One theory, called purchasing-power parity, holds that currencies will move in line with the prices of tradable goods.
Thus if purchasing power parity holds, the three series must be cointegrated.
Their findings in both papers coincide with Sonora's: absolute price parity holds in the long run.
However, if purchasing power parity holds then there is a stable, long-term relationship between the price levels in the two countries when expressed in terms of a common currency.
This relationship can be employed to test whether uncovered interest rate parity holds, for which economists have found mixed results.
If uncovered interest rate parity holds, such that an investor is indifferent between dollar versus euro deposits, then any excess return on euro deposits must be offset by some expected loss from depreciation of the euro against the dollar.
When both covered and uncovered interest rate parity (UIRP) hold, such a condition sheds light on a noteworthy relationship between the forward and expected future spot exchange rates, as demonstrated below.
When both UIRP (particularly in its approximation form) and purchasing power parity (PPP) hold, the two parity conditions together reveal a relationship among expected real interest rates, wherein changes in expected real interest rates reflect expected changes in the real exchange rate.
