Supply-side Effects of Pandemic Mortality: Insights from an Overlapping-generations Model

A.1. Mortality Rates

Let M R a , t U S be the mortality rate of individuals aged a in period t in the United States that is due to influenza. We measure the mortality rate as

where P o p u l a t i o n a , t U S is the U.S. civilian non-institutional population. The mortality rates in excess of normal yearly mortality due to influenza, which we use in the model simulations, are discussed below.

We focus on the civilian population because the Bureau of the Census reports deaths for the civilian population and the military population separately, with the latter subpopulation being much smaller and the information much less detailed. Moreover, the Great Influenza began as a large number of persons served in World War I; these persons faced mortality risk that arguably was not necessarily representative of the population. That said, many of those mobilized were young adults, a category that was hit severely by the disease.

There are a few methodological challenges in translating death and population data from the Bureau of the Census into mortality rate statistics. One challenge is that only a subset of states reported mortality statistics. As Table A.1 shows, the number of reporting areas grew steadily throughout the 1910s as new states joined the United States and as some existing states began to report data. Hawaii joined the United States as a territory in 1917 but the Bureau opted to report its deaths separately from those of other states “because of the distant location of Hawaii and the peculiar constitution of its population.”

Estimates of the size of the U.S. and reporting-area populations are subject to some uncertainty, especially during intercensal periods. The population estimates produced late in the 1910s were unusually uncertain because WWI led to significant movements of the population. For these reasons, and to ensure consistency across mortality and population sources, the population statistics reported in Table A.1 come from the report Mortality Statistics 1920, which includes information from the 1920 census. In contrast to population estimates, death counts and death causes are generally not revised from one report to the next, even after new census information is published. Mortality statistics are published for 5-year age bins starting with the bin “0–4 years” and ending with the bin “95–99 years.” The yearly reports also include statistics per years of age through age 4 years (to focus on early childhood mortality) and for 100 years and over. Our interpolation to a quarterly age frequency uses the most disaggregated information by age where possible.

In our analysis, we treat deaths from non-reporting states and Hawaii as missing at random—that is, we assume that the individuals in reporting and non-reporting areas face the same mortality risk. Accordingly, we approximate the population-wide mortality rates using those for reporting areas (which use “RA” superscripts):

Another complication is that we do not have population statistics by years of age in the reporting areas. We posit that the age composition in reporting areas is the same as for the overall U.S. population. Population counts by years of age are available for most age groups in the Bureau’s 2016 vintage of historical data. One exception is for people aged 75 years or more, which are aggregated into a single age category. As an alternative, we use the mid-year population estimates generated by our model; these estimates use population, life cycle, and migration information to populate all age periods and are consistent with the 2016 vintage. See the technical appendix to Gagnon, Johannsen, and López-Salido (Forthcoming) for our methodology. The 2016 historical total population estimates differ a little—by about 1% or less—from the 1922 total population estimates shown in Table A.1, in part because of small differences in the coverage of states and territories. We adjust the population estimates to account for these small differences. The imputed population by age in reporting areas is

As a check on the mortality rates, we can look at estimates produced by Davis and Mitchell (1920) in a special Bureau report on the death counts in the final four months of 1918 for Indiana, Kansas, and Philadelphia, PA. These estimates use unpublished population counts by age in these areas. The mortality rates for Philadelphia, at around 4% for young adults, were among the highest recorded at the time and thus cannot be assumed to be representative of the rates for the U.S. population. That said, the broader age pattern of mortality is consistent with our estimates for all reporting areas.

A.2. Excess mortality rates

Influenza is a cause of death each year; therefore, its typical effects are incorporated into life-cycle mortality tables. For this reason, our modeling work focuses on the excess mortality rate, which is the difference between the mortality rates registered during the pandemic and the counterfactual mortality rates that would have been registered if the pandemic had not happened. To obtain the latter counterfactual, we compute the average mortality rate by years of age in the five-year period that preceded the Great Influenza (that is, for the 1913–1917 period). We then calculate the excess mortality rates by age as

Because the death counts suggest that older generations enjoyed some protection from the virus strain that caused the Great Influenza, our excess mortality rate estimates for older generations are negative.

A final complication is that many deaths related to the Great Influenza are miscategorized. Although the yearly reports contain death counts specific to influenza, the Bureau of the Census warned, in its Mortality Statistics 1919 report, that “in studying the effects of the pandemic of influenza, it is not believed to be best to study separately influenza and the various forms of pneumonia, bronchitis, and the respiratory diseases, for doubtless many cases were returned as influenza when the deaths were caused by pneumonia, and vice versa. The best method, therefore, seems to be to study as one group deaths from influenza and pneumonia (all forms), disregarding deaths from the other respiratory diseases, which were comparatively few.” For this reason, we measure excess mortality due to the Great Influenza in terms of excess mortality in the categories “10: influenza,” “91: Bronchopneumonia,” and “92: Pneumonia (Lobarpneumonia and pneumonia (undefined)).”

In our implementation, we calculate excess mortality rates by age due to the Great Influenza separately for the years 1918, 1919, and 1920. We then calculate cumulative excess mortality rates during the Great Influenza epidemic by summing up the excess mortality rates for those three years, as if the virus had hit in a single wave. We make no adjustment for the fact that people had different ages during the three waves; doing so would have at most a tiny effect on the total death counts in proportion to the population and accompanying macroeconomic effects.