The welfare impacts of a positive (consumption) externality

Back in 2023, I wrote a post about the welfare impacts of a negative consumption externality. I think I always meant to follow up that post with a companion post about the welfare impacts of a positive consumption externality, but I never did. So here goes!

To recap, an externality is the uncompensated impact of the actions of one person on the wellbeing of a third party. A positive externality makes the third party better off, while a negative externality makes the third party worse off. They are called externalities because they lie outside the original decision, i.e. some of the costs or benefits are external to the person whose action creates them.

There are fewer examples of positive externalities that come readily to mind than negative externalities, but let me use the example from my ECONS102 class: vaccinations. A person who gets vaccinated receives some benefit themselves, because they are less likely to get infected by whatever they have been vaccinated against. However, they also provide a benefit for other people (including those who are unvaccinated), because other people are less likely to catch the infection as well (because they are less likely to catch it from the vaccinated person).

Consider the market for vaccinations as shown in the diagram below. The market will operate at the quantity where supply (S) meets demand (D) - that is, the quantity traded will be QM, and the price of vaccinations will be PM.

However, the vaccine recipients create a positive externality for other people. Since this externality arises from the buyers of vaccinations, we show this externality on the demand side of the market - we refer to it as a positive consumption externality.[*] This means that the benefits that vaccine recipients receive themselves from getting vaccinated are lower than the benefits that society receives from those vaccinations - the difference is the benefit that is received by other people. We show this on the diagram by differentiating between the marginal social benefit (MSB) and the marginal private benefit (MPB). The MPB is the benefit that vaccine recipients receive for themselves. The MSB is the marginal private benefit, plus the benefit of the externality - the marginal external benefit (MEB).

Now, society prefers the quantity of vaccinations to be the quantity where marginal social benefit (MSB) is equal to marginal social cost (MSC) - I'll explain why a little later in this post. That is the quantity QS, and one way to get to the quantity QS is if the price of vaccinations decreased to PC (because then, more people would be willing to get vaccinated). Notice that in the diagram, relative to the quantity that society prefers (QS), the market produces too little (QM). There are too few vaccinations (or too few people getting vaccinated).

Why does society prefer QS (the quantity where MSB = MSC)? It's because that's the quantity that maximises economic welfare. Economic welfare is the sum of all of the net benefits arising from the market. First, the consumers receive some net benefit from participating in the market. Consumer surplus is the difference between the amount that consumers are willing to pay (shown by the demand curve), and the amount they actually pay (the price). In the diagram, at the equilibrium price and quantity, consumer surplus is the area FEPM. Second, producers receive some net benefit from participating in the market. Producer surplus is the difference between the amount the sellers receive (the price), and their costs (shown by the supply curve). In the diagram, at the equilibrium price and quantity, producer surplus is the area PMEH. Third, the third parties are positively affected by the market. The welfare benefit of the positive externality is the area in-between marginal social benefit and marginal private benefit, up to the quantity of vaccinations received (in this case, QM). That is the area AGEF, and it is added to total welfare. Total welfare is the sum of consumer surplus and producer surplus (which is the area FEH), plus the area of the positive externality (AGEF), and is equal to the area (AGEH).

Now consider the market operating at the quantity QS (with the price PC). The consumer surplus is the area FJPC. The producer surplus is tricky, because to get the market to produce QS, that would require the seller to accept a price that is below their costs (notice that the price PC is below the firms' costs shown by the supply curve). In reality, the government would probably subsidise this good to achieve the optimal outcome, but we will instead assume that the government mandates that the seller provide vaccinations at below cost, to anyone who is willing to pay the price PC (this might make some sense in a public health care system like New Zealand, but is still just a simplifying assumption rather than a description of how this would work in practice). The producer surplus is therefore the area -PCHBJ (it is all negative, because every vaccination is provided for a price that is below the sellers' costs). The area of the positive externality is the area ABJF. Total welfare at QS is equal to ABH.[**] Notice that this total welfare is larger when the quantity is QS than when the quantity is QM. If the market is left alone, there are too few vaccinations (or too few people getting vaccinated), and this decreases total welfare by the area GBE. That area GBE is the deadweight loss of the externality.

Since the market produces too little, a relevant question is how could we get the market to produce more? A Pigovian subsidy (named after 20th Century economist Arthur Pigou) is one option, since subsidies increase the quantity of a good that is traded (for more on that, see this post). Of course, determining the exact optimal quantity QS is difficult in practice. However, we can be sure that it isn't the quantity that is provided by the market.

*****

[*] In contrast, when producers produce a positive externality as a consequence of manufacturing other goods (for example), that is a positive production externality, which we would show on the supply side of the market. An example of a positive production externality is the smell of freshly baked bread emanating from a bakery (at least, it's a positive externality for those who like the smell of bread).

[**] Calculating total welfare involves adding the consumer surplus and externality (adding FJPC and ABJF gives the area ABJPC) and then subtracting the negative producer surplus of PCHBJ, which leaves the area ABH.

Mariana Mortágua on why crypto-assets are not money

Economists typically identify money by the extent to which an asset satisfies three functions. First, it needs to be a medium of exchange, meaning that you give it up when you buy goods or services, and you can receive it when you sell goods or services. Second, it needs to be a unit of account, meaning that you can measure the value of something using the amount of money it is worth. And third, it needs to be a store of value, meaning that you can keep it and expect it to retain a reasonable proportion of its purchasing power into the future. These functions of money go back to William Stanley Jevons in 1875.[*]

There has been a lot of debate about whether crypto-assets such as Bitcoin or stablecoins are money (see the posts linked at the bottom of this post for some examples focused on Bitcoin). This recent article by Mariana Mortágua (ISCTE-University Institute of Lisbon), published in the Cambridge Journal of Economics (sorry, I don't see an ungated version online) wades into the debate, broadening the scope to consider crypto-assets more generally.

Mortágua concludes that crypto-assets are not money. However, unlike much of the debate, she doesn't focus on the volatility of crypto-assets and how that impedes the 'store of value' function. Instead, she adds to the argument that crypto-assets are not a unit of account. Specifically:

Reserves, cash, and bank deposits are titles of debt, claims denominated in one unit of account. Although the issuer of such a claim is not always a State entity (like a central bank), privately issued money is apparently indistinguishable from central bank money because it is issued using the same denomination (the generally accepted unit of account)...

While claiming that cryptocurrencies, like Bitcoin, can become money, their enthusiasts fail to explain how a system of bilateral transactions in one medium of exchange would give rise to a unique unit of account or why people should accept that medium of exchange in the first place...

Indeed, though cryptocurrencies have their own self-attributed trademarks, their prices are denominated in one already established unit of account. Even the most known and utilised cryptocurrency, Bitcoin, is very far from serving as a measure of value of services or assets. On the contrary, Bitcoin is priced in USD, and... only central (political) authorities have the power to determine the ‘meaning of a dollar’.

So, because we don't measure the value of things in terms of crypto-assets, they aren't money. It isn't enough that you can buy or sell things using crypto-assets like Bitcoin. That is an example of a crypto-asset serving the function of a medium of exchange. The transactions are priced in dollars (or other currency), which means that the unit of account is not the crypto-asset, but the currency.

The argument that cryptocurrencies like Bitcoin are not a unit of account is not new (see the links at the end of this post for more). What Mortágua adds is a broader theoretical argument about the nature of money itself, based on the idea that money represents claims denominated in an established unit of account (like dollars). She argues that this distinction is important not just for Bitcoin, but for crypto-assets more generally.

There is, however, an interesting complication here. The dollars in your bank account don't have their own unit of account either. A bank deposit is a claim on the bank, denominated in dollars, but we still count bank deposits as money. Mortágua's argument rests on the credit theory of money, which sees money as part of a system of debts and claims, denominated in a commonly accepted unit of account. Bank deposits are widely accepted as money because the banking system allows them to be used to settle debts.

Stablecoins are not as straightforward. While a dollar-backed stablecoin may also represent a claim on its issuer for US dollars, the arrangements supporting that claim are different from those supporting bank deposits. So, the question is whether those stablecoins have the institutional backing and general acceptability of money. Mortágua argues that they don't.

So, it's not just Bitcoin. Mortágua concludes that crypto-assets in general are not money. However, stablecoins show us that the distinction between money and other financial assets is not always straightforward.

*****

[*] Jevons noted a fourth function, a standard of value (a way of valuing debts), which we now consider to be much the same as being a unit of account.

Read more:

• You may be able to buy Coke with Bitcoin, but that still doesn't make Bitcoin money
• No, El Salvador hasn't just turned Bitcoin into money
• Bitcoin still isn't money, because people aren't using it as if it was

Inequality is not robustly associated with lower subjective wellbeing or worse mental health

When I cover inequality with my ECONS102 class, we talk about some of the many problems that have been associated with inequality, such as unequal access to political representation, lower social cohesion, and less interaction between increasingly segregated social groups. I also talk about the theory that links higher inequality with lower economic growth, though noting that the research is far from settled on that issue (see here and here, for example).

In that class, I don't discuss the research linking inequality with lower physical or mental health. That goes back to my objections to the Wilkinson and Pickett book The Spirit Level (which I discussed here). It turns out that might have been a good choice, at least in terms of mental health.

This recent article by Nicolas Sommet (Université de Lausanne) and co-authors, published in the high-profile journal Nature (ungated earlier version here), presents the results of meta-analyses of the relationship between inequality and subjective wellbeing, and inequality and mental health. Meta-analysis is a way of combining the results of many studies to generate an estimate of the overall effect size.

Their meta-analysis of inequality and subjective wellbeing included 152 estimates from 100 different studies, and they found that inequality was not significantly associated with subjective wellbeing. Their results were qualitatively the same whether subjective wellbeing was measured as life satisfaction or happiness, and did not depend on study quality. That is worth noting, given that about 80 percent of the studies included in the two meta-analyses were judged to be at high or very high risk of bias.

Sommet et al.'s meta-analysis of inequality and mental health included 99 estimates from 75 different studies, and they found a small negative association between inequality and mental health. Specifically:

A 0.05-point increase in the Gini coefficient predicted a 4% (1/0.961) increase in the odds of experiencing a mental-health issue.

The Gini coefficient measures inequality on a scale of 0 to 1, and a 0.05-point increase is similar to the difference between New Zealand (0.326, above the OECD average) and Denmark (0.276, close to the lowest inequality among OECD countries - see Figure 6.1 in this report). Similar to subjective wellbeing, the results were qualitatively the same whether mental health was measured as depression or 'other mental disorders', and did not depend on study quality. The effect was larger when inequality was measured at the 'macro level', meaning the country level (or large subnational areas with populations over one million), although the effect was also statistically significant when inequality was measured at the 'meso level' (small subnational areas, such as counties).

Not so fast, though. After correcting for publication bias (the tendency for statistically significant results to be more likely to be published), Sommet et al. find that, for mental health:

The median bias-corrected estimate was OR+0.05 = 1.018 (0.986–1.051), P = 0.266, thereby confirming the lack of a significant association after correcting for publication bias.

Moreover, Sommet et al. conduct a specification-curve analysis, which tests how sensitive the results are to different modelling choices. They find that their conclusions are robust across approximately 95 percent of 768 alternative model specifications.

The overall result is that inequality is not statistically significantly associated with either subjective wellbeing or mental health, at least not robustly so. However, Sommet et al. then dig a little further, finding some interesting differences in the estimated effects across countries with different characteristics. First, for mental health, they find that the negative association is significant in lower-income samples, but not in higher-income samples. They replicate this result using data from the Gallup World Poll, using average national income to distinguish between lower- and higher-income countries. They explain this as suggesting that:

...inequality may be particularly harmful to low-income populations, possibly by undermining community cohesion... fostering adverse social comparison... or fuelling perceptions of unfairness...

Second, for subjective wellbeing they find that there is a negative association with inequality in high-inflation countries, but a positive association with inequality in low-inflation countries. They also replicate this finding using data from the Gallup World Poll. They explain this in the following way:

Rising costs of living drive distress... and inequality may exacerbate the burden of inflation by increasing social discontent and resentment. Conversely, when prices are stable, inequality might be interpreted as a signal of future economic mobility and foster hope... That is, inequality may only harm well-being under degraded economic conditions (here, high inflation) and have positive effects under others (low inflation).

Their explanations are speculative, and I would be cautious about over-interpreting the mechanisms underlying these latter results. Nevertheless, the fact that both findings were replicated using the Gallup World Poll should provide some comfort about the results. Overall, the results of this meta-analysis can be taken to mean that, while there may be a relationship among some subgroups or some countries at some points in time, there is not a robust overall association between inequality and lower subjective wellbeing or worse mental health.

[HT: Marginal Revolution, last year]

Two papers on inequality in pre-industrial times, that extend our view over two millennia

Back in 2015, I wrote a post about some research by Branko Milanovic (City University of New York) on inequality in ancient times. Milanovic is a prolific inequality researcher, but I only recently got time to read this 2019 article of his, published in the journal Review of Income and Wealth (ungated version here). The article is something of a sequel to the earlier article, tracking changes in income inequality from 14 to 700 C.E. in Europe and the Mediterranean.

This involves combining data from a variety of other studies, first to estimate changes in mean income, then overall and regional inequality, before turning to individual inequality. The resulting estimates are summarised in Figure 2 from the paper, which shows upper and lower bounds on the estimated Gini index:

The 'social table' referred to in Figure 2 comes from this earlier paper by Scheidel and Friesen, with an estimated Gini index of 41.3. The decline from there to a Gini index of between 3 and 13 represents both an unprecedented decline, and an extraordinarily low level of inequality by 700 C.E. Milanovic notes the apparent disconnect between the low inequality he estimates and the impressions of contemporary accounts of poverty, and explains that:

We believe that it is possible to reconcile the conjectured low measured inequality with the impression of a high post-300 inequality because the latter may, in reality, refer to the speculation (or a fact) that the elite was appropriating proportionally much more of the surplus above subsistence than before... Those who observed poverty of most contrasted to the wealth of the very few tended to conclude that inequality must have unambiguously risen. But they might have failed to account for the fact that the numerous poor were now all equally impoverished, and that measured inequality (calculated across all individuals) could not, on that account alone, have been very high...

It is worth noting that these low estimates depend on an assumption that average incomes were barely above subsistence. When almost everyone is extremely poor, even a rich elite that appropriates most of the surplus above subsistence might not produce a particularly high overall Gini index. So, we should be careful that we don't mistake low inequality for prosperity, because it certainly isn't implying that. Nevertheless, the results remain somewhat extraordinary, and it will be interesting to see other estimates of inequality during that time, taking advantage of different data sources or methods.

Milanovic's paper finishes with 700 C.E. What happened to inequality after that? This 2021 article by Guido Alfani (Bocconi University), published in the Journal of Economic Literature (ungated earlier version here), picks up the story in 1300 C.E. and takes it through until the end of the 18th Century, synthesising estimates from a number of other studies of inequality in various parts of Europe. Alfani makes note of Milanovic's results (from the paper I noted above), but doesn't really critically appraise them, which is fine because Alfani is more interested in the period from the late Middle Ages to the early modern period. The studies he synthesises are summarised in Figure 2 Panel A from his paper, which again focuses on the measures of the Gini index, although note that this is for wealth inequality (rather than income inequality):

Alfani uses this to suggest that the evidence supports two stylised facts about inequality in this period: (1) that inequality in Europe increased from 1450 or 1500 until 1800; and (2) before 1450, there was a period of declining inequality that coincides with the Black Death. The decreasing inequality during the Black Death is consistent with an explanation that my ECONS102 students will be familiar with - agricultural wages increased dramatically during that period, alongside a decrease in land rents (as discussed in the book The Rise of the Western World by North and Thomas, which I reviewed here). Alfani then goes on to explore reasons that might explain the overall increase in inequality. He dismisses economic growth as the main explanation, noting that inequality appeared to increase even during periods of economic decline (aside from during the Black Death). Instead, Alfani points to the importance of institutions, and in particular the rise of the fiscal-military state, alongside generally regressive taxation, as well as inheritance systems that protected wealth within families. He concludes that:

The different, and sometimes partly contrasting, explanatory factors for long-term inequality change discussed above lead to a clear conclusion, which can be summarized as follows:

(i) In preindustrial times, there was no necessary cause of inequality growth (like for example, economic growth).

(ii) There were instead a number of sufficient causes of inequality growth, among which we could name economic growth, demographic factors (including urbanization growth), institutional change and politics, “proletarianization” (i.e., the crisis of small ownership), and so on. When one or more of these potential causes became active, inequality grew.

(iii) The bottom line being, in the long preindustrial period it was seemingly much easier for inequality to grow than to decline—and indeed, we have very few examples of long-lasting inequality decline, and almost all of them can be connected to large-scale catastrophes.

Finally, Alfani takes a longer view of wealth inequality through to modern times, by comparing his estimates (based on an average of the various studies included in his synthesis) to those of Thomas Piketty, which begin in 1800. The results are shown in Figure 8 in the paper, which shows the share of wealth held by the richest 10 percent, rather than the Gini index:

So, now we are getting a longer-term picture of nearly two millennia of changes in inequality in Europe, albeit with some important gaps. Milanovic's results suggest that income inequality declined dramatically after the fall of Rome, while Alfani's results suggest that wealth inequality declined around the time of the Black Death, before increasing through to the early 20th Century. In the 20th Century, wealth inequality saw another period of rapid decline (but nothing like the decline in income inequality after the fall of Rome), before increasing again in the second half of the century. Of course, income inequality and wealth inequality are not directly comparable, even if they tend to be correlated. So we should be cautious about drawing conclusions about the overall trajectories of both types of inequality. More studies are needed to confirm these long-run patterns, as well as to fill in the gaps and to extend these results to consider other regions outside of Europe.

Read more:

• Inequality was similar, or higher, in ancient times than it is today
• The last two centuries of global inequality
• Changing global inequality, migration and open borders
• More evidence of declining global inequality
• Chinese growth and global inequality
• Several research articles on inequality
• The global inequality boomerang