Financial Market Integration A Summary of Parity Conditions 1

Covered Interest Parity Covered interest parity is a condition that relates interest differentials to the forward premium or discount. It begins with the interest parity condition: (1+R) = (1+R*)(F/S) The condition can be rewritten, and with a slight approximation, yields: R - R* = (F-S)/S. Daniels and VanHoose Real Interest Parity

Uncovered Interest Parity UIP is a condition relating interest differentials to an expected change in the spot exchange rate of the domestic currency. If a savings decision is uncovered, the individual is basing their decision on their expectation of the future spot exchange rate. The expected future spot exchange rate is expressed as Se+1. Daniels and VanHoose Real Interest Parity

Uncovered Interest Parity Using this expression for the expected future spot rate, UIP can be written as: R – R* = (Se+1 – S)/S. In words, the right-hand-side of the UIP condition is the expected change in the spot rate over the relevant time period. Daniels and VanHoose Real Interest Parity

The Fisher Effect The Fisher Effect is a condition relating interest rates and prices. It postulates that the nominal interest rate for a given time period is equal to the real interest rate plus the rate of inflation that is expected to prevail over that period. i = r +  Daniels and VanHoose Real Interest Parity

The Fisher Effect Let d denote the rate for the domestic country and f denote the rate for the foreign country. id = rd + Ed and if = rf + Ef Then id - if = (rd - rf) + (Ed - Ef) If the real rate is constant and equal across both countries, id - if = Ed - Ef Daniels and VanHoose Real Interest Parity

ex ante PPP Recall that relative PPP is: So = d - f Then ex ante PPP is: ESt = Ed - Ef So ESt = Ed - Ef = id - if Daniels and VanHoose Real Interest Parity

Real Interest Parity Using, ESt = Ed - Ef = id - if, we can focus on the last two terms to form the real interest parity condition. Adding if to each side and subtracting Ed from each side of the equation we have: (id - Ed) = (if - Ef). That is, when parity holds, real interest rates are equal across countries. Daniels and VanHoose Real Interest Parity

Real Interest Parity Again, using ESt = Ed - Ef = id - if, we can also write an expression relating the real exchange rate to the real interest rate by subtracting the middle term from each side. ESt - (Ed - Ef) = (id - Ed) - (if - Ef). That is, the real interest differential should equal expected real exchange rate movements. Daniels and VanHoose Real Interest Parity

Feldstein - Horioka Savings and Investment Relation Based on a closed economy income condition: y = c + i + g. Rearrange as: y - c - g = i. Daniels and VanHoose Real Interest Parity

Feldstein - Horioka Rearranged as: y - c - g = i. Note that y - c - g equals savings, s. Then: s = i. In a closed economy, domestic investment must correlate with domestic saving. Correlation coefficient would be significant close to unity in value. Daniels and VanHoose Real Interest Parity