Determining Exchange Rates: “Interest Rate Parity” and “Purchasing Power Parity” theories


Purchasing Power Parity comes in two
flavors: there’s absolute Purchasing Power Parity theory, and there’s relative
Purchasing Power Parity theory. We can speak of the goods prices
internationally and domestically being linked by the exchange rate, or we can
speak of inflation rates domestically and internationally being linked by the
exchange rate changes. One almost has to ask: what is the origin of this theory, so
that it could have been established and accepted for as long as it was accepted?
So we have the Purchasing Power Parity Theory rewritten: E equals P over P*,
which almost makes no sense as a theory determining the exchange rate. It makes
sense for each good for whom the price is being compared, but when we aggregate
from one good to all goods in the price index, it is hard to accept that the
exchange rate is determined by the price levels across international boundaries.
In fact we will easily come to the conclusion that the exchange rate is
determined by many things beyond the price levels of goods. So there are many
other variables or factors that belong in that exchange rate equation. One of my
major criticisms of purchasing power parity is that we cannot go from the
level of good being traded to the level of all goods in the Consumer Price Index.
It’s a fallacy of composition, but we get away with it if we make the assumption
that all goods in the country are tradable goods and you import everything
you consume, and you export everything that you produce. That is the most likely
scenario under which purchasing power parity will obtain. And certainly, if your
economy is a small economy, this certainly is an open economy if all of
your goods are being traded. But it is also a small economy.
It’s very likely that Purchasing Power Parity will apply reasonably well as
a theory of exchange rate determination. So I say that purchasing power parity
might hold at the level of a good that is traded, but we cannot generalize from
a single traded good or set of traded goods, to all prices of all goods in the
domestic Consumer Price Index. Here we have it then: you cannot easily compare
the U.S. CPI with the British CPI and expect that the ratio of these two CPI’s
will be the exchange rate. We have kind of a theory, but it is certainly not a
robust theory because of that fallacy of composition. Here is another perspective
on that: because all goods in the CPI of a country will not be tradable goods,
then as soon as the non-traded goods sector is large enough, and the prices in
the non-traded goods sector are determined by domestic demand and supply,
we move away from a theory of exchange rates being determined by the price
levels, because the non traded prices are weighted more heavily in that formula
determining the CPI. The larger is alpha, the more accurate is the assumption
concerning the domestic price level being approximated by traded prices or
correlating with traded prices. We therefore reiterate a point that PPP
works better when alpha is large, when the country is heavily dependent on
international trade. Interest rate parity: This is the asset equivalent of the law
of one price, which is another name for Purchasing Power Parity theory. The law
of one price effectively says that the price of a given good will be the same
all around the world adjusted by the exchange rate value. IRP theory states that
the return on equivalent assets internationally should be the same. Since
the returns on assets involve a time dimension, and asset investments require
foreign exchange rates to be considered, the simplest analysis compares two
countries and two assets. The assets here are going to be interest-bearing assets
domestically and internationally, and exchange rates today and exchange rates
in the future. The exchange rate in the future could be determined by a
speculative price, or it could be a forward market contract in the foreign
exchange market. So a forward contract will be different than a spot exchange
and therefore those would be considered two different assets. Again we are trying
to say the simplest analysis compares two countries, and two assets: the interest
bearing asset, and the exchange rate based asset. Here is how the analysis works. We
have an investor who can invest in a domestic interest bearing asset, so we
start in the upper left-hand corner. You can take your US dollars today and
invest them have some interest rate for a period such as one year, knowing the
interest rate and knowing what level of return you will obtain after one year. So
we have your dollar investment times 1 + i, where i is the interest rate
yielding the dollar amount to be received at the end of the contract
period. The alternative is to invest in a foreign asset, in which case the investor
has to convert her dollars into foreign currency, invest in the foreign asset and
at the end of the period reconvert her foreign currency back to domestic
currency. There’s risk if you cannot contract the price at which you trade
the foreign exchange – even if you know the the foreign interest rate. So we say
you have a sure thing – the domestic investment, and a risky thing – the foreign
investment. It need not be risky if the forward market price for foreign
currency is predetermined, but then the individual would have a clear decision
and the individual will allocate her portfolio across domestic and foreign
interest bearing assets based on her own desire to diversify. But if the returns
are all known, it really doesn’t matter where you invest. The better arrangement
here would be to have a risky foreign investment, so the investment might yield
of known return in the foreign country, but the risk would be the foreign
exchange risk. So instead of F1, we have E1 – the exchange rate in the future, and
since an exchange rate in the future does not exist today it would have to be
an expected exchange rate and that would be how we measure the riskiness of the
foreign investment. Working with the sure thing, the forward contracted investment,
we will be able to determine the equilibrium between domestic investment
and foreign investment, and if there is a disequilibrium, more resources will go to
the country that has the higher return and, like water finding its own level, the
interest rates will adjust so that the returns are the same. So, in the case of
Mexico in 1994, there was an inflow of funds into Mexico, and this is largely
NAFTA based. Mexico signed the NAFTA and effective January 1 1994, many US dollar
investments flowed into Mexico – there are several reasons for this. One
can say that the opening of the trade floodgates with the free trade agreement
would naturally result in an inflow of foreign currencies into the country
where the return on interest-bearing assets is higher, so the question arises:
why was the return on Mexican assets higher? Is it because Mexico artificially
pushed the rates up or alternatively the U.S. pushed its rates down? Or was it in
the foreign exchange markets that the disequilibrium occurred? One could say
based on this first equation that if in the case of – let Mexico will be the
domestic economy, so the left-hand side of our equation is the Mexican
investment return. So we’re saying that the return in Mexico is higher, and if
that is the case, there’s a “>” sign rather than “=” sign. The way to
fix that would be either to lower the interest rate in Mexico or to raise the
U.S. interest rate or to raise the F1 value or the expected E1 value. What does
it mean to raise the expected E1 value? It means that there’s an expectation
that a foreign currency will rise in price in the future ,so that the
expectation would have been that the US dollar would appreciate in value in the
future. People are investing in Mexico because they’re buying cheap US Dollars,
moving them to Mexico, expecting the price of the dollar to go
up, and they’re going to get a windfall of some sort on that appreciating US
dollar or depreciating Mexican peso. Come payday, the Mexican peso needs to go
down in value – there’s pressure for that to go down, so that the investors can actually
capture their higher return by investing in Mexico. You can almost say then that
the Mexican peso had to devalue because the Mexican interest rate was
sufficiently higher than the US interest rate. What we know happened is that the
U.S. started to raise this interest rate, and that sort of closed the gap so that
the equation came back towards an equilibrium. The rest of the equation
would be that the expectation that the dollar will increase in price will be
mitigated if the government in the US or the central bank is raising the interest
rate. Of course if the US government is going to raise the domestic interest
rate then monies would naturally flow back into the United States because the
return here is getting more attractive than it used to be. There are problems with
both Interest Rate Parity theory and Purchasing Power Parity theory. Notice
they only focus on prices and they never tell you the mechanism whereby the price
is determined. It’s sort of like focusing on the CPI without asking questions
about the quantities of goods that are being produced or bought, or focusing on
the Dow Jones Industrial Average without speaking to the amount of trade in the
stocks that is occurring. So these theories are what I would call
half-baked theories because they focus on prices as though there are “sui
generis” – as though these four prices are intricately related with no questions
being asked about where the prices are coming from. One has to remember that the
question as to where the price is coming from has to be addressed otherwise the
theory is not well articulated. So the bottom of our screen we have the risky
counterpart. The risky counterpart of interest parity is called Uncovered
Interest Rate Parity and the risk-free version is called Covered Interest Rate
Parity, because you’ve covered yourself with a forward market contract.

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