Adam Smith on the gravity model of trade

I've written a number of posts that reference gravity models, including a lot of my own research. For example, see here for a post about my own research using the gravity model of internal migration flows, or here for a post about joint work with one of my PhD students on using the gravity model of international trade flows. Essentially, a gravity model suggests that the flow (of people in a migration model, or goods and services in a trade model) between two regions is positively related to the 'economic mass' (usually measured as population in a migration model, or economic output or GDP in a trade model) of the origin and the 'economics mass' of the destination, and negatively related to the distance between the two places. This idea of gravity models in migration goes back to work by Ernst Georg Ravenstein in the 1880s, and then developed mathematically by George Kingsley Zipf in the 1940s. In trade, the mathematical gravity model is usually attributed to Walter Isard in the 1950s.

So, the gravity model is old. But, as the inside joke among economists goes, there's been nothing new in economics since Adam Smith. And it turns out that Smith had a number of things to say in his most famous 1776 book The Wealth of Nations, as related by Bruce Elmslie (University of New Hampshire, and previously a visitor at Waikato) in this 2018 article published in the Journal of Economic Perspectives (open access). Elmslie notes a number of places where Smith alludes to gravity in the context of international trade, in Book IV, Chapter III, Part II of the Wealth of Nations. Elmslie writes that:

Smith (1776, pp. 624–25; emphases added) compares the trade that could take place between England and France if his system of natural liberty prevailed versus the forced, policy-driven trade between England and the North American colonies, and between France and its colonies:

[T]he commerce of France might be more advantageous to Great Britain than that of any other country, and for the same reason that of Great Britain to France. France is the nearest neighbor to Great Britain. In the trade between the southern coast of England and the northern and north-western coasts of France, the returns might be expected, in the same manner as in the inland trade, four, five, or six times in the year. The capital, therefore, employed in this trade, could in each of the two countries keep in motion four, five, or six times the quantity of industry, and afford employment and subsistence to four, five, or six times the number of people, which an equal capital could do in the greater part of the other branches of foreign trade. . . . It would be, at least, three times more advantageous, than the boasted trade with our North American colonies . . . France, besides, is supposed to contain twenty-four millions of inhabitants. Our North American colonies were never supposed to contain more than three millions: And France is a much richer country than North America; . . . France therefore could afford a market at least eight times more extensive, and, on account of the superior frequency of the returns, four-and-twenty times more advantageous, than that which our North American colonies ever afforded. The trade of Great Britain would be just as advantageous to France, and, in proportion to the wealth, population and proximity of the respective countries...

Thus, Smith holds that if the trade volume between two countries is determined by each country’s consideration of “their real interest, without either mercantile jealousy or national animosity” (p. 624), it will be in relation to the size of the national produce of each country and the distance or proximity between them.

Notice that the three passages that Elmslie has emphasised in italics in the quote from Adam Smith all seem to relate to the gravity model of trade. How did Smith come upon the gravity model? Interestingly, Elmslie notes that:

Smith did not use the “gravity” terminology explicitly, but it is intriguing that for the determinants of the volume of trade Smith emphasized mass and distance, which is of course similar to Isaac Newton’s theory of gravity. Smith gives no direct indication that he had Newton’s gravity model in mind, but a connection is not implausible. Newton’s work had a significant impact on Smith’s methodology in the Wealth of Nations... In an earlier work written prior to 1758, Smith (1795) calls Newton’s theory of gravity “the greatest discovery that ever was made by man”...

So, there you have it. Adam Smith may actually have laid some of the initial foundations for the gravity model of trade (and migration), having been inspired by the work of Sir Isaac Newton.

Radio broadcasts and the 1960s race riots in the U.S. South

The role of social media in recent periods of unrest comes as no surprise to us. From the Arab Spring uprisings in 2011, to the U.S. Capitol riot in January this year, to anti-lockdown protests in Melbourne, social media have helped turn a small spark of resistance into a large-scale anti-establishment event. It is tempting to think that the role of media (as exemplified by social media in modern times) in these sorts of incidents is a recent phenomenon. However, that seems unlikely, and this 2020 working paper by Andrea Bernini (University of Oxford) provides one example. Bernini studies the effect of black-appeal radio programming on the 1960s race riots in the U.S. South. For those of you who aren't intimately familiar with those riots (which included me):

In the eight-year period between 1964 and 1971, 752 riots occurred. These totaled to 1,802 days of civil unrest, leading to 228 deaths, 12,741 injuries, 69,099 arrests, as well as 15,835 episodes of arson and other destructive events.

Bernini collected data at the county level on the occurrence and severity of riots (where severity was and index calculated as the average of the number of days of rioting, number of deaths, injuries, arrests, and episodes of arson occurring in each county, as a proportion of the total across all counties and all years). He also collected data on the coverage of black-appeal radio stations (defined as those "airing at least 12 hours of black-appeal programming a week"). The radio coverage was calculated based on a model of electromagnetic signal propagation that incorporates the terrain, using satellite data from NASA - each county was then classified based on the share of the county that was coverage by black-appeal radio broadcasts, or a dummy variable that classified each county into whether or not more than 50 percent of the county was covered.

Looking at the relationship between radio coverage and riots, Bernini found that:

In the preferred specification, a marginal increase in the share of the county receiving the signal from a black-appeal radio station is estimated to lead to a 7% and 15% rise in the mean levels of the likelihood and intensity of riots, respectively.

Here's where the paper goes a little off the rails though, as the interpretations are not quite intuitive. That result isn't the effect of all black-appeal radio stations, but is the effect of black-appeal radio stations that have 100 percent black-appeal programming. The effect for radio stations with less black-appeal programming is smaller (which is, in itself, an important finding). Also, I believe that in saying "a marginal increase", Bernini is actually referring to a one-unit increase in the radio coverage variable. Since that variable ranges from zero (no coverage) to one (complete coverage), then the correct interpretation of these results is that the difference between a county with no black-appear radio coverage and one with complete coverage, holding other variables constant, is a 7 percent increase in the likelihood of a riot, and a 15 percent increase in riot intensity. Those effects are large, but not necessarily as large as the phrase "a marginal increase" in coverage would imply.

Taking things a bit further, and comparing counties covered by radio stations in the top tertile (the top one-third) of the distribution in terms of the proportion of programming devoted to "news, interviews, religion, and public service" with counties in the middle and bottom tertiles, Bernini finds that:

...the content of the programming does have an important effect on the likelihood of a city experiencing a riot. In fact, it is only in the subset of counties receiving the signal from a 100% black-appeal radio station with a high level of political content programming, that a riot does emerge. The coefficient on the other 100% black-appeal radio stations, albeit positive, does not reach statistical significance at conventional levels. On the other hand... there is not a meaningful difference on the severity of riots between the two categories [low and high political content] of radio stations.

It is interesting that 'more political' radio stations increased the likelihood of a riot occurring, but not the severity of the riot. The radio stations provided the spark that ignited the riot, but after that, it was up to the rioters (and the authorities) what happened.

Bernini then went on to look at variations over time. All of the above analyses were based on the distribution of radio stations in 1964 (and not a year-by-year change). He also has data on the 1968 distribution of radio stations. However, from the paper it is difficult to understand exactly how he treated the panel data, since he had only two annual observations of radio coverage, but eight years of data.

Bernini presents an array of different econometric specifications in the paper. The instrumental variables (IV) analysis relies on a number of instruments. However, one of the instruments is the enrolment in Historically Black Colleges and Universities (HBCUs), measured in 1976. This is likely a good example of what econometricians refer to as a 'bad control', because HBCUs enrolment in the 1970s might have been affected the extent of riots in the 1960s. So, I don't find the IV analyses to be particularly convincing (although perhaps dropping the HBCU variable as an instrument would have little effect - maybe journal reviewers will test this point as this paper moves towards peer-reviewed publication).

Despite those gripes, this is a really interesting paper. It surprised me that the research literature hadn't previously established the importance of this relationship quantitatively. Bernini concludes that:

Black-appeal radio stations significantly changed the fabric of southern counties, through their sizable and robust impact on the likelihood and on the severity of the 1960s race riots.

The role of media (and now, social media) in influencing social movements is important, then as now.

[HT: Marginal Revolution, last year]

Is alcohol too cheap?

Alcohol Healthwatch was in the news this week, having released a report on alcohol prices in New Zealand. As the New Zealand Herald reported:

There are calls for the price of alcohol to increase after a new "Cheap Drinks" audit found it costs as little as 77 cents per standard drink to buy booze at some supermarkets and bottle stores.

While those standard drinks can't be bought per glass, it does mean that heavy drinkers can buy cask wine, cheap bottles of wine and large packs of beers for what is being described as "pocket money" prices.

The headline result in the report is the cheapest prices for each type of alcohol, where cask wine is found to be the cheapest way to get drunk. At 77 cents per standard drink, that rates it much cheaper than wine (85-88 cents), beer (98 cents), cider ($1.08), or RTDs ($1.14). The data in the report was collected from 22 off-licence outlets across Auckland (it says it's 'online data', so presumably was collected from store websites. In my experience (more on that a bit later), the in-store prices can actually be lower than those advertised on the store websites. And some independent stores will negotiate with you, offering an even lower price.

Is the price of alcohol too low though? That's pretty subjective, and the report doesn't link the low alcohol prices directly to alcohol consumption or to alcohol-related harm. We are left to infer that those links exist (and, to be fair, there is plenty of literature that does link alcohol consumption and harm).

Alcohol Healthwatch's preferred solution is (emphasis is theirs):

A combination of excise tax increases and minimum unit pricing is required to reduce consumption across the population. Whilst the latter specifically targets the cheapest alcohol in the market, the former is primarily aimed at increasing the overall price of alcohol so that population-level excessive alcohol use and alcohol-related harm is reduced. Across the board price increases will assist in the prevention of ‘moderate’ drinkers becoming heavy drinkers, and in heavy drinkers becoming dependent drinkers. Importantly, higher prices provide a supportive environment for the thousands of New Zealanders who indicate that they want to cut back their drinking.

I've discussed minimum unit prices and alcohol excise taxes before (see here). Raising the alcohol excise tax would increase the price paid by consumers, and reduce the quantity of alcohol demanded. Minimum unit pricing would also raise the price paid by consumers, and reduce the quantity of alcohol demanded.

Given that both policies appear to have the same effects, you could argue that we don't really need both. However, past research has shown that it may be optimal to have both an excise tax and minimum unit pricing simultaneously. In this post, I noted that:

As Paul Calcott (Victoria University of Wellington) showed in this 2019 article published in the Journal of Health Economics (sorry, I don't see an ungated version online), the combination of minimum unit pricing with an excise tax may be optimal:

...when relatively cheap forms of alcohol are undertaxed, and the quality and quantity of alcohol are substitutes.

Raising alcohol excise tax raises the price of all alcohol, and decreases alcohol consumption. However, some consumers will simply switch to lower quality (and lower priced) alcohol instead. At the bottom of the quality (and price) distribution, where consumption (and alcohol-related harm) might be the highest, then it makes sense also to have minimum unit prices.

The problem with this suggestion is that it is not well supported by the public. As I noted in this post, minimum unit pricing was the alcohol regulation that had the lowest support of all the seven options that were presented to survey participants. Only 33 percent of people supported minimum pricing, while 'having fewer places selling alcohol' had 54 percent support. Interestingly, having fewer places selling alcohol could have the effect of raising prices, if there is local price competition between stores.

However, the research evidence that there is such local price competition is scarce. I have been collecting a long-run dataset of alcohol pricing at all off-licences in South Auckland and Hamilton City for over ten years. The purpose of collecting that data is to test whether competition between outlets affects pricing (and opening hours). Local competition doesn't appear to have much effect in a cross-section, hence the need to collect some longitudinal data (where there is observed changes over time in local competition). I hope that post about that research sometime next year.

Read more:

• Alcohol minimum pricing, elasticity and profits
• Alcohol minimum pricing vs. taxes

Why relatively poor people are not more supportive of redistribution

Redistribution of income from richer people to poorer people seems like something that poorer people should be more supportive of than are richer people. After all, they would benefit directly from such redistribution, and it would reduce inequality of income. However, as I've noted in posts before (see here and here), perhaps people don't prefer lower inequality, they prefer greater fairness. So, people's preferences for redistribution are somewhat more complicated than simply being based on their relative position in the income distribution.

A new article by Christopher Hoy (Australian National University) and Franziska Mager (Oxfam Great Britain), published in the American Economic Journal: Economic Policy (ungated earlier version here), provides some real food for thought on the topic of preferences for redistribution. They first note three assumptions that underlie the seminal theories of preferences for redistribution:

Firstly, most people are averse to large income differences in their country, and this is particularly the case for relatively poor people. Secondly, people who are more concerned about inequality tend to be more supportive of redistribution. Thirdly, poorer people should be more supportive of redistribution than richer people, as they benefit directly.

Hoy and Mager note that most people have a 'median bias' in their belief about their position in the income distribution. That is, poorer people tend to believe that they are richer than they really are, while richer people tend to believe that they are poorer than they really are. Hoy and Mager essentially tests what happens when you give people information about their actual position in the income distribution, on preferences for redistribution. As they explain:

Surveys across a range of high-income countries have shown that most people tend to think that they are positioned around the middle of the national income distribution regardless of whether they are rich or poor... This raises the question that if relatively poor people were made aware of their position in the national income distribution, would they be more concerned about inequality and supportive of redistribution?

We test how informing people that they are relatively poorer than they thought impacts their concern about inequality and support for redistribution through a randomized survey experiment with over 30,000 respondents in 10 countries (Australia, India, Mexico, Morocco, the Netherlands, Nigeria, South Africa, Spain, the United Kingdom, and the United States)... Respondents in each country were randomly allocated to receive either information about their position in the national income distribution (treatment group) or no information (control group). Prior to the treatment, respondents revealed their perception of the level of national inequality, their preferred level of national inequality, and their perceived place in the national income distribution... After the treatment, respondents were asked standard questions from the existing literature regarding their views about whether the gap between the rich and poor is too large in their country and whether they think the government is responsible for closing this gap...

Hoy and Mager note that:

Seminal theories of preferences for redistribution imply that informing people that they are relatively poorer than they thought would lead to greater concern about inequality and support for redistribution...

However, they find in their sample that:

...respondents in the poorest two quintiles of the national income distribution who were told they are relatively poorer than they thought are less concerned about the gap between the rich and poor in their country and are not any more supportive of the government closing this gap compared to respondents in the control group. This result occurs in seven countries (India, Mexico, Morocco, the Netherlands, Nigeria, South Africa, and Spain), and there was no effect caused by this information in the remaining three countries (Australia, the United Kingdom, and the United States).

In other words, this is the opposite of what the seminal theories would predict. Hoy and Mager then use a theoretical model to explain what might be causing these surprising results:

We illustrate that the likely channel causing the effect is people using their own standard of living as a “benchmark” for what they consider acceptable for others... People had perceived themselves to have an “average” living standard compared to other people in their country prior to the treatment even though they were actually relatively poor. Their previous assessment of their relative status implies that they thought there were similar shares of people poorer and richer than them in their country (this is as a result of placing oneself as being around the middle of the national income distribution). Upon receiving the treatment, this led people to realize two points. Firstly, there are fewer people in their country poorer than them than they had thought. Secondly, what they had considered to be an average living standard (i.e., their own standard of living) is actually relatively poor. In other words, relatively poor people consume more than they thought. Both of these points would suggest that the treatment provided to respondents would lead them to become less concerned about the living standard of poor people in their country.

Notice that this also accords with the idea that people prefer more fairness in the income distribution. Providing relatively poor people more accurate information about their position in the income distribution might make them believe that the distribution is fairer than they previously thought (after all, they are richer than they thought they were, relatively to others around them), and reduce their preferences for redistribution.

It is rare that a new study overturns some important seminal theory in such a convincing way as this study does. However, it would be easy to overstate what this study tells us about people's attitudes to inequality. In particular, it is important to note that these results are about preferences for redistribution, not aversion to inequality. As Hoy and Mager note:

...the results of our experiment illustrate that relatively poor people’s misperceptions of their position in the distribution do not appear to be lowering their concern about inequality. We provide evidence that the opposite is true. Relatively poor people would be even less concerned about inequality if they knew their true position in the national income distribution. In addition, we show that the elasticity of respondents’ preferences for redistribution to the treatment is substantially greater in middle-income countries than in high-income countries. This is a novel finding, as it suggests the literature on preferences for redistribution may well be qualitatively different if more research were to be conducted in these settings.

And that points to the importance of doing more research on this topic, in a wider range of countries. It also suggests that, if people in developed countries are given accurate information about where they are placed in the global income distribution, they may become more favourably disposed towards global redistribution. This assumes that the effect on relatively richer people works in exactly the opposite manner to the effect that Hoy and Mager find for poorer people (they don't show the effects on richer people in their study, but something similar was found in this study). That would suggest a way for advocacy groups to increase the support in developed countries for foreign aid, or perhaps to increase donations from 'ordinary people' in developed countries targeted at poverty reduction in developing countries. Changing preferences for global redistribution could have substantial global-welfare-improving implications.

Read more:

• Who cares about income inequality?
• Changes over time in attitudes towards redistribution in the U.S.
• Inequality, redistribution, and fairness
• People want fairness, not equality