Under the theory of Purchasing Power Parity, the change in the exchange rate between two countries currencies is determined by the change in their relative price levels locally that are affected by inflation. It is generally agreed that this theory mostly holds true over the long run, but economists have found that it can suffer distortions over the short term because of trade and investment barriers, local taxation, and other factors.

As a result of this relationship, one can expect the currencies of countries with higher inflation rates to weaken over time versus their peers, whereas currencies of countries with lower inflation rates tend to strengthen. In economies with weak production of local goods and services, the depreciation of the local currency can at times even be accelerated by the "pass-through effect" of importing foreign goods with relatively higher prices.

When a country‘s inflation rate rises relative to that of another country, decreased exports and increased imports depress the high-inflation country‘s currency because of worsening trade and current account balances. Purchasing Power Parity (PPP) theory attempts to quantify this inflation-exchange rate relationship.

## Interpretations of PPP

• The absolute form of PPP is an extension of the law of one price. It suggests that the prices of the same products in different countries should be equal when measured in a common
• The relative form of PPP accounts for market distortions like transportation costs, labor costs, tariffs, taxes, and quotas. It states that the rate of price changes should be similar.

## Rationale behind PPP Theory

Suppose U.S. inflation > U.K. inflation.

->U.S. imports from U.K.

­ U.S. exports to U.K., and U.S. current account

Downward pressure (depreciation) is placed on the \$. This shift in consumption and the \$‘s depreciation will continue until

in the U.S.: price U.K. goods ≥price U.S. goods

and in the U.K.: price U.S. goods ≤ price U.K. goods

## Derivation of PPP

Assume that PPP holds. Over time, as inflation occurs exchange rates adjust to maintain PPP: Ph1 → Ph0 (1 + Ih)

Where Ph1=home country‘s price index, year-1 end Ih =home country‘s inflation rate for the year

Pf1→ Pf0 (1 + If )(1 + ef ) where Pf = foreign country‘s price index

If = foreign country‘s inflation rate ef = foreign currency‘s % in value

If PPP holds Þ Ph1 = Pf1 and Ph0 (1 + Ih ) = Pf0 (1 + If ) (1 + ef )

Solving for ef = (1 + Ih ) / (1 + If ) -1

Ih > If Þ ef > 0 i.e. foreign currency appreciates Ih < If Þ ef < 0 i.e. foreign currency depreciates Example: Suppose IU.S. = 9% and IU.K. = 5% .

Then e £ ={ (1 + 0.09 ) / (1+0.05)}– 1 = 3.81%

When the inflation differential is small, the PPP relationship can be simplified as ef @ Ih – If

## Graphic Analysis of Purchasing Power Parity

Testing the PPP Theory Conceptual Test

Plot actual inflation differentials and spot exchange rate changes for two or more countries on a graph. If the points deviate significantly from the PPP line over time, then PPP does not hold.

## Statistical Test

Apply regression analysis to historical exchange rates and inflation differentials:

ef = a0 + a1 [ (1+ Ih)/(1+ If) – 1 ] + m

Then apply t-tests to the regression coefficients (Test for a 0 = 0 and a 1 = 1.) .If any coefficient differs significantly from what was expected, PPP does not hold.

Empirical studies indicate that the relationship between inflation differentials and exchange rates is not perfect even in the long run. However, the use of inflation differentials to forecast long-run movements in exchange rates is supported. A limitation in the tests is that the choice of the base period will affect the result.

PPP does not occur consistently due to confounding effects, and a lack of substitutes for some traded goods. Exchange rates are also affected by differences in inflation, interest rates, income levels, government controls, and expectations of future rates.

PPP can be tested by assessing a ―real‖ exchange rate over time (e.g., crawling pegs). The real exchange rate is the actual exchange rate adjusted for inflationary effects in the two countries of concern. If the real exchange rate follows a random walk, it cannot be viewed as being a constant in the long run. Then PPP does not hold.