# What is the difference between the international Fisher effect and uncovered interest rate parity?

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As far as I can tell, these two are the same. What is the difference? (Is the former a statement without taking expectation over future exchange rate, and thus, a stronger prediction?)

They are related and have very similar implications but they are not the same. I will try to provide simple explanation here for more nuance you can have look at for example Mogaji (2019) and sources cited therein.

Uncovered interest rate parity (UIP) says that the ratio expected exchange rate $$E_t[S_{t+k}]$$ to spot exchange rate $$S_t$$, has to be equal to nominal interest rates between home $$i$$ and foreign $$i_f$$ country.

$$\frac{E_{t}(S_{{t+k}})}{S_{t}} = {\frac {(1+i)}{(1+i_{f})}} \implies E_t [\Delta S] \approx i - i_f$$

This is based on the idea that there should be no possibility of arbitrage (riskless profit) in the market resulting from different nominal interest rates.

For example, if interest rate in US would be $$10\%$$ and interest rate in UK would be $$5\%$$ and if exchange rate would be exactly $$1{\\\}=1£$$, anyone who could would stop saving in UK and just transfer all their savings into US. However, to do so they have to go through forex market and by creating new demand for USD they should change exchange rate sufficiently enough to eliminate the arbitrage opportunity.

The UIP simply posits that due to this possibility the ratio between expected exchange rate and spot exchange rate must be equal to the ratio of interest rates otherwise people would start entering forex market and making trades that would force the above parity hold true.

International Fisher effect (IFE) is based on the idea that ultimately exchange rate must reflect differences in price levels between two countries the expected change in exchange rate must reflect the relative differences in expected inflation rates between two countries ($$E_t[\pi]$$ and $$E[\pi_f]$$), since if change in price levels between two countries would not be balanced there would be arbitrages in goods market and violations of the law of one price. Hence we should have:

$$E_t[\Delta S_t] \approx E_t[\pi] - E_t[\pi_f]$$

Now in turn by Fisher equation the rate of inflation is approximately equal tot he difference between nominal ($$i$$) and real $$(r)$$ interest rate $$e_t[\pi] \approx i-r$$. Furthermore, IFE assumes that due to perfect capital mobility the real interest rate must be everywhere equal $$r=r_f$$. Well given these assumptions we will find out that change in the exchange rate should be given by change in nominal interest rates since:

$$E_t[\Delta S_t] \approx E_t[\pi] - E_t[\pi_f] \approx i-r - (i_f-r_f) \approx i - i_f$$

Hence there are subtle differences between these theories as the mechanisms in UIP and IFE are different. UIP is based on an idea of impossibility of arbitrage in money market. IFE is based on the idea that there cannot be arbitrage in goods market.

Sometimes two different theories might predict the same outcome, this is known in science as observational equivalence. Observational equivalence does not necessarily mean there is no difference between two theories as two different mechanisms can sometimes give rise to same outcome.

• "UIP is based on an idea of impossibility of arbitrage. IFE is based on the idea that..."---both are no-arbitrage conditions, though, just for different markets: international "money market" vs. goods market. – Michael Nov 21 '20 at 15:11
• @Michael you are right I actually mentioned that in the body but screwed the summary - I edited it now. Thanks for your useful comment! – 1muflon1 Nov 21 '20 at 15:14