Now, let's consider something called the gravity equation,
and this is aimed toward trying to understand
why the costs of trade are often so high.
We have something called the gravity equation in physics,
and this is stipulating, among other things,
that the further away two objects are from each other,
the weaker the attraction.
For economics, our gravity equation is going to say,
"The further away our two countries, the weaker the trade attraction."
Now, let's consider a very simple form of a gravity equation
just so you get a sense of how it works.
On the left-hand side, we have trade which is what we're trying to explain.
That's the quantity of trade,
and it's between nations I and nations J as represented by the subscripts here.
On the right-hand side, you can, in simple versions,
treat this G as a simple constant.
On top, you have M sub I x M sub J.
Think of that as the size of one economy multiplied by the size of the other.
So, in general in gravity equations,
the larger the economy's you're dealing with,
the less distance is going to matter.
And then on the bottom, we have D, the all-important distance,
and that's the distance between country I and country J,
again, represented by the subscript here.
As a distance increases, trade does go down,
but in more complicated forms of a gravity equation,
this is often something exponential.
So you could imagine it being D squared, or D to the 1.25, or whatever,
and those would indicate that, as distance increases,
the possibility of trade is increasingly decaying,
the costs of trade are becoming increasingly larger at a faster rate.
Empirically, consider this graph here.
The horizontal axis is basically telling you
how large a country is in economic terms.
The vertical axis is basically telling you
how much that country trades with the United States.
As shown here, well, which are the two countries
trading the most with the United States?
There is Canada and there is Mexico.
But if you ask how large are those economies,
well, they're not especially large compared to a lot of other places.
Why are they trading so much with the United States?
Well, it seems at least one big reason is because they are so close.
If you're wondering how gravity approaches fit into
the broader picture of international trade,
they are actually consistent with a lot of different international trade theories
such as increasing returns or the Heckscher-Ohlin theorem.
So finding for the importance of gravity doesn't rule out
the relevance of any of these theorems,
but, still, it can be said, to the extent, that gravity theories of trade matter.
That means an underlying model of international trade
probably does require some specialization,
because if trade costs are really that high,
well, then you need specialization to be getting trade off the ground at all.
And let's take a look at just how high the costs of trade seem to be
in the gravity literature,
and let's start with industrialized countries.
To take one known estimate, again, for developed nations
from Anderson and Wincoop,
the costs of trade across borders are on average about 170%.
Of that sum they estimate that about 21% is transportation costs, --
about 44% is border-related costs;
having to deal with paperwork, or bureaucracy,
or tariffs, or different cultures, or different regulatory standards.
And, indeed, breaking down that 44%, they find 8% of policy barrier,
7% of language barrier, 14% of different currency barrier,
6% in information cost barrier, 3% to security barrier,
but, again, these are just averages, these are examples giving you
one way of thinking about where some of these gravity costs come from.
Finally, again, according to Anderson and Wincoop,
55% of that 170% is coming from retail and wholesale margins
as trade crosses barriers.
By the way, if you're wondering how that all adds up,
you can see it's given by this equation here.
One quite striking result we learn from the gravity literature
is that, overall, tariffs are a relatively small barrier to trade
especially once we get past agriculture
or outside of the very most protectionist countries such as North Korea.
Overall, most of the costs of international trade
come from other obstacles in having to cross borders.
And you'll know those numbers come from developed countries
which, on average, tend to be more efficient and better at trading.
For developing countries, trade costs can actually be at least two times higher.
We also find empirically that trade costs vary with the product line
and they can vary by a factor of ten or more.
It really does depend what you're trading
and these numbers are just estimates, just averages.
Early in this video, we offered a very simple form of a gravity equation,
but, actually, the more accurate forms of gravity equation
define distance costs relative to available alternatives.
So let's consider a comparison here, using data from the 1990s,
and on one side of the comparison stands Australia and New Zealand,
and on the other stands Austria and Portugal, both of course in Europe.
Comparing these four nations,
while Australia and New Zealand are roughly the same distance apart
as are Austria and Portugal.
Furthermore, if you're taking the product of the size of the economies
or the GDPs,
again, this comparison you will get something pretty close to equality.
And yet, there's quite a striking truth here.
In 1993 Australia-New Zealand trade is about nine times greater
than the trade between Portugal and Austria.
Why is that? Well, Austria and Portugal are both located in Europe
and they have nearby a lot of other countries to trade with.
Australia and New Zealand are much more isolated, relatively speaking,
in the Pacific, and thus they end up trading much more with each other
because they have fewer other natural trade partners.
Here's the comparison.
Let's take within the United States the average of state to state trade.
And we're going to divide that by the average state to province trade
where, by province, we mean Canadian province.
And, on average, that figure is about 1.5.
So that means a given US state is more likely to be trading
with another US state than with a Canadian province,
but only by about 50%.
From a Canadian perspective, a similar ratio will look quite different.
So let's take the average province to province trade,
and this is within Canada, and divide that by the average state,
meaning US state to Canadian province trade.
And there the ratio is much larger.
It's quite striking, it's going to be 16.4 times higher.
That is a given Canadian province is way more likely to be trading
with another Canadian province than with a US state.
But why are these two ratios so different?
Consider some comparative statics.
Say we start with the case where there are no costs of trade at all across borders,
and then we introduce some kind of trade barrier
which makes it harder to consummate these exchanges.
As a result,
both Canada and the United States would trade more with themselves,
that is, they would trade more internally rather than exporting and importing,
but, in proportional terms, this is going to be a larger effect
for the smaller, more open economy, namely Canada.
This is part of a broader and more general truth
that simply any increase in trade costs will have a larger impact
on the smaller and more open countries.
Let's think this through with a simple example using tourists.
Here's the US-Canada border as represented at Niagara Falls.
Right now it's pretty easy to cross that border,
but let's say it became a lot more difficult,
the lines were longer, or a passport cost more to get,
or security procedures would be tougher.
How would this have differential effects on the United States and Canada?
Well, the United States is a larger economic unit,
so it's the case that, in proportional terms,
we have more United States citizens taking their vacations already
within the United States.
So if passport costs go up, this has a moderate effect,
but actually tourist sites in the United States
do not become that much more crowded.
Canada is a smaller and more open economy,
so, proportionally speaking, more of its citizens are traveling abroad.
If passport costs go up, more of those citizens stay in Canada,
and that will make Canadian tourist sites much more crowded.
So here we have higher passport costs,
meaning that Canada gets much more internal tourism
or you could say much more internal trade,
and the higher passport costs mean the United States,
the larger country economically speaking,
is only getting a bit more internal tourism and a bit more internal trade.
That's all just another way of thinking about how the gravity equation works.
Another way to put this is simply to note that,
in more sophisticated forms of the gravity equation,
relative trade barriers are what matter, not just absolute distance.
For core readings on the gravity equation and how it's applied,
I would very much recommend all of these sources
the bottom being you can simply Google gravity equation trade.
Here are also some other reasons on the gravity equation approach.
These are important articles,
but they're also more technical or more difficult,
and I would recommend them only to more advanced students of this topic.