Risk, uncertainty and COVID-19: A stark choice

By: |
April 25, 2020 6:10 AM

Risk has a known probability distribution. For uncertainty, the probability distribution is unknown. Covid-19 makes us confront uncertainty, not risk

There is risk and there is uncertainty. Since the days of Frank Knight, economists have differentiated the two. Risk has a known probability distribution. For uncertainty, the probability distribution is unknown. Covid-19 makes us confront uncertainty, not risk. In either event, agents maximise expected payoffs. For risk, there is a given probability distribution that can be used by everyone. For uncertainty, there is a subjective probability distribution, which can, and does, vary from individual to individual. How do I devise this subjective probability distribution? Through information and experience I already possess. There are various rationality assumptions used by economists. They are often violated. Otherwise, behavioural economics wouldn’t have taken off. Typically, given a situation, when your decision doesn’t agree with mine, I say you are irrational. However, with uncertainty, the problem may not be with rationality assumptions, but with differences in subjective probability distributions. Because of Covid-19, there is a certain risk of getting infected. Let us call this the infection rate—total infections divided by total population. Do I know what this infection rate is, for India, or any other country for that matter? I don’t. I am not being pedantic. To the best of my knowledge, no country has done universal testing.

No country has done universal testing for a proper random sample either. ICMR has told us more than 75% of Indian patients will be asymptomatic. Who do we test? Those who show symptoms, those who have been in contact with confirmed patients, and those who suffer from severe respiratory diseases. Most countries do something similar. In other words, when I work out an infection rate based on those tested, there is a sampling bias. This isn’t a proper infection rate. To the best of my understanding, the only country where we have had something like a random sample is Iceland. There, the infection rate was 0.8%. There are similar caveats about the death rate. If I mechanically divide India’s Covid-19 deaths by its total number of confirmed cases, I will get a death rate just over 3%. The global figure is a little less than 7%. But, neither of these is a death rate for the total population, since only those with severe symptoms are included in infection numbers. Thus, 3% or 7% are over-estimates. In a controlled environment like Diamond Princess, death rate as a ratio of total passengers, and not those infected, was less than 0.4%. The true infection rate and true death rate are not alarming numbers.

What does this have to do with differential subjective probability distributions? There are slices in India’s population pyramid, with rural/urban and other spatial differences too. Consider two extremes. (a) There are those who are globalised in information access and morbidity. Life expectancy is 80+ and there are lifestyle diseases like diabetes and high blood pressure. This co-morbidity increases possible death rates, and thanks to globalised access to information, certainly increases perceptions about death rates, making them out to be higher than they are. Some of them have fixed incomes, regardless of what happens to lockdown. Therefore, if you think in terms of maximising expected payoffs with a subjective distribution, high probability is attached to loss of life and low probability to loss of livelihood. I have simplified, but you get the general idea. (b) Contrast this with someone whose life expectancy is 60, without a fixed income stream and whose health concerns are tuberculosis and water-borne diseases, not Covid-19. Nor is access to information that globalised. High subjective probability will be attached to loss of livelihood and low probability to death from Covid-19. Both (a) and (b) reflect subjective probabilities. Neither is “irrational”. There is tension between (a) and (b). (a)-types would like lockdown to continue indefinitely, until the long tail of the infection curve tapers off, perhaps beyond September. (b) Types would like lockdown to be eased soon, with necessary restrictions in hotspots. There is indeed tension between lives and livelihood. Even if health outcomes and information access are like (a)-types, but income is contingent on growth, preferences might mirror the (b)-type.

Public policy needs to balance such differential individual preferences. This used to be the aggregation issue of the once fashionable, and somewhat esoteric, social/collective choice theory. Doing injustice to that entire literature and reducing it to column-type language, if preferences are heterogeneous, one set of individuals imposes its choice on the rest. (a)-types disproportionately influence policy. This determination of aggregate preferences is a dynamic process.

Therefore, sooner or later, (b)-types contest this, and as lockdown is prolonged and livelihood costs mount, discontent surfaces, as it has across a range of countries. There were also welfare economics notions that pre-dated social choice theory, such as compensation principles of Kaldor, Hicks and Scitovsky. The point can be made using those stereotypes of (a) and (b). Specifically, (a)-types need to compensate (b)-types for their losses. To state it starkly, livelihood losses suffered by (b)-types need to be compensated by the government through redistributive measures and this has to be financed by higher taxes imposed on (a)-types. The right question for (a)-types is not whether they want lockdown to continue, but whether they are willing to pay a Covid-tax to support lockdown extension.

This is meant to be a caricature, but it illustrates the public policy dilemma. Note that without growth revival, tax-paying capacity of (b)-types is limited and with job losses, some (a)-types become (b)-types. The choice is starker.

The author is Chairman, Economic Advisory Council to the PM
Views are personal

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