with our prior rate of return results: larger gains come from improving the effectiveness of self-protection.