Topic 3: Purchasing Power Parity and Real Interest Rate Parity

Question 1

Why study PPP?

Answer 1

i) undervaluation/overvaluation
ii) use the PPP-implied exchange rate to compare job offers in different currencies if maintaining lifestyle is important

Question 2

$ price level at t, P(t, $)

Answer 2

The $ price of a typical consumption bundle of N goods and services

Question 3

Changes in the $ price level from t to t+1

Answer 3

𝑃(𝑡+1,$) /𝑃(𝑡,$) = [1 + 𝜋(𝑡 + 1,$)]
→ 𝝅(𝒕 + 𝟏,$)= 𝑷(𝒕+𝟏,$) – 1

If that number is +ve, means inflation
If that number is -ve, means deflation

If inflation, you have to pay more nominal money.

Question 4

Internal purchasing power of $1 in U.S. at t:

Answer 4

$1 x (1/ 𝑃(𝑡,$)) consumption bundle

Question 5

External purhchasing power of $1 in U.K. at t:

Answer 5

$1 x [1 / S(t, $/£)] x [1 / 𝑃(𝑡,$)] consumption bundle

Question 6

Absolute PPP

Answer 6

the equilibrium spot exchange rate
(Sppp(t, $/£)) is obtained when
(Sppp(t, $/£)) = 𝑃(𝑡,$) /𝑃(𝑡,£)

Question 7

Goods market arbitrage

Answer 7

If S(t, $/£) ≠ Sppp(t, $/£) on the FX market, buy the consumption bundle from the country with a cheaper price and export it to the country with a higher price

Question 8

Relative PPP

Answer 8

exchange rates will change in response to differences in inflation across countries

Question 9

Relative PPP interpretation

Answer 9

If 𝝅 𝒕 + 𝟏, $ > 𝝅 𝒕 + 𝟏, £ , then 𝐒(𝐭 + 𝟏, $/£) > 𝐒(𝐭, $/£).

In words, a currency with a higher inflation ($) from t
to t+1 depreciates from t to t+1 against a currency with a lower inflation (£) from t to t+1

Question 10

Real exchange rate for $/£ at time t

Answer 10

RS(t, $/£) =
[𝑷(𝒕,$)/𝑷(𝒕,£)] × [𝑷(𝒕,$)/𝑷(𝒕,£)] =1

and if RPPP holds,
𝑹𝑺(𝒕,$/£) = 𝐇 x [𝑷(𝒕,$)/𝑷(𝒕,£)] × [𝑷(𝒕,$)/𝑷(𝒕,£)] = 𝐇

Question 11

Real appreciations and depreciations

Answer 11

100 × [𝑅𝑆(𝑡+1,$/£) −𝑅𝑆(𝑡,$/£)] / 𝑅𝑆(𝑡,$/£)

Question 12

[Real interest rate]
Ex-post real interest rate at t+1

Answer 12

r𝑒𝑝(t+1) ≈ i(t) − 𝜋(t+1)

Question 13

[Real interest rate]
Expected (or ex-ante) real interest rate at time t

Answer 13

Et[𝑟𝑒𝑝(t+1)] ≈ i(t) − Et[𝜋(t+1)]

Question 14

[The Fisher Hypothesis]
Ex-post at t+1

Answer 14

i(t) ≈ r𝑒𝑝(t+1) + 𝜋(t+1)

Question 15

[The Fisher Hypothesis]
Ex-ante at t

Answer 15

i(t) ≈ Et[𝑟𝑒𝑝(t+1)] + Et[𝜋(t+1)]

Question 16

Real interest rate parity

Answer 16

(expected) Real interest rates are same across countries at a given point in time

Et[r𝑒𝑝,𝐷(t+1)] = Et[r𝑒𝑝,𝐹(t+1)] for all t

Question 17

3 conditions for RIP to hold

Answer 17

RIP holds when the CIP, the UIP, and expected RPPP hold