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Lesson M10.L02: Purchasing Power Parity and Interest Rate Parity

Module: Exchange Rates and the Open Economy Level: intro Duration: 30 minutes Learning Objective: Apply relative PPP to predict exchange rate movements from inflation differentials. Data as of: 2024 Provenance: OpenStax Macro 3e | RBA Education | Khan Academy Macro

Explanation

Purchasing Power Parity (PPP) is the theory that exchange rates should adjust so that identical goods cost the same in different countries when expressed in a common currency. There are two versions:

Absolute PPP: The nominal exchange rate equals the ratio of price levels: e = P/P*. In practice, this rarely holds due to transport costs, tariffs, and non-traded goods.

Relative PPP is more useful for prediction. It states that the percentage change in the exchange rate equals the inflation differential between the two countries:

% change in e ā‰ˆ Ļ€_foreign āˆ’ Ļ€_domestic

where Ļ€ is the inflation rate. If Australia has higher inflation than the US, the AUD should depreciate (e falls) to maintain equal purchasing power.

Interest Rate Parity (IRP) is the financial market counterpart. It states that the return on investing in Australia (earning the Australian interest rate i_A) must equal the return on investing in the US (earning i_US plus any expected exchange rate gain). Uncovered IRP:

i_A ā‰ˆ i_US + (% expected AUD depreciation)

Or equivalently: the expected AUD depreciation ā‰ˆ i_A āˆ’ i_US.

When Australia's RBA sets higher interest rates than the US Fed, the AUD tends to appreciate ā€” foreign capital flows in seeking higher returns, bidding up the AUD. This carry trade dynamic is a key driver of AUD volatility.

In 2022ā€“23, the RBA's rate hiking cycle coincided with similar moves by the Fed, limiting the AUD's upside despite domestic rate rises.

Worked Example

Scenario: Relative PPP in action ā€” AUD/USD

Given: - Current AUD/USD: eā‚€ = 0.65 - Australian inflation over the next year: Ļ€_AUS = 4.0% - US inflation over the next year: Ļ€_US = 2.5%

Step 1 ā€” Calculate the inflation differential:

Ļ€_US āˆ’ Ļ€_AUS = 2.5% āˆ’ 4.0% = āˆ’1.5%

Australia has higher inflation ā†’ relative PPP predicts the AUD will depreciate by approximately 1.5% (e falls by 1.5%).

Step 2 ā€” Calculate the predicted new exchange rate:

eā‚ = eā‚€ Ɨ (1 āˆ’ 0.015) eā‚ = 0.65 Ɨ 0.985 eā‚ = 0.65 Ɨ 0.985 = 0.6403

Step 3 ā€” Verify the logic:

Change in e = (0.6403 āˆ’ 0.65) / 0.65 Ɨ 100 = (āˆ’0.0097 / 0.65) Ɨ 100 = āˆ’1.49% ā‰ˆ āˆ’1.5% āœ“

The AUD/USD rate falls from 0.65 to approximately 0.64.

Step 4 ā€” Interest Rate Parity check:

Suppose Australia's cash rate = 4.35%, US fed funds rate = 5.25%.

Expected AUD change (IRP) = i_AUS āˆ’ i_US = 4.35% āˆ’ 5.25% = āˆ’0.90%

IRP predicts AUD should depreciate ~0.9% as capital seeks higher US returns. The PPP prediction (āˆ’1.5%) and IRP prediction (āˆ’0.9%) both point to AUD depreciation, consistent with the 2023ā€“24 AUD trading below 0.65.

Common Misconception

Misconception: "Relative PPP perfectly predicts short-run exchange rate movements ā€” if Australia has higher inflation, the AUD will definitely fall."

Correction: Relative PPP is a long-run theory. In the short run, exchange rates are driven by capital flows, risk sentiment, commodity prices, and interest differentials ā€” not just inflation. The AUD can appreciate even when Australian inflation is high if commodity prices surge or if global risk appetite improves (the AUD is a "risk-on" currency). Empirical studies show PPP holds reasonably well over 5ā€“10 year horizons but has poor short-run predictive power.

Practice Prompts

  1. Explain intuitively why a country with persistently higher inflation than its trading partners should see its currency depreciate over time, according to relative PPP. ā†’ Answer: If Australian prices rise faster than US prices, Australian goods become relatively more expensive. To maintain competitiveness (so that the same good costs the same in both countries), the AUD must depreciate ā€” each Australian dollar must buy fewer US dollars. Otherwise, Australian exporters lose competitiveness and imports become cheap, creating downward pressure on the AUD until purchasing power is equalised. This is the core intuition of relative PPP.

  2. NUMERICAL CALCULATION: The AUD/USD is currently 0.72. Australia's expected inflation is 3.5% and the US expected inflation is 1.8%. Using relative PPP, (a) predict the direction and magnitude of AUD movement, and (b) calculate the predicted AUD/USD rate in one year. ā†’ Answer: (a) Inflation differential = Ļ€_AUS āˆ’ Ļ€_US = 3.5% āˆ’ 1.8% = +1.7% Australia has higher inflation ā†’ AUD should depreciate by approximately 1.7%. (b) Predicted rate: eā‚ = 0.72 Ɨ (1 āˆ’ 0.017) = 0.72 Ɨ 0.983 = 0.72 Ɨ 0.983 = 0.7078 The AUD/USD falls from 0.72 to approximately 0.708. Check: (0.7078 āˆ’ 0.72) / 0.72 Ɨ 100 = āˆ’0.0122/0.72 Ɨ 100 = āˆ’1.69% ā‰ˆ āˆ’1.7% āœ“

  3. In 2022ā€“23 the RBA raised the cash rate from 0.10% to 4.35% while the US Fed raised rates from near zero to 5.25%. Despite Australia's large rate hike, the AUD/USD remained weak. Use interest rate parity to explain this outcome. ā†’ Answer: Uncovered IRP predicts AUD depreciation ā‰ˆ i_AUS āˆ’ i_US. With Australia's rate (4.35%) below the US rate (5.25%), IRP predicts the AUD should depreciate by about 0.9% to compensate investors for the lower Australian return. Because US rates rose more than Australian rates, the interest differential favoured the USD ā€” capital flowed toward US assets, weakening the AUD. Even though the RBA hiked aggressively, the Fed hiked more, meaning the carry trade ran against the AUD. This explains why the AUD remained near or below 0.65 throughout 2022ā€“24.

Further Resources