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Gravity equations have been widely used to infer trade flow effects of various institutional arrangements. James Anderson discusses a method to solve the famous McCallum border puzzle.

Image courtesy of interviewee. November 9, 2023

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This video discusses the application of Newtonian physics concepts to economic interactions, particularly through the lens of the gravitational model of trade. Initially, the discussion outlines how the gravitational model originated from the "two-body problem" in physics, which describes the forces between two bodies based on their masses and the distance between them. This video metaphor was applied to economic scenarios, such as migration, trade, and capital flow, where the size and distance between markets affect interactions.

However, the metaphor has limitations, as it fails to account for the influence of additional parties (e.g., third nations or markets). The speaker introduces multilateral resistance, which considers the attractiveness of trade relative to many potential sources and destinations rather than just bilaterally. This video complex interplay of factors results in a more accurate model of trade dynamics.

The discussion highlights the "border puzzle," where trades between regions are heavily influenced by geographical borders, even between similar economies. The speaker explains how distinct market sizes and multilateral resistances contribute to different trade patterns—larger markets tend to have lower resistance to trade due to reduced distances and fewer barriers, leading to different trading behaviors and amounts.

The conversation also touches upon how this theoretical framework applies to various economic phenomena, including migration patterns and direct investments, and hints at its relevance to contemporary issues like Brexit. The insights point to the natural tendency for larger economies to trade more within their borders compared to smaller ones, emphasizing the role of distance and border effects on trade relations.

Finally, the speaker conveys optimism about applying the gravity model across diverse human interactions, suggesting its applicability to other aspects beyond trade, such as social interactions and cultural exchanges. Overall, the text explores the intersection of physics and economics, demonstrating how adapting physical models can deepen our understanding of complex economic systems.

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1. **Gravity Model Origin**: The gravity model in economics is analogous to Newtonian physics, particularly the two-body problem. It suggests that economic interactions, such as trade or migration, are influenced by the size (mass) of economies or populations and the distance between them.

2. **Bilateral vs. Multilateral Resistance**: The initial insight from the gravity model needed to account for third-party influences on economic interactions. Multilateral resistance factors are introduced, which consider the attractiveness of a market relative to all others. This results in a more comprehensive understanding of economic interactions beyond simple bilateral analysis.

3. **Border Puzzle**: The video discusses the "border puzzle" posed by John McCallum, which showed that trade between Canadian provinces and U.S. states, which are equidistant from each other, differed significantly due to the presence of the border. Research later revealed that multilateral resistances play a crucial role in understanding these discrepancies.

4. **Impact of Country Size**: It is noted that larger economic entities tend to trade more within their local markets compared to smaller entities. This leads to differences in multilateral resistances, where smaller countries have higher resistances due to more pronounced distances and border effects in international trade.

5. **Applications Beyond Trade**: The gravity model has extensive applicability beyond trade, including migration and other forms of interaction. The insights gained from the model inform economic policies and strategic decisions about trade agreements, migration policy, and understanding regional economic interactions.

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Here are some key quotes extracted from the video :

1. **Newtonian Physics Analogy**:
- "Well, it originated, of course, from Newtonian, uh, physics for the, the two body problem where, uh, the force between the two bodies is, uh, proportional to the product of the masses and inversely proportional to the square of the distance between them."

2. **Economic Interactions**:
- "And that was a metaphor that was then taken to various economic interactions where it seemed like a reasonable sort of thing to say, well, there's a, there's a mass, maybe the size of the market or the, the number of people, uh, at the origin of the destination."

3. **The Border Puzzle**:
- "He then realized, well, um, I can take out distance by getting trade between a, a province and another province, and, and that same province and another American state that's the same distance away, basically."

4. **Multilateral Resistance**:
- "It turns out it was possible to sort of summarize that into what a second, effectively a two body problem again, because you could say, well, there's the market. I'm focused on how much I sell there."

5. **Seeking Equilibrium**:
- "All of that stuff in equilibrium says there's no more profit to be made from any moving around."

6. **Understanding Trade Dynamics**:
- "But what's left over? It's actually been a, you know, really, once we really understood better how to do this, it's, it's been quite an interesting, uh, journey."

7. **Practical Ramifications**:
- "Brexit looked incredibly foolish from the point of view of gravity."

8. **Local Markets vs. Distance**:
- "Local markets are cheaper to serve, you know, there's less friction there."

9. **General Insight on Human Interaction**:
- "It’s kind of amazing how, how ubiquitous, uh, this, this gravity, uh, model of human interaction really is."

10. **Final Reflection**:
- "It works pretty darn well for all kinds of interactions."

These quotes highlight the thematic focus on the metaphor of gravity in economic interactions, the complexities of trade dynamics, and the empirical relationships that arise from these theories, including the significant impact of distances and borders on trade.

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Here are some articles similar to the video, which discusses the application of Newtonian physics analogies in economics, particularly in understanding trade flows, multilateral resistance, and the border effect:

1. **"The Gravity Model of International Trade: A Survey"** - This article discusses the origins and applications of the gravity model in international trade. It elaborates on how this model explains trade flows between countries based on economic size and distance, similar to gravitational forces in physics.

2. **"Border Effects on Trade: A Review of the Literature"** - This review summarizes various studies that have explored the impact of borders on trade, emphasizing how institutional and geographical factors create frictions that can affect trade volumes.

3. **"Multilateral Resistance and the Gravity Model"** - This paper delves into the concept of multilateral resistance in trade theory, explaining how bilateral trade flows can be influenced by the presence of other countries and their respective trade frictions.

4. **"Trade and Migration: An Empirical Analysis"** - This research examines the parallels between trade models and migration patterns, applying economic theories and models that have traditionally been used for trade to understand migrations.

5. **"Explaining the Border Puzzle with Gravity Models"** - This article provides insights into the "border puzzle," investigating why trade between countries is significantly affected by borders despite geographical proximity and shared languages.

6. **"Applications of Gravity Models in Regional Economics"** - This article discusses how gravity models have been applied in regional economic analyses, including urban interactions, migration patterns, and transportation flows.

7. **"Understanding Trade Flows: The Role of Distance and Economic Size"** - This explores the factors influencing trade flows, reinforcing the idea that distance and the economic size of countries play crucial roles, akin to the concepts introduced in Newtonian physics.

These articles collectively cover concepts related to the application of physical models in economics, specifically in understanding trade dynamics, market interactions, and the implications of borders on economic behavior.

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Well, it originated, of course, from Newtonian, physics for the,

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the two body problem where, the,

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the force between the two bodies is,

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proportional to the product of the masses and inversely proportional to the

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square of the distance between them.

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And that was a metaphor that was then taken to various

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economic interactions where it seemed like a reasonable sort of thing to say,

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well, there's a, there's a mass, maybe the size of the market or the,

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the number of people, at the origin of the destination.

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And then there's a distance between them.

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And then we realized there might be some other things as well as just purely

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physical distance that also affect this flow.

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But also in a kind of inversely proportional way,

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there's a sort of friction which limits it.

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And so it turns out that just using that metaphor,

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and lining it up with data,

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it actually works incredibly well for all kinds of interactions. Um,

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migration,

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where there's the size of the population in the city of origin and the city of

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destination and distance between them, for goods,

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which actually came a bit later in terms of, you know, the historical, you know,

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applications of this sort of thing. Uh, and then the flow of,

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of capital between origin and destination.

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So all of these sorts of things,

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were telling us this is a really important empirical relationship. Um,

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but there was, there was,

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actually always something a bit puzzling about it in terms of economics,

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because you, you would say, well, sure, that's, that's a good insight. I mean,

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we do know there's economic interaction and we know now it's empirically,

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you know, somewhat,

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it's actually not more than so much very extremely robustly connected in this

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way. So the, the problem was though that, well,

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we know that as in actually Newtonian physics,

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the two body problem is a very, very simple special case.

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And if there's a third body somewhere nearby, that's massive enough,

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it's certainly going to influence the trade between those two bodies.

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And at this point,

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the analogy with physics really breaks down because, what's known about the,

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the multiple body problem in physics gives you some very different kinds of

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structures. But for economics, we're sort of left with this puzzle. Well,

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we got this metaphor that we started with. It works well,

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but there's a problem with that because third party interactions are

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not somehow influencing that, that bilateral, interaction.

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And so,

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that was the starting point actually of my research in this, where,

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I figured out a way to, introduce the third,

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party, et cetera interactions,

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which has to do with, first of all, thinking, well, the once,

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once you have many by many flows, and you're trying to solve for that,

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or you realize, well, the, the, the attractiveness force in,

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in a particular bilateral is of course relative to the attractive force

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of going to all the other possible, pairs. And so,

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this is solved in economic terms with a very simple kind of, idea about,

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well profit maximizing behavior by people that are trying to take advantage of

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price differences is going to be deal, do what we call arbitrage.

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And so spatial arbitrage is going to actually very strongly modify

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what, you know, just some raw forces, might be if you,

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if you forget about the third party interaction. So that was,

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actually then boiled down, into, it. Turns out,

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you can think of the multilateral part of this

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as, as there's two parts. So, so one is,

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on the, the, the seller's part. The seller can sell into a particular market,

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but also, into all these other possible third markets.

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And it turns out it was possible to sort of summarize that into what a second,

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effectively a two body problem again, because you could say, well,

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there's the market. I'm focused on how much I sell there.

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And then there's a kind of average of all the other,

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frictions that I face trying to reach all the other markets.

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And so that's, that's out outward multilateral resistance.

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And then on the buyer side, well, the same thing. You know,

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the attractiveness of buying from some particular,

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origin is relative to, well, I could buy, you know, similar,

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not exactly the same, but similar goods,

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from all those other possible origins. And so again,

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that's all captured in it now. It's,

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it's called inward multilateral resistance,

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and it's how hard it is to buy from all those other sources.

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And the balance of those two things is what actually enters into

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what the equilibrium is when the arbitrages,

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the people who are actually sort of doing all this calculation of how I can make

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money by switching a unit from, partner one to partner two,

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all of that stuff in equilibrium says there's no more profit to be made from any

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moving around. And, and so in the equilibrium,

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you then get this sort of nice insight,

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which says that the bilateral resistance,

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which is what we were started with originally with this sort of simple idea,

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now we can bring in the multilateral resistances.

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And it turns out it's actually a product. So it's, it's the,

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it's the bilateral resistance relative to the product of the inward and outward

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multilateral resistances that conditions how much you actually see bilaterally,

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in, in, in, in the, in the real world.

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And so then taking that model to data,

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then gives us a model that's economically satisfactory.

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Uh, and it turns out to have some important practical consequences too.

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Of course, as you might, as you might well imagine,

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after some years and years of, of, you know, people sort of using this,

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for various kinds of, of of flows, we had, this famous border puzzle,

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posed by, a, a famous paper by John McCallum. Uh,

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he was able to take advantage of very good,

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data on the trade of Canadian provinces, and the,

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the, where they went. So they would go to other provinces,

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but they also went to American states.

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And so this data was like very good quality data for reasons that have

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to do with how come they wanted to keep track of all this stuff inside Canada.

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Um, and so he then realized, well,

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I can take out distance by getting trade between

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a, a, a, a province and another province, and,

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and that same province and another American state that's the same distance away,

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basically. And so, so I'm now taking out all the huge effects, obviously,

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of distance and what's left over. Well, that's,

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that's a border effect. That's saying that just crossing that border.

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And, I don't know what, he actually expected when he, when he did this,

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but what he found was borders have a huge effect, which was like really,

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really puzzling because, you know, very, very similar countries,

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in a lot of ways the language is common, the legal origins are common,

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and they are neighbors and they understand a lot about each other, and so,

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and so well, why should we be getting this big, big border effect?

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Um, and then the,

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the origin of the paper we're talking about was that,

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a subsequent, working,

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working paper that I saw by, by Eric Van WinCo actually had,

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using the same kind of, gravity model that that McCall did,

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which was not a county for multilateral resistance.

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And so what he saw was from that, that,

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that if you did the same thing with the reverse flow American states,

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the Canadian provinces, and so now we're getting, you know, the,

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the reverse flow effect. Well,

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the border of effect was way, way, way smaller,

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like an order of magnitude smaller, 10 times smaller.

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And so this was like a huge additional puzzle.

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And then I realized that at that point, that I could,

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maybe combine, with Eric and,

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and we could tackle this problem appropriately using this idea that while they

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have these multilateral resistances that we are, are,

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are running around in there.

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And so that the paper in question figured out a way to

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actually calculate what those multilateral resistances are,

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which essentially they are,

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a trade weighted average of all the bilateral frictions where the trade weights

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are of course endogenous to the equilibrium. They're being determined,

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simultaneously with the whole equilibrium. So you, you,

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you actually had something that was a very important endogenous variable.

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These multilateral resistance had to be all worked out simultaneously in,

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in a way that was consistent with, economic theory and, and,

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what put the kind of EE econometric practice that we could use.

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And so we figured out a way to do that. Um, and what that did,

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was in a sense resolve the border puzzle.

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And so, the resolution of the border puzzle involves a key insight,

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which is after the fact. You sort of look at it and you, you say, well, gee,

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that's really obvious. So, so another regularity,

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of,

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in the data all also long known is that larger economic entities

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trade more when in their local markets than they do, markets further away.

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And so that's another very strong regularity. So you would say, well,

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now let's take the entities of the United States and Canada.

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The United States is an order of magnitude bigger than Canada.

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And so that means that the US naturally US states naturally are trading a lot

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more with other US states. Uh,

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that is the case with Canadian provinces trading with other Canadian provinces.

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And so once you see that, where you say, well, the, the, the,

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the multi multilateral resistance that Canadians face on their international

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interactions is gonna be way bigger because they inevitably have to do

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more of their trade outside of Canada over longer distances and crossing

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borders.

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And so the multilateral resistances are given a kind of very natural

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explanation for why they're so different between Canada and the United States.

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And so what had been the puzzling border effect was really just the effect of

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the relative size of countries on the multilateral resistances.

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And so we now had a kind of understanding,

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of why the multilateral resistances, you know,

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quite naturally have to differ quite a bit. Um, and, and so this was,

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this was, because the puzzle itself was considered so interesting,

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and there was always this feeling, well, gee, I mean,

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gravity works really well empirically, but we just don't understand why,

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you know, and so now we've got all of that kind of wrapped together in a, in a,

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in a nice,

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sort of understanding that that deepens really our understanding of how the

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world works. Obviously,

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tariffs are explicitly taxes posed at the border.

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Uh, there are various other kinds of, of rules and,

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and so on that, influence that and including,

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the fact that, you

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Know, border officials may be,

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doing things unfairly in a way favoring some,

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some kinds of transactions over others. Uh, and of course,

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there're differences that are less maybe susceptible to policymakers

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actively, you know, trying to do anything which nevertheless,

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maybe over more time you could think more about well harmonizing your

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regulations. Uh, so it's easier to, you know,

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sort of keep track of the,

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like the sanitary regulations and so forth. You know, you write,

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you write the rules in a way that everybody says, okay, well that's,

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we're all gonna keep track of things just that way.

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So then you can sort of see whether you've, you've, you know,

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improved trade just because of simplifying that stuff. So,

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so there's a lot of stuff that's maybe susceptible that isn't just attacks,

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but sort of acts like attacks.

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And then there's other stuff that probably you can't do much about. Uh,

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you know, that that whether you have a common language or not, you know,

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the common legal origins of laws. And so it's,

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it's just harder for businessmen to figure out if the laws are are different.

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So those, those things are, you know, much less susceptible and then,

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you know, what's left over. It's actually been a, you know, really,

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once we really understood better how to do this, it's,

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it's been quite an interesting, journey into, again,

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not in sense posing second order puzzles that are super interesting,

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like historically. Uh, one of the things that struck, struck me with was,

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the, the German, londa that,

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that were part of the ine of the 19th century,

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which precedes the creation of imperial Germany. That those, those,

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those londa or, or promises or whatever they were, you know, like originally,

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they, they actually all else equal, they trade more with each other than,

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than those who are, which were not mutually part of the ine.

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So there, there's,

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there's a lot of other historical things that sort of looked like that saying,

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boy, there's this incredible persistence that, you know,

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shows up in the data after you do your best to control for everything else.

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Well, that thing is still there. So, we've, we've,

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we've found pondering, the, the border, puzzle, you know, quite,

14:05.415 --> 14:09.765
quite, quite fruitful. And it's had effects on,

14:09.765 --> 14:14.245
thinking about, things like Brexit. Like Brexit.

14:14.505 --> 14:19.125
Brexit looked incredibly foolish from the point of view of gravity. Uh,

14:19.305 --> 14:24.045
you know, the, the idea that you're gonna make up, by, you know,

14:24.095 --> 14:27.885
doing trade deals with North America, what you're losing by getting out of the,

14:27.905 --> 14:30.205
the, the EU when, you know,

14:30.205 --> 14:34.565
roughly speaking North America is 10 times further away than, than is,

14:34.635 --> 14:37.285
than you say eu. I mean, this is, this is, you know,

14:37.285 --> 14:41.205
obviously a dramatic example, but, but less dramatic examples would be,

14:41.205 --> 14:44.525
you know, Scotland's, thinking of exit and,

14:44.545 --> 14:49.205
and or Catalonia thinking of exit. And, I guess,

14:49.505 --> 14:50.338
you know,

14:51.015 --> 14:55.125
Other things that are maybe forces for dissolution within the eu. So,

14:55.265 --> 14:56.805
so these are, and, and you know,

14:56.945 --> 15:00.245
of course it's less serious in the case of the United States. I mean,

15:00.265 --> 15:01.845
the Civil War seems to have settled,

15:01.845 --> 15:05.805
settled whether you can have secession or not. But, you know,

15:05.945 --> 15:08.325
it still comes up once in a while as this kind of, you know,

15:08.425 --> 15:11.525
pie in the sky type talk. But so,

15:11.665 --> 15:15.285
so understanding all this stuff about, about border effects, you know,

15:15.345 --> 15:19.205
has ramification interesting ramifications for lots of other,

15:19.525 --> 15:24.245
phenomena using demand structure to say, well, there's, there's a, a,

15:25.385 --> 15:28.325
an object that's easy to measure, which was your expenditure share,

15:28.325 --> 15:33.165
which would be be what you spend on the goods you're importing or buying

15:33.165 --> 15:37.085
from home divided by total expenditure. So that, that, that share,

15:37.085 --> 15:38.925
that budget share,

15:39.345 --> 15:42.525
is something to model as sensitive to price and,

15:42.525 --> 15:47.045
and the price that the buyer has to pay is re is going to have embodied in and

15:47.045 --> 15:49.765
all this sort of stuff with, with resistance to trade.

15:50.905 --> 15:54.175
So by writing a, a,

15:54.335 --> 15:59.055
a pretty simple restrictive kind of demand system, we were able to get, an,

15:59.195 --> 16:03.095
an expression which says, in equilibrium,

16:03.095 --> 16:06.895
what you should see in equilibrium would be that the, the,

16:06.995 --> 16:10.575
the share that you can observe would be,

16:12.055 --> 16:17.055
proportional to, well, the size of the origin country,

16:17.315 --> 16:21.775
that's coming in there. And then a second term, which,

16:22.035 --> 16:26.975
is decreasing in the relative resistance, which is the,

16:26.995 --> 16:30.815
the bilateral resistance divided by the product of inward and outward

16:30.815 --> 16:35.095
multilateral resistance. That turns out to be the equation. And so,

16:35.835 --> 16:40.295
we can then, you know, fit that equation, to, to data.

16:40.995 --> 16:43.015
And along with that,

16:43.065 --> 16:46.335
there are equations for what the multilateral resistances are.

16:46.615 --> 16:51.295
'cause the multilateral resistances are, well, for the, for the inward one,

16:51.525 --> 16:54.855
it's, it's, it's, it's the shares that you already got, the shares,

16:54.865 --> 16:56.815
those shares, which are of course moving around,

16:56.995 --> 17:00.255
but in equilibrium settle down into this form,

17:00.815 --> 17:05.575
relative resistance form tho those shares times, the, the,

17:05.675 --> 17:07.135
the friction,

17:07.195 --> 17:10.495
the bilateral friction from all the places that you're buying that,

17:10.725 --> 17:15.495
that turns out to be the, the outward multilateral resistance. And so it's,

17:15.765 --> 17:20.175
it's, it's something which is endogenous, to the equilibrium.

17:20.475 --> 17:23.135
So you have to, you know, estimate things, but,

17:23.235 --> 17:26.735
but you do it all kind of simultaneously. Um,

17:27.635 --> 17:31.615
and so, so, so there's, there's, there's, again, on the, on the,

17:31.615 --> 17:34.855
on the seller side, of course, there's an adding up condition that says,

17:35.155 --> 17:37.735
you know, my total sales have to get distributed everywhere.

17:38.435 --> 17:43.415
And so that gives you another sort of linear equation with shares in it,

17:43.585 --> 17:46.615
which you are then able to,

17:46.625 --> 17:48.895
manipulate in just the same way and estimate.

17:49.025 --> 17:54.005
And so our original, gravity with gravitas paper did, did that.

17:54.545 --> 17:59.045
And so doing it in that kind of complicated way was,

17:59.505 --> 18:03.085
useful at the time. Anyway, in emphasizing to everyone that, look, this,

18:03.235 --> 18:05.125
this is all like being, this,

18:05.155 --> 18:09.005
there's a simultaneous equilibrium here involving all these pairwise

18:09.005 --> 18:09.838
relationships,

18:10.105 --> 18:14.125
but boiled down into things that we can actually handle pretty easily.

18:15.225 --> 18:17.925
Um, it, it turns out that once that was well understood,

18:17.955 --> 18:22.085
then that's an unnecessarily cumbersome way of trying to estimate the whole

18:22.085 --> 18:25.245
thing. But that's, that's, that's another story.

18:25.945 --> 18:29.005
The puzzle was that if you, if you did this

18:30.665 --> 18:35.115
sort of gravity structure naively, where you just think about the border,

18:35.655 --> 18:36.305

18:36.305 --> 18:41.075
without worrying about the pieces of the border that our model

18:41.185 --> 18:44.715
lets you, you, you deal with, what you find is,

18:45.025 --> 18:49.355
that borders matter enormously more to smaller countries than to bigger

18:49.675 --> 18:54.515
countries. I mean, that was the original sort of issue posed by McCollum.

18:54.515 --> 18:57.115
And then the subsequent war corporate was sort of looking at the states,

18:57.255 --> 19:00.635
you know, trading with, with other states versus the provinces. So

19:02.585 --> 19:07.435
the understanding that we had, once we, you know,

19:07.435 --> 19:10.275
sort of get the results and think about it, the understanding that we had was,

19:10.275 --> 19:15.035
well, of course, outward multilateral resistance is, is this,

19:15.185 --> 19:18.955
this sort of trade weighted,

19:19.065 --> 19:23.955
average of all of the frictions involved in selling every place else.

19:24.305 --> 19:29.155
Well, your, your, your domestic frictions are there, of course,

19:29.675 --> 19:33.115
distribution, you know, is, is is costly everywhere, but, but your,

19:33.145 --> 19:38.115
your domestic frictions are systematically lower than the frictions to go

19:38.115 --> 19:40.355
long distances and also to cross borders.

19:40.895 --> 19:45.675
So all of that stuff gets put into this index that

19:45.735 --> 19:47.675
is an index, a number of,

19:47.735 --> 19:51.875
so the weights that sum to one times all of those frictions, well,

19:52.755 --> 19:55.875
a very powerful regularity then is, well,

19:56.565 --> 20:00.395
local markets are cheaper to serve, you know, there's less friction there. So,

20:00.455 --> 20:04.515
so local markets, the bigger they are, the bigger the share they're gonna have,

20:04.535 --> 20:08.595
and that's the lowest, that's the lowest friction. So,

20:08.855 --> 20:11.155
so you've got the biggest weight on the lowest friction.

20:11.175 --> 20:15.515
So big countries are going to have smaller multilateral resistances than our

20:15.515 --> 20:16.075
small countries.

20:16.075 --> 20:19.755
And that's just sort of built in to what it means to be big or small.

20:21.335 --> 20:26.075
So, you know, getting, getting this sort of right solution says, well, you, you,

20:26.175 --> 20:29.315
you, what you really wanna do to really understand the, the, the, the,

20:29.455 --> 20:33.035
the structure of trade is you want to take out that effect of those

20:33.035 --> 20:34.235
multilateral, I mean, they're,

20:34.235 --> 20:36.595
they're really important and interesting objects in themselves, but,

20:36.855 --> 20:40.355
but to sort of properly understand what's determining trade, you, you,

20:40.375 --> 20:44.115
you wanna be controlling for that, roughly speaking, you know, the,

20:44.135 --> 20:46.315
the Canadian border going out is,

20:46.415 --> 20:51.245
is is an enormously much bigger thing than the border for the US crossing

20:51.245 --> 20:55.165
back in. And so, well, it's the same border, so that that can't be right.

20:55.185 --> 20:57.605
You know, there's gotta be something just really,

20:57.605 --> 21:00.365
really wrong with that when it's an order of magnitude different.

21:00.785 --> 21:04.605
And now we get through multilateral resistance where you say, well, yeah,

21:04.605 --> 21:08.005
there's a very good economic reasons for exactly why that part is true.

21:08.675 --> 21:12.885
What happened, well to some extent at the,

21:12.885 --> 21:16.525
around the same time. Uh, and then subsequently, you can,

21:17.265 --> 21:20.285
you can apply, we, we applied it to trade flows,

21:20.665 --> 21:23.365
but you could apply the model to, to migration,

21:23.365 --> 21:28.205
which actually historically had been done back in the 1880s. And then,

21:28.865 --> 21:33.355
the, the modeling that,

21:33.575 --> 21:37.595
is done there often, although not necessarily, you know,

21:37.595 --> 21:39.355
a hundred percent necessary to do it that way,

21:39.375 --> 21:43.865
but often the modeling there was done with,

21:44.165 --> 21:48.105
the, the equivalent of shares, you know, they sum to one,

21:48.105 --> 21:50.905
they're all positive. The share is, is like probabilities.

21:52.005 --> 21:56.985
And so probabilities are useful in thinking about

21:57.025 --> 22:00.465
discreet choice, like, the, the, you know,

22:00.465 --> 22:03.865
people have different choices and different people make, you know, d different,

22:03.865 --> 22:06.385
different decisions. And we can say, well,

22:06.615 --> 22:10.105
from the point of view of the econometrician people that are otherwise equal,

22:10.525 --> 22:13.785
some of them make one decision, some make another. So, so this,

22:13.785 --> 22:14.985
this is the discrete choice.

22:15.135 --> 22:19.665
Like you get a probability that a person that is drawn from this

22:19.985 --> 22:22.905
distribution of people that you've controlled for all the things that would make

22:22.905 --> 22:24.225
them different. You say, well, okay,

22:24.725 --> 22:28.945
the rest of the heterogeneity is just because of stuff you can't observe that

22:28.945 --> 22:33.305
you think is random. And so discrete choice,

22:33.315 --> 22:34.745
means that you have a, a,

22:34.745 --> 22:39.305
there are these extreme value distributions that are used to describe those

22:39.305 --> 22:43.785
probabilities, and then we can fit those. And so we get a model which,

22:44.405 --> 22:48.785
actually has exactly the same kind of, of, structure that,

22:48.785 --> 22:49.705
that there's, there's,

22:49.775 --> 22:52.945
there's inward and outward multilateral resistance that the bilateral

22:53.265 --> 22:56.225
resistance, and that's all sort of built into a,

22:56.385 --> 23:00.825
a model that can fit the data very well. And so that's used for migration.

23:01.805 --> 23:06.625
Um, it's used for, you know, at least,

23:07.245 --> 23:11.265
not portfolio capital, but, but, to form direct investment that kind of,

23:11.265 --> 23:13.345
you know, specific capital. So that's,

23:14.085 --> 23:18.145
that's successfully treated with that same, that same model,

23:18.885 --> 23:23.555
and the use of this, which I've seen some people,

23:23.895 --> 23:27.555
you know, of course I get papers where people do this stuff. I mean, it's,

23:27.585 --> 23:32.445
it's very tempting to use this for the flow of ideas, and,

23:32.825 --> 23:36.525
you know, other sorts of, you know, cultural interactions and so forth.

23:37.145 --> 23:41.445
And again, the, the gravity model works, but it's,

23:41.715 --> 23:44.725
it's not exactly clear how all of those things can be

23:44.745 --> 23:49.165
Fit into this, this framework. Uh, and so there's people that,

23:49.945 --> 23:52.765
not me, I haven't actually gotten more than just, you know,

23:52.765 --> 23:56.325
kind of interested in, but you know, other people are, you know, they, I,

23:56.465 --> 24:01.125
I'm sure working on it because it's, it's, it, it's, it's kind of amazing how,

24:01.225 --> 24:05.285
how ubiquitous, this, this gravity,

24:05.615 --> 24:09.485
model of human interaction really is. Um, and

24:11.125 --> 24:14.085
I mean, it must have some limits where yeah, it's, it's a complete plus.

24:14.285 --> 24:17.565
I be surprised if it, if it doesn't, but, but it, boy,

24:17.565 --> 24:22.245
it works pretty darn well for all kinds of interactions. Um, you know, I,

24:22.705 --> 24:24.405
one of my examples is, you know,

24:24.485 --> 24:28.125
I interact more with the people that are on my side of the building. You know,

24:28.125 --> 24:31.205
we have one floor, the economics department, and a big building.

24:31.265 --> 24:34.365
And so I interact more with the people on my side than on the other side.

24:34.945 --> 24:37.205
All that well, you know, distance, you know,

24:37.205 --> 24:41.205
even though it's maybe a two minute walk across the building. So

24:42.715 --> 24:46.765
it's, it, it, it just works, you know, it's a very strong thing,

24:47.105 --> 24:49.165
and it's tempting to think that, well, okay,

24:49.165 --> 24:52.125
maybe some of these insights here could be useful somewhere else too.

00:00 - Well, it originated, of course, from Newtonian, physics for the, the two body problem where, the, the force between the two bodies is, proportional to the product of the masses and inversely proportional to the square of the distance between them. And that was a metaphor that was then taken to various

00:22 - economic interactions where it seemed like a reasonable sort of thing to say, well, there's a, there's a mass, maybe the size of the market or the, the number of people, at the origin of the destination. And then there's a distance between them. And then we realized there might be some other things as well as just purely physical distance that also affect this flow. But also in a kind of inversely proportional way, there's a sort of friction which limits it. And so it turns out that just using that metaphor, and lining it up with data,

00:54 - it actually works incredibly well for all kinds of interactions. migration, where there's the size of the population in the city of origin and the city of destination and distance between them, for goods, which actually came a bit later in terms of, you know, the historical, you know, applications of this sort of thing. and then the flow of, of capital between origin and destination. So all of these sorts of things, were telling us this is a really important empirical relationship. but there was, there was,

01:31 - actually always something a bit puzzling about it in terms of economics, because you, you would say, well, sure, that's, that's a good insight. I mean, we do know there's economic interaction and we know now it's empirically, you know, somewhat, it's actually not more than so much very extremely robustly connected in this way. So the, the problem was though that, well, we know that as in actually Newtonian physics, the two body problem is a very, very simple special case. And if there's a third body somewhere nearby, that's massive enough, it's certainly going to influence the trade between those two bodies.

02:09 - And at this point, the analogy with physics really breaks down because, what's known about the, the multiple body problem in physics gives you some very different kinds of structures. But for economics, we're sort of left with this puzzle. Well, we got this metaphor that we started with. It works well, but there's a problem with that because third party interactions are not somehow influencing that, that bilateral, interaction. And so, that was the starting point actually of my research in this, where, I figured out a way to, introduce the third,

02:47 - party, et cetera interactions, which has to do with, first of all, thinking, well, the once, once you have many by many flows, and you're trying to solve for that, or you realize, well, the, the, the attractiveness force in, in a particular bilateral is of course relative to the attractive force of going to all the other possible, pairs. And so, this is solved in economic terms with a very simple kind of, idea about, well profit maximizing behavior by people that are trying to take advantage of price differences is going to be deal, do what we call arbitrage.

03:30 - And so spatial arbitrage is going to actually very strongly modify what, you know, just some raw forces, might be if you, if you forget about the third party interaction. So that was, actually then boiled down, into, it. Turns out, you can think of the multilateral part of this as, as there's two parts. So, so one is, on the, the, the seller's part. The seller can sell into a particular market, but also, into all these other possible third markets. And it turns out it was possible to sort of summarize that into what a second, effectively a two body problem again, because you could say, well,

04:13 - there's the market. I'm focused on how much I sell there. And then there's a kind of average of all the other, frictions that I face trying to reach all the other markets. And so that's, that's out outward multilateral resistance. And then on the buyer side, well, the same thing. You know, the attractiveness of buying from some particular, origin is relative to, well, I could buy, you know, similar, not exactly the same, but similar goods, from all those other possible origins. And so again, that's all captured in it now. It's,

04:50 - it's called inward multilateral resistance, and it's how hard it is to buy from all those other sources. And the balance of those two things is what actually enters into what the equilibrium is when the arbitrages, the people who are actually sort of doing all this calculation of how I can make money by switching a unit from, partner one to partner two, all of that stuff in equilibrium says there's no more profit to be made from any moving around. And, and so in the equilibrium, you then get this sort of nice insight, which says that the bilateral resistance,

05:25 - which is what we were started with originally with this sort of simple idea, now we can bring in the multilateral resistances. And it turns out it's actually a product. So it's, it's the, it's the bilateral resistance relative to the product of the inward and outward multilateral resistances that conditions how much you actually see bilaterally, in, in, in, in the, in the real world. And so then taking that model to data, then gives us a model that's economically satisfactory. and it turns out to have some important practical consequences too. Of course, as you might, as you might well imagine,

06:01 - after some years and years of, of, you know, people sort of using this, for various kinds of, of of flows, we had, this famous border puzzle, posed by, a, a famous paper by John McCallum. he was able to take advantage of very good, data on the trade of Canadian provinces, and the, the, where they went. So they would go to other provinces, but they also went to American states. And so this data was like very good quality data for reasons that have to do with how come they wanted to keep track of all this stuff inside Canada. and so he then realized, well,

06:43 - I can take out distance by getting trade between a, a, a, a province and another province, and, and that same province and another American state that's the same distance away, basically. And so, so I'm now taking out all the huge effects, obviously, of distance and what's left over. Well, that's, that's a border effect. That's saying that just crossing that border. And, I don't know what, he actually expected when he, when he did this, but what he found was borders have a huge effect, which was like really, really puzzling because, you know, very, very similar countries, in a lot of ways the language is common, the legal origins are common,

07:29 - and they are neighbors and they understand a lot about each other, and so, and so well, why should we be getting this big, big border effect? and then the, the origin of the paper we're talking about was that, a subsequent, working, working paper that I saw by, by Eric Van WinCo actually had, using the same kind of, gravity model that that McCall did, which was not a county for multilateral resistance. And so what he saw was from that, that, that if you did the same thing with the reverse flow American states,

08:07 - the Canadian provinces, and so now we're getting, you know, the, the reverse flow effect. Well, the border of effect was way, way, way smaller, like an order of magnitude smaller, 10 times smaller. And so this was like a huge additional puzzle. And then I realized that at that point, that I could, maybe combine, with Eric and, and we could tackle this problem appropriately using this idea that while they have these multilateral resistances that we are, are, are running around in there.

08:40 - And so that the paper in question figured out a way to actually calculate what those multilateral resistances are, which essentially they are, a trade weighted average of all the bilateral frictions where the trade weights are of course endogenous to the equilibrium. They're being determined, simultaneously with the whole equilibrium. So you, you, you actually had something that was a very important endogenous variable. These multilateral resistance had to be all worked out simultaneously in, in a way that was consistent with, economic theory and, and, what put the kind of EE econometric practice that we could use.

09:23 - And so we figured out a way to do that. and what that did, was in a sense resolve the border puzzle. And so, the resolution of the border puzzle involves a key insight, which is after the fact. You sort of look at it and you, you say, well, gee, that's really obvious. So, so another regularity, of, in the data all also long known is that larger economic entities trade more when in their local markets than they do, markets further away. And so that's another very strong regularity. So you would say, well, now let's take the entities of the United States and Canada.

10:07 - The United States is an order of magnitude bigger than Canada. And so that means that the US naturally US states naturally are trading a lot more with other US states. that is the case with Canadian provinces trading with other Canadian provinces. And so once you see that, where you say, well, the, the, the, the multi multilateral resistance that Canadians face on their international interactions is gonna be way bigger because they inevitably have to do more of their trade outside of Canada over longer distances and crossing borders. And so the multilateral resistances are given a kind of very natural

10:50 - explanation for why they're so different between Canada and the United States. And so what had been the puzzling border effect was really just the effect of the relative size of countries on the multilateral resistances. And so we now had a kind of understanding, of why the multilateral resistances, you know, quite naturally have to differ quite a bit. and, and so this was, this was, because the puzzle itself was considered so interesting, and there was always this feeling, well, gee, I mean, gravity works really well empirically, but we just don't understand why, you know, and so now we've got all of that kind of wrapped together in a, in a,

11:28 - in a nice, sort of understanding that that deepens really our understanding of how the world works. Obviously, tariffs are explicitly taxes posed at the border. there are various other kinds of, of rules and, and so on that, influence that and including, the fact that, you Know, border officials may be, doing things unfairly in a way favoring some, some kinds of transactions over others. and of course,

12:03 - there're differences that are less maybe susceptible to policymakers actively, you know, trying to do anything which nevertheless, maybe over more time you could think more about well harmonizing your regulations. so it's easier to, you know, sort of keep track of the, like the sanitary regulations and so forth. You know, you write, you write the rules in a way that everybody says, okay, well that's, we're all gonna keep track of things just that way. So then you can sort of see whether you've, you've, you know, improved trade just because of simplifying that stuff. So,

12:38 - so there's a lot of stuff that's maybe susceptible that isn't just attacks, but sort of acts like attacks. And then there's other stuff that probably you can't do much about. you know, that that whether you have a common language or not, you know, the common legal origins of laws. And so it's, it's just harder for businessmen to figure out if the laws are are different. So those, those things are, you know, much less susceptible and then, you know, what's left over. It's actually been a, you know, really, once we really understood better how to do this, it's, it's been quite an interesting, journey into, again,

13:14 - not in sense posing second order puzzles that are super interesting, like historically. one of the things that struck, struck me with was, the, the German, londa that, that were part of the ine of the 19th century, which precedes the creation of imperial Germany. That those, those, those londa or, or promises or whatever they were, you know, like originally, they, they actually all else equal, they trade more with each other than, than those who are, which were not mutually part of the ine. So there, there's, there's a lot of other historical things that sort of looked like that saying,

13:50 - boy, there's this incredible persistence that, you know, shows up in the data after you do your best to control for everything else. Well, that thing is still there. So, we've, we've, we've found pondering, the, the border, puzzle, you know, quite, quite, quite fruitful. And it's had effects on, thinking about, things like Brexit. Like Brexit. Brexit looked incredibly foolish from the point of view of gravity. you know, the, the idea that you're gonna make up, by, you know, doing trade deals with North America, what you're losing by getting out of the, the, the EU when, you know,

14:30 - roughly speaking North America is 10 times further away than, than is, than you say eu. I mean, this is, this is, you know, obviously a dramatic example, but, but less dramatic examples would be, you know, Scotland's, thinking of exit and, and or Catalonia thinking of exit. And, I guess, you know, Other things that are maybe forces for dissolution within the eu. So, so these are, and, and you know, of course it's less serious in the case of the United States. I mean, the Civil War seems to have settled,

15:01 - settled whether you can have secession or not. But, you know, it still comes up once in a while as this kind of, you know, pie in the sky type talk. But so, so understanding all this stuff about, about border effects, you know, has ramification interesting ramifications for lots of other, phenomena using demand structure to say, well, there's, there's a, a, an object that's easy to measure, which was your expenditure share, which would be be what you spend on the goods you're importing or buying from home divided by total expenditure. So that, that, that share, that budget share,

15:39 - is something to model as sensitive to price and, and the price that the buyer has to pay is re is going to have embodied in and all this sort of stuff with, with resistance to trade. So by writing a, a, a pretty simple restrictive kind of demand system, we were able to get, an, an expression which says, in equilibrium, what you should see in equilibrium would be that the, the, the share that you can observe would be, proportional to, well, the size of the origin country, that's coming in there. And then a second term, which,

16:22 - is decreasing in the relative resistance, which is the, the bilateral resistance divided by the product of inward and outward multilateral resistance. That turns out to be the equation. And so, we can then, you know, fit that equation, to, to data. And along with that, there are equations for what the multilateral resistances are. 'cause the multilateral resistances are, well, for the, for the inward one, it's, it's, it's, it's the shares that you already got, the shares, those shares, which are of course moving around, but in equilibrium settle down into this form,

17:00 - relative resistance form tho those shares times, the, the, the friction, the bilateral friction from all the places that you're buying that, that turns out to be the, the outward multilateral resistance. And so it's, it's, it's something which is endogenous, to the equilibrium. So you have to, you know, estimate things, but, but you do it all kind of simultaneously. and so, so, so there's, there's, there's, again, on the, on the, on the seller side, of course, there's an adding up condition that says, you know, my total sales have to get distributed everywhere.

17:38 - And so that gives you another sort of linear equation with shares in it, which you are then able to, manipulate in just the same way and estimate. And so our original, gravity with gravitas paper did, did that. And so doing it in that kind of complicated way was, useful at the time. Anyway, in emphasizing to everyone that, look, this, this is all like being, this, there's a simultaneous equilibrium here involving all these pairwise relationships, but boiled down into things that we can actually handle pretty easily.

18:15 - it, it turns out that once that was well understood, then that's an unnecessarily cumbersome way of trying to estimate the whole thing. But that's, that's, that's another story. The puzzle was that if you, if you did this sort of gravity structure naively, where you just think about the border, without worrying about the pieces of the border that our model lets you, you, you deal with, what you find is, that borders matter enormously more to smaller countries than to bigger countries. I mean, that was the original sort of issue posed by McCollum.

18:54 - And then the subsequent war corporate was sort of looking at the states, you know, trading with, with other states versus the provinces. So the understanding that we had, once we, you know, sort of get the results and think about it, the understanding that we had was, well, of course, outward multilateral resistance is, is this, this sort of trade weighted, average of all of the frictions involved in selling every place else. Well, your, your, your domestic frictions are there, of course, distribution, you know, is, is is costly everywhere, but, but your, your domestic frictions are systematically lower than the frictions to go

19:38 - long distances and also to cross borders. So all of that stuff gets put into this index that is an index, a number of, so the weights that sum to one times all of those frictions, well, a very powerful regularity then is, well, local markets are cheaper to serve, you know, there's less friction there. So, so local markets, the bigger they are, the bigger the share they're gonna have, and that's the lowest, that's the lowest friction. So, so you've got the biggest weight on the lowest friction. So big countries are going to have smaller multilateral resistances than our

20:15 - small countries. And that's just sort of built in to what it means to be big or small. So, you know, getting, getting this sort of right solution says, well, you, you, you, what you really wanna do to really understand the, the, the, the, the structure of trade is you want to take out that effect of those multilateral, I mean, they're, they're really important and interesting objects in themselves, but, but to sort of properly understand what's determining trade, you, you, you wanna be controlling for that, roughly speaking, you know, the, the Canadian border going out is,

20:46 - is is an enormously much bigger thing than the border for the US crossing back in. And so, well, it's the same border, so that that can't be right. You know, there's gotta be something just really, really wrong with that when it's an order of magnitude different. And now we get through multilateral resistance where you say, well, yeah, there's a very good economic reasons for exactly why that part is true. What happened, well to some extent at the, around the same time. and then subsequently, you can, you can apply, we, we applied it to trade flows, but you could apply the model to, to migration,

21:23 - which actually historically had been done back in the 1880s. And then, the, the modeling that, is done there often, although not necessarily, you know, a hundred percent necessary to do it that way, but often the modeling there was done with, the, the equivalent of shares, you know, they sum to one, they're all positive. The share is, is like probabilities. And so probabilities are useful in thinking about discreet choice, like, the, the, you know, people have different choices and different people make, you know, d different,

22:03 - different decisions. And we can say, well, from the point of view of the econometrician people that are otherwise equal, some of them make one decision, some make another. So, so this, this is the discrete choice. Like you get a probability that a person that is drawn from this distribution of people that you've controlled for all the things that would make them different. You say, well, okay, the rest of the heterogeneity is just because of stuff you can't observe that you think is random. And so discrete choice, means that you have a, a,

22:34 - there are these extreme value distributions that are used to describe those probabilities, and then we can fit those. And so we get a model which, actually has exactly the same kind of, of, structure that, that there's, there's, there's inward and outward multilateral resistance that the bilateral resistance, and that's all sort of built into a, a model that can fit the data very well. And so that's used for migration. it's used for, you know, at least, not portfolio capital, but, but, to form direct investment that kind of, you know, specific capital. So that's,

23:14 - that's successfully treated with that same, that same model, and the use of this, which I've seen some people, you know, of course I get papers where people do this stuff. I mean, it's, it's very tempting to use this for the flow of ideas, and, you know, other sorts of, you know, cultural interactions and so forth. And again, the, the gravity model works, but it's, it's not exactly clear how all of those things can be Fit into this, this framework. and so there's people that, not me, I haven't actually gotten more than just, you know, kind of interested in, but you know, other people are, you know, they, I,

23:56 - I'm sure working on it because it's, it's, it, it's, it's kind of amazing how, how ubiquitous, this, this gravity, model of human interaction really is. and I mean, it must have some limits where yeah, it's, it's a complete plus. I be surprised if it, if it doesn't, but, but it, boy, it works pretty darn well for all kinds of interactions. you know, I, one of my examples is, you know, I interact more with the people that are on my side of the building. You know, we have one floor, the economics department, and a big building. And so I interact more with the people on my side than on the other side.

24:34 - All that well, you know, distance, you know, even though it's maybe a two minute walk across the building. So it's, it, it, it just works, you know, it's a very strong thing, and it's tempting to think that, well, okay, maybe some of these insights here could be useful somewhere else too.

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