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The context of this discussion of exchange rate passthrough in
theory would be a discussion of the Real Exchange Rate.
So, what is the Real Exchange Rate?
Well, the Real Exchange Rate is the relative price of a basket of goods in one
country compared to another, after you've translated into a common currency.
So, if you look at this slide here, if I define the Real Exchange Rate as Q,
you get the price in some home country.
You can imagine that's the US, divided by the price level in a foreign
country times the exchange rate to convert that price level into dollars.
Well, of course, in this notation it would mean
that the exchange rate is the number of US dollars per foreign currency unit.
And PPP are the purchasing power parity
theory that would suggest this price levels are exactly the same.
It can be translated essentially as saying that the real exchange rate is equal
to one.
Now, most basic theories, things that you covered as undergrads,
presumably, that tried to put a little structure
on what would be the determinant of this real exchange rate.
This separate essentially, goods into traded and non-traded goods.
And if you do so, under the assumption of Cobb Douglas
preferences over those traded and non-traded goods,
you can see you get a price index of the kind that I'm circling here on the slide.
And so of course, you can inject that back into the initial equation and
basically divide up the real exchange rate into a traded component and
a non-traded component.
And, it's in that context that a lot of basic theories like
the way I teach undergrads or MBAs Balassa-Samuelson.
You assume that this first term,
this traded sector term is where the law of one price is most likely to hold.
If there is a place where PPP in theory would hold or law of one price better put.
You think it's in the traded sector where arbitrage would be an important
disciplining force.
So of course, it's a natural place to begin empirical analyses of how prices
vary across countries and that's that's sort of where we'll get going.
So if you take and focus just on that traded sector and
you think about a typical kind of passthrough relationship.
What you probably have in mind is this idea that the price of some
good z in country i, let's imagine country i is the US, so
you can think of this as the US dollar price at time t of that good z.
You want to relate it and under the law of one price would exactly equal,
that foreign price in country j of that good z,
translated into dollars by multiplying it by E.
And that of course, if you then take log differences, motivates a pass
through regression of the kind I'm circling here in the middle of the screen.
In principle,you should have something like the log change on the left hand side
of the import price if i is the US and it's an importer in dollars, let's say.
As a linear function, the sum of two linearly additive terms,
the log change in the exchange rate.
Well, remember this would be denoted as $1 depreciation given the way
we've defined the E, and the change in the price abroad.
And this exchange rate passthrough regression is of course implemented in
many different ways and
many different levels of aggregation using many different types of data.
Quite commonly the treatment of this foreign prices either ignored or
assumed away or proxied with a price index of some kind,
where then the passthrough coefficient of interest is this beta.
The idea that law of one price would imply a beta value equal to 1.
But a very long rich history has shown,
literature has shown that beta estimates are almost never at one,
particularly in the literature looking at passthrough into US import prices.
One of the puzzles, one of the interesting features is that in recent decades beta
has been estimated at being quite low, okay?
So that's, sort of the setting in which we're at.
Now, before I get into kind of how to think in theory about incomplete
passthrough, just want to motivate why we might care about it.
One is, anytime we're writing down a multicountry model and
in the end of today's section, for example, I'll describe such a model.
One of the ways that shocks transmit across countries is through prices.
And so understanding the nature of that transmission and the extent of that
transmission is important and of course very closely related to passthrough.
Passthrough rates are going to show up in frameworks on optimal monetary policy.
It's going to matter for
optimal trade policy if you wanted to put in a strategic tariff.
For example, or for
those that remember the discussion of border adjustment taxes in 2016 and 2017.
A critical issue in thinking about that public finance issue
was what was the degree of pass through.
And because as we'll get to in a second passthrough tells us something about
how when an exchange rate changes, marginal costs, and markups change.
It's also very closely related to understanding how globalization and
trade relates to competition, productivity.
And finally, the most sort of dry straightforward,
I don't mean dry in a negative sense, but
the most straightforward interest in exchange rate passthrough.
Might just come from an interest in understanding
a country's inflation dynamics.
If your country has an exchange rate movement and
you want to understand what that's likely to mean for your country's inflation,
obviously, you need to think about pass through, okay?
So the way I would start is with the most basic first
order condition that's going to come out of any super simple
static flexible price maximization problem.
Where a firm wants to maximize revenues, less costs by setting a price.
And you get this expression that the price P, and in this case, let's assume
it's the dollar price that an exporter would be setting on sales to the US,
is equal to some markup term here times the marginal cost expressed in dollars.
Again, I'm going to stick with the convention that E is the dollar price
of a unit of foreign-currency, such that MC then
would be the foreign-currency denominated marginal cost.
Now this markup of course,
is itself a function of the elasticity of demand for the good.
So it's the elasticity minus elasticity minus 1,
where this E or epsilon might be something like 2,
3, 4, a positive value.
Now, if you take log differences of this top expression,
then you get that the change in or you should really think of this as
the percentage change, because it's a it's a log change.
In the import price, is equal to the percentage change
in the markup plus the percentage change in the marginal cost
plus the percentage depreciation in the value of the dollar.
And you can essentially think of it this way,
that the percentage change in the import price relative to
the percentage change in the exchange rate is going to be equal to 1.
Unless there's some countervailing or
offsetting force imposed by changes in markups, or in marginal costs.
Why in theory, would there potentially be a change in markup in response to
a change in the exchange rate?
Well, imagine that the dollar, it depreciates and
you're a Japanese exporter to the US, so the yen is strengthened.
Well then all else equal, you're much less competitive in the US market or
else equal your good will now cost more, your market share might go down.
And in a lot of demand systems in order to preserve the maximal level of profits,
you'll want in response to that to lower your markups,
to charge a more competitive price.
Therefore, you can imagine that this term would be negative.
Why might the marginal cost change in response to the exchange rates movement?
There's really two key issues that I'll get to in a second.
One would be if you happen to be an importer of goods that are used as
inputs into production.
Imagine that Japanese exporter was also an importer of
intermediate inputs from the US.
Well, then it's true that the yen's appreciation,
that I just used as an example, would kind of hurt them on the export side.
But it would also potentially lower the price of their intermediate inputs,
therefore offering some offset there.
Another reason why the marginal cost might move with the exchange rate is just if you
have non-constant returns to scale.
If the exchange rate moves and your price and
therefore your quantity is going to move all those equal.
And you either have an increasing or
decreasing marginal cost of production at that point in the production schedule,
well then that's yet another force that will matter for pesto.
Okay, so if there's no change in markups, no change in marginal costs,
in a static flexible price world, you'll have passthrough equal to 1.
Incomplete passthrough again, when we have a flexible prices sort of static setting,
it can be attributed to this change in marginal cost or
change in the markup co moving with the exchange rate.
So how do you generate such co movement?
Here I'm going to have to largely just give you a bunch of references and
suggests that those that haven't worked in this area, but
want to embed this sort of dynamic in their work.
What I would recommend is that you go through some of these different
frameworks and derive the elasticity of demand that emerges yourself.
And you'll be able to, from that elasticity of demand,
determine if markups will be variable or not.
And therefore, if that channel can lead to incomplete pass through or not.
So the most standard, I would argue, are one of the most standard demand setups in
these frameworks is a CES demand framework.
I'm going to assume everyone knows what that means.
But here you can see I've written it as,
imagine you have CES demand over varieties v or sectors v.
Well these sectors each have an elasticity of demand for
their goods equal to sigma, and precisely sigma, where sigma is a parameter.
So as a result whether one of these v's gets more or less expensive,
increases or decreases its market share, the demand for
it will still be characterized by an elasticity of sigma.
And therefore the optimal markup will not change,
the markup would be set at sigma over sigma -1, and that's it, okay?
So that's not a system that would lead to variable markups,
other systems through that do, I would start with a nested CES demand system.
Imagine we kept the same structure at the sector level where v is a sector.
But we allowed each v each good or sector v to itself be
a CES aggregation over let's call them varieties z,
that's why it's called the nested CES.
Where the elasticity is differ in this case,
the inner nest has an elasticity of theta, the outer nest has an elasticity of sigma.
And you'd most naturally think of sigma by the way as lower than theta.
because you might think of sigma as governing the elasticity between
buying automobiles and healthcare and real estate.
Whereas theta would be about the elasticity of goods within healthcare or
within real estate, or within education.
And so, that difference between sigma and theta in these models
generates a formula like this, for the elasticity of substitution.
Where you get that it's variable and
is essentially a weighted average of the two elasticities where
the weight here s of z is the market share of that good z in that sector v.
You get a slightly different weighted average if you assume quantity competition
versus price competition.
But the point is this is a model where, when the exchange rate moves,
a firm's position in its market will change.
Its elasticity will therefore change and its markup will therefore change, okay?
If I asked you to take any paper and sort of derive it, pen and paper,
as an exercise and make sure you could derive yourself,
these elasticity is to really deeply understand where all this comes about.
I would refer you to Atkeson and Burstein in 2008,
the very last page of my slides gives the full references for all these.
And a very minor aside, this was the genesis of my job market paper.
For those that are looking for inspiration, I tried to literally derive
every single expression in Atkeson and Burstein when it was a working paper.
And only in doing that did I get some ideas that ultimately literally became my
job market paper.
Linear demand is another form of demand that will lead to a variable elasticity of
demand and variable markups.
This is what a linear demand system looks like and I would refer you
to the Melitz and Octaviano paper as a great source to try to drive that.
See the advantages or disadvantages of generating variable markups that way.
Bergen and
Feenstra is a nice example of how to do it in a symmetric translog system.
Klenow and Willis in 2016, sort of have an implementation of the kinked
demand system from Myles Kimball's work I think from 1995.
Again that's going to generate an elasticity that changes over based on
the firm's position in the market and therefore generates variable markups.
I think Gopinath, Istkhoki and Rigobon, is a very nice implementation
of that demand structure to generate incomplete passthrough.
Getting toward the end, but I want to just quickly note again that, in addition to,
variable markups generating incomplete passthrough,
variable marginal costs can generate incomplete passthrough.
I should say variable marginal costs are marginal costs that vary with
the exchange rate.
So one way that this can occur, of course,
is if you have simply non-constant returns to scale, so that's an easy one.
But then also, imagine that the firm, as I mentioned,
that's exporting is also importing.
And so its marginal cost is not only a function of its own country's wage,
but also of the foreign countries wage,
that's producing the good that it uses as an input.
And if you imagine that they combine domestic and foreign inputs in
a Cobb Douglas sort of way with an output, or Cobb Douglas output elasticity beta.
You get something like this, in this setup holding wages fixed,
but allowing the exchange rate to vary.
You'd get a change in the marginal cost of beta- 1,
which since beta ranges between 0 and 1, is a negative number.
So of course, this means that even if markups didn't move,
you had a CES structure.
If you allow for intermediate inputs to be imported from abroad,
you can get passthrough to be less than 1 or
in the case I just described equal essentially to beta.
Now everything I just described is in a flexible price static setup
where prices are constantly changing in the real world.
So of course quite important to think about price stickiness for passthrough.
Historically, we thought of a world where exporters always set their
prices in their own currency.
And therefore, during the period in which their prices were sticky in their own
currency that's something called Producer Currency Pricing or PCP.
Passthrough by definition by construction would equal 1.
An alternative that became popular in models after people observed
that the US dollar share of imports into the US was quite high was LCP.
Which is when you think of the prices being sticky in the country to which
you're selling.
In that case, over the period of time that you don't change,
the sticker price of the good passthrough necessarily is zero.
Then finally there's been a lot of recent work, particularly by Gita Gopinath and
co authors describing as Dominant Currency Pricing.
The idea that maybe a dominant currency in this case,
they have in mind the US dollar is what most goods are invoiced in.
Then of course, it's an intermediate range, right, it's not just 0 or 1.
It sort of depends on how that country's bilateral exchange
rate with the dollar moves.
Because I'm a little bit low on time and
want to make sure that Alberto can tell you more about the data.
Just kind of wannna note that in a dynamic setting, even above and
beyond the price stickiness issues I just described,
many other factors can play in and causing complete passthrough.
On the previous slide I mentioned things like real rigidities and
strategic complementarities.
Imagine my prices change in even months, but
Alberto is a competitor firm whose prices change in odd months.
Well then we might want to limit the extent to which we fully achieve our ideal
price, because we don't want to have our relative prices move too quickly
relative to each other.
One might expect mean reversion in the exchange rate shocks, which in
a dynamic setting with some price rigidity could cause incomplete passthrough.
There's also investment style models, things that are worth exploring
that can cause exchange rate passthrough to be intermediate.
Where perhaps you want to have a cheap price in the beginning of the life of
the good to gain market share and then increase it later.
So let me wrap up just with this final reference list for future readings.
But for those that are interested in deriving those elasticities I mentioned
earlier I believe they're all listed here.
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