War, famine, pestilence and their economic costs

Апофеоз войны (“The Apotheosis of War“), Vasily Vereshchagin (1871)

Most people are undoubtedly thinking about both the (huge) potential loss of human life and the (huge) semi-related economic loss associated with the recent COVID-19 pandemic.  Indeed, debate around COVID-19 health and economic policy both suggests the human and economic costs are inextricably intertwined, and that it is perhaps not possible to adequately solve the economic problems without also solving the health problems.  Sadly, the world is now well into the 3rd month of a pandemic caused by a virus from the coronavirus family that has been causing very similar pandemics for over 120 years; particularly, the Spanish Flu Pandemic of 1918-1920, which spread to most all parts of the world.  And yet, despite having over 100 years of experience with coronavirus pandemics, we still don’t quite know what to do … or so it seems.

But a review of the last 120 years of history also suggests that it is not only pestilence that afflicts humanity; war and famine are arguably as horrific as disease in their effects on human life and economy … and it can be shown that war, famine, and pestilence are intertwined.  All this suggests—at least to an economist—that we need to understand the effects of war, famine, and pestilence on both the human population and the economy; not only in a general qualitative sense, but also in a concrete quantitative sense. Why? Because our economic decisions ultimately influence life and health, and our healthcare decisions ultimately influence our economy; health and economy are reflexive; we can’t separate the decisions … which makes them both essentially moral and ethical decisions.

This article presents several econometric models that allow us to make estimates of, and inferences about, the (minimum) effects of war, famine, and pestilence on both the global economy and global population; as well as an estimate of the minimum total economic cost of war, famine, and pestilence over about the last 120 years. This is not exactly an easy task and I make no particular claims about the accuracy of such estimates other than to say that–to the best of my knowledge and belief–the econometric models were not developed in a biased or misleading way; i.e., I have not made any significant assumptions that I’ve not disclosed in this article. But I do think it’s important to disclose that my personal belief is that–as many with think as they read this article–the actual cost vastly exceeds the estimate developed here … and that is a basic point of the article: Both the human and economic costs of war, famine, and pestilence are huge by any standard … and we should strive mightily to avoid them. Please read on!

1. Population and economic output are closely related

It is always important to start with a theory of causal relationships when developing econometric models and estimates. In the context of the economic costs of war, famine, and pestilence, a natural place to start is the relationship between total economic output–most commonly measured as gross domestic product (GDP)–and total human population. The basic idea here is that humans produce the goods and services they consume; and, except for the production of goods that can be stored (e.g., certain agricultural products like grains) or are long-lived capital goods (e.g., airplanes, industrial equipment, infrastructure and buildings), economic output is consumed near the time it is produced. Because humans require basic food, clothing, and shelter to survive, and–in the longer term–many other products to thrive, this implies a close causal relationship between the existence of humans and their economic outputs.

Indeed, the relationship is quite clear as seen in the following graph of the the (linear-in-logarithms) relationship between aggregated GDP and population for roughly the largest 43 countries in the world between 1900 and 1916:

The graph is based on natural logarithmic transformations of both GDP and population data for countries with substantially complete data beginning in 1900, which were obtained from the Madison Project Database. The data generally represents countries that were either developed or developing economies at 1900, and the GDP data is based on constant 2011 US Dollars; thus representing estimated real GDP.

It can be seen that the relationship is approximately linear-in-logarithms with some apparently minor deviations, suggesting that data is largely consistent with the theory that humans are the primary cause of economic output and growth (as opposed to natural resources and technology, per se). While the availability of natural resources is, of course, a constraint on both output and population, and technology ultimately results in a non-linear relationship between output and population, this simplistic theory will be adequate to study the economic costs of war, famine, and pestilence.

2. War, famine, and pestilence disturb the relationship

Real GDP and population growth rates. Although the simplistic theory and empirical data presented above are consistent with a causal relationship between GDP and population, it is perhaps possible that they are jointly caused by other variable(s); resulting in what economists refer to as a spurious relationship. The standard approach to minimizing the likelihood of misinterpreting time-trending statistical data as a causal relationship is to examine the relationship between differences (changes) in, or the growth rates of, the variables. Accordingly, consider the following graph of the GDP and population growth rates obtained from the data underlying the above graph:

The graph suggests there is no obvious relationship–and perhaps no relationship whatsoever–between GDP and population growth; and, hence, no causal relationship between GDP and population per se. But we can see, unsurprisingly, that there is at least a clear relationship between aggregate GDP growth and global war, famine, and pestilence (WFP) events. Because the short-run growth in GDP and population seem unrelated while the theory and evidence on the long-run relationship seems clear, a more sophisticated econometric analysis will be needed to better understand the relationships between GDP, population, the effects of WFP events and their economic costs.

Global war, famine, and pestilence events. There is perhaps no unique way to define global war, famine, and pestilence events, but the following events were identified from a review of major global events over the last 120 years:

The extent to which such events actually influence either GDP growth or population growth is, of course, an empirical issue, which will be examined later below.

Significant assumption 1. Many readers will likely question my characterization of banking panics, financial crises, recessions, and depressions as WFP events, but the rationale for this is the a priori assumption that economic wealth and human health are intimately intertwined: greater wealth generally results in greater health or vice versa, at least on average. For those who object to this idea, it is important to note that the idea is neither non-intuitive or new (just ask the average person without health insurance). From an historical perspective, a careful reading of the Book of Revelations written by John of Patmos, circa 1st century A.D., presents a clear hypothesized relationship between conquest, war, economic controls, and death … by violence, famine, and pestilence. (The interested reader will perhaps be comforted by knowing that I estimated and tested several econometric models–not shown in this article–supporting this assumption, which showed that population growth was indeed positively associated with lagged GDP growth … and this generally means negative GDP growth leads to negative population growth: Economic contractions cause death.)

Population growth and WFP events. Because the scale of population growth rates is significantly smaller than that of GDP growth rates, it is helpful to examine a graph of population growth rates independent of GDP growth rates over the same 1900-1916 period to see things a bit more clearly:

Because of the overlapping of many global WFP events (e.g., World War 1, the Spanish Flu pandemic, and the 1920-1921 depression), it is not completely clear whether WFP events that are primarily economic in nature cause differences in population growths or vice versa. But the above graph does at least seem clear with respect to the major WFP events between 1900 and 1960, which appear to have had significant negative effects on population growth.

The above graphs suggest a clear limit to what we can learn from graphs, which is directly related to their fundamentally two-dimensional nature. To better understand the relationships, we need to use methods that allow for higher dimensional analysis and, accordingly, we need econometric methods–designed specifically for this purpose–to estimate and isolate the effects of WFP events on GDP and population.

3. Estimating economic effects of war, famine, and pestilence

Deviations from the long-run GDP-population relationship. Although we already saw that there is a long-term, linear-in-logarithms relationship between GDP and population, it is helpful to consider the untransformed relationship between GDP and population:

To understand this estimated long-run relationship more clearly, first consider the basic long-run prediction of GDP conditional on population and year between 1900 and 1960:

Consistent with our intuition about WFP events, the graph shows negative deviations from the long-run GDP-population relationship during the periods spanned by World War 1, the Spanish Flu, the Great Depression (1929-1939), and the Chinese Famine of 1958-1962. Now consider the basic long-run prediction of GDP conditional on population and year between 1960 and 2016:

In contrast to the 1900-1960 period, periods of deviation from the long-run relationship were more persistent in the 1960-2016 period, with both persistent positive deviations (1960-1982 and 2006-2016) and persistent negative deviations (1983-2005). If we maintain the hypothesis that there is, indeed, a long-run relationship between GDP and population, then we can infer from the above graph that there are likely factors–perhaps including WFP events–that influence the short-run deviations from the relationship.

Econometric model of GDP and population growth. Based on the hypothesis of a long-run relationship between GDP and population, the following error correction model was estimated using the Madison Project data discussed above:

The GDP and population growth rates are calculated as logarithmic changes; for example, the natural logarithm of the ratio of GDP(1901) / GDP(1900).

The model includes estimates of both the average short-run relationship between GDP and population growth rates, and an estimate of average annual convergence of deviations from the hypothesized long-run relationship toward the expected long-run equilibrium. WFP events are measured as indicator variables equal to 1 during years spanned by each event (else 0), and a control variable for US central bank asset expansion is measured as an index with the 2005 base year assets normalized to 100. The model parameters–i.e., the numerical coefficients related to each variable–were estimated using the least squares method, where all parameters were significantly different from zero (“statistically significant“) at conventional levels except for those related to variables with the superscript ns (“not significant”).

To develop a sense of what the estimated model is predicting, and the quality of the predictions, it is helpful to see the following graph of the model predictions and the related actual observations of real GDP growth over the 1900-2016 period:

As seen, model does not predict the GDP growth rate anywhere near perfectly, but as econometric models go it is actually not too bad: The error correction portion of the model is entirely consistent with a causal relationship between economic output and human population, parameter estimates with respect to statistically significant WFP events are generally consistent with intuition, and the model explains about 68% over the variation in GDP growth rates over the 1900-2016 sample period. Most importantly, however, is that the model seems to capture both the short- and long-run dynamics of the relationship between GDP and population well enough to allow us to develop meaningful estimates of the effects of WFP events … and, ultimately, their economic cost.

To see this more clearly, note that the estimated model parameters are interpreted generally as marginal effects of each variable on the GDP growth rate; and, so, because the model is linear in the WFP variables, it follows that the estimated model includes the estimated linearly-independent marginal effect of each WFP variable on GDP growth rates. It therefore follows that such independent marginal effects represent a logical basis for estimating the economic costs of WFP events.

Significant assumption 2. Although not all of the parameters on the WFP variables are statistically significant, they will nonetheless be used in developing an estimate of the economic cost of WFP events below. Specifically, the estimate is based on the significant assumption that (i) the above parameter estimates represent unbiased estimates of the marginal effects of WFP events on global GDP growth, but–because WFP events are measured as binary variables that capture both negative effects of the events on specific countries and the countervailing positive effects on other countries–(ii) only estimated negative marginal effects are used in developing the estimate of WFP costs. The rationale here is based on the well-known idea that wars often result in trade agreements that benefit some countries and hurt others; and the intent of this article is to estimate the (minimum) cost, rather than the benefits, of WFP events. A more sophisticated measurement and analysis of WFP events would perhaps result in more accurate estimates, but I will defer this exercise to potential future articles.

4. Capital market pricing of war, famine, and pestilence

To estimate the minimum total economic cost of WFP events occurring between 1900 and 2016, it is necessary to aggregate the cost at a particular point in time (because of the time value of money), and for this estimate I will choose (31 December) 2019. To adjust the estimated historical WFP costs to their present value at that date, it is necessary to estimate either a risk-adjusted expected market rate of return or the certainty-equivalent values of the historical WFP losses (see, e.g., the discussion of the certainty-equivalent valuation method discussed in my article on distressed credit portfolio valuation).

Because there are actually a number of different risks influencing WFP losses, which are likely to be priced independently in the global capital markets, it is somewhat less complex to estimate certainty-equivalent values of WFP losses. To develop this estimate, the following empirical model of the relationship between (i) the excess of the S&P 500 portfolio returns over the yield-to-maturity of US Treasury 3 month securities and (ii) the GDP growth rate, (iii) selected WFP event variables, and (iv) a control variable for US central bank asset expansion was estimated:

The model includes only a subset of the WFP variables, which were statistically significant at conventional levels (p < .10, one-sided) based on the objective of estimating only marginal risk prices that would usually be regarded as reliably priced in the capital markets over the 1900-2016 sample period. The S&P 500 portfolio return data was obtained from www.officialdata.org, US Treasury yields were constructed from US Census Bureau data and Investing.com data, and data on the other variables were obtained from sources described previously. The model parameters were estimated using the least absolute deviation (LAD) method, which is a robust regression method generally used to minimize the effects of extreme observations and skewness in the data.

Note that the model presented above is not intended to predict excess returns per se, but rather to predict the marginal excess return associated with each risk factor in the model. To understand how the parameter estimates shown above represent predictions of marginal excess returns, simply note that–for example–the 3.3228 marginal excess return to the GDP growth rate risk factor is considered to be an intertemporal constant … and therefore a marginal prediction over time. Again, it is perhaps helpful to see a graph of the aggregate model predictions and actual returns over the 1900-2016 period:

The above estimated model can be used to estimate the (median) certainty-equivalent GDP growth rate by setting excess return to zero–which is the condition under which the risky S&P 500 return is equivalent to the risk-free return–and all risk factors other than GDP growth to zero, then solving for the certainty-equivalent value:

The above expression omits the effects of all WFP events because they are (we hope and pray) transitory and generally non-recurring events. Accordingly, the above expression and resulting median certainty-equivalent value of GDP growth rate represents a long-run expectation rather than a short-run expectation.

This certainty-equivalent (CE) value has the following relationship to the median GDP growth rate for the 1900-2016 period, which will be used to adjust the marginal effects of WFP events on GDP growth to their CE values:

For clarity, the CE adjustment factor of .4684 is used to adjust the marginal effects of WFP events on the GDP growth rate to their CE values, which can then be discounted using a risk-free discount rate.

Significant assumption 3. The use of US capital market data to estimate the CE value of GDP growth rates is based on the assumption that global capital markets are integrated, which would imply that capital market risk factor pricing is the same in the US capital market as in the global capital market. (For more on this idea and an important example of where US risk pricing is not the same as in the global capital market, see my article “Estimating the global price of USD inflation risk.”)

5. Aggregate cost of war, famine, and pestilence 1900-2016

Based on the above data, analyses, estimates, and assumptions, the present value of the stream of marginal effects of WFP events on GDP can be written and calculated as follows:

(Data and calculations are available on request; just e-mail me below!)

Although USD $46.6 trillion is a lot of money–it is USD $46,600 billion–this probably does not have much meaning for many of us. So, to make the number more understandable, consider that for each of the approximately 5.2 billion people in the 43 countries used in the above analyses it represents about USD $9,300. While this is perhaps not an earth-shattering number, it’s important to recognize that for reasons discussed in the preceding sections, it probably represents the approximate minimum economic cost of WFP events. Even if this does not impress the average reader, my personal view is that USD $9,300 per person in many countries can make the difference between life and death for a meaningful period of time.

Some implications for asset valuation under COVID-19. The primary impetus for this article was my necessity to develop estimates of the economic effects of the COVID-19 pandemic, and the long-term capital market risk pricing of economic return streams spanning WFP events, for use in providing valuation services to my clients. Although I will not bore the reader with the calculation details, the estimated models presented in this article suggest the following:

  • If the COVID-19 pandemic is substantially equivalent to the Spanish Flu pandemic of 1918-1920, then it will result in a marginal contraction of the global economy by approximately 3.8% over a three year period.
  • If the COVID-19 pandemic has a knock-on economic depression substantially equivalent to the Economic Depression of 1920-1921, then the resulting depression will result in a marginal contraction of the global economy by approximately 5.2% over a two year period.

How such estimates would reasonably influence the expected cash flow streams of individual capital assets and businesses would be highly conditional, but I think this–and this article in general–is a helpful starting point to begin to address COVID-19 valuation issues.

Closing thoughts. Because of time constraints, there are many interesting aspects to the history of WFP events over the last 120 years, and their effects on human population and economic growth, that I didn’t discuss. But I did want to mention some things that I was repeatedly struck by in the histories and data: (i) A careful examination of the data shows that after almost every significant WFP event, population and economic growth not only recovered but recovered to a higher growth rate. (ii) The current COVID-19 pandemic pales in comparison to a number of past pandemics, and certainly in comparison to the stunning loss of human life and the aggregate human suffering caused by war, and to a lesser extent poverty. The implication is, of course, that we should be of good cheer: We will survive COVID-19 perhaps as well as we survived past pandemics, in which case all we really need do then is avoid the senseless economic costs of war.

São Paulo

Caveats.  Please note: (i) views presented above are my own and do not reflect those of others; (ii) like anyone, I’m not infallible and am responsible for any errors; (iii) I greatly appreciate being informed of any significant errors in facts, logic, or inferences and am happy to give credit to anyone doing so; (iv) the above article is subject to revision and correction; and, (v) the article cannot be construed as investment or financial advice and is intended merely for educational purposes.  MMc