Cambridge A‑Level Economics (9708) – Trade‑Weighted Exchange Rates
1. What is a Trade‑Weighted Exchange Rate (TWR)?
- Nominal exchange rate (e): price of one unit of foreign currency in terms of the home currency (e.g. USD/GBP).
- Real exchange rate (RER): nominal rate adjusted for relative price levels
RER = (e × Phome) / Pforeign.
- Trade‑Weighted Index (TWI): a **nominal** index that aggregates a country’s bilateral exchange rates against a basket of its main trading partners, weighted by their share of trade.
- Real Trade‑Weighted Index (RTWI): the TWI divided by the home‑country price index, giving a real‑terms measure of competitiveness.
2. Why Use a TWR?
- A single bilateral rate ignores the fact that a country trades with many partners; the TWI reflects the overall “effective” value of the currency.
- It allows policymakers to judge whether the currency is **over‑ or undervalued** relative to the pattern of trade.
- Changes in the TWI can be linked to the AD/AS model, the current‑account balance, and the Marshall‑Lerner condition.
3. Determinants of Bilateral Exchange Rates (Syllabus 6.4)
- Interest‑rate differentials – higher domestic rates attract capital, causing appreciation.
- Inflation differentials – higher domestic inflation erodes purchasing power, leading to depreciation.
- Expectations of future rates – speculation on future movements can cause immediate adjustments.
- Relative economic performance – stronger growth raises demand for the domestic currency.
- Government and central‑bank actions – direct intervention, reserve sales/purchases, capital controls.
4. Constructing a Nominal TWI
4.1 Formula
\[
\text{TWI}_{t}= \frac{\displaystyle\sum_{i=1}^{n} w_{i}\,\frac{e_{i,t}}{e_{i,0}}}{\displaystyle\sum_{i=1}^{n} w_{i}}\times 100
\]
- wi = trade share of partner i (export‑share or import‑share – must be stated).
- e_{i,t} = nominal bilateral rate in period t (home‑currency per unit of partner i’s currency).
- e_{i,0} = rate in the chosen base year 0 (index set to 100).
- If the shares are expressed as percentages, \(\sum w_i = 1\) and the denominator can be omitted for simplicity.
4.2 Real Trade‑Weighted Index
\[
\text{RTWI}_{t}= \frac{\text{TWI}_{t}}{P_{t}}\times 100
\]
where \(P_{t}\) is the home‑country price index (e.g., CPI).
4.3 Step‑by‑Step Construction
- Select a base year and set the index to 100.
- Choose the weighting method (export‑share for export‑competitiveness, import‑share for import‑price competitiveness) and justify the choice.
- Collect trade data for each partner (latest export or import values).
- Calculate trade shares \(w_i = \dfrac{\text{Trade with }i}{\text{Total trade}}\).
- Obtain nominal bilateral rates for the base year and the current year.
- Apply the TWI formula to get the nominal index.
- Convert to a real index (optional) by dividing by the home‑country price index.
5. Illustrative Example – United Kingdom (Export‑Share Weighting)
| Partner |
Exports 2020 (£m) |
Export Share \(w_i\) |
Nominal Rate 2020 (USD/GBP) |
Nominal Rate 2019 (USD/GBP) |
| United States |
30,000 |
0.40 |
1.30 |
1.25 |
| Germany |
20,000 |
0.27 |
1.10 |
1.12 |
| China |
25,000 |
0.33 |
0.15 |
0.14 |
Base‑year check (2019) – by definition the index equals 100.
2020 calculation:
\[
\text{TWI}_{2020}= \frac{0.40\frac{1.30}{1.25}+0.27\frac{1.10}{1.12}+0.33\frac{0.15}{0.14}}{1}\times100
= \frac{0.416+0.265+0.353}{1}\times100 = 103.4
\]
The pound **appreciated** against the weighted basket (TWI rose from 100 to 103.4).
Real TWI (CPI up 2 % in 2020):
\[
\text{RTWI}_{2020}= \frac{103.4}{1.02}\times100 \approx 101.4
\]
6. Linking the TWI to the AD/AS Model and the Current Account
- A **falling TWI** (depreciation) makes exports cheaper and imports more expensive → net exports (NX) rise → AD shifts **right** → higher output and possibly higher price level.
- A **rising TWI** (appreciation) has the opposite effect – AD shifts **left**.
- Because the current account (CA) = NX + net income + net transfers, a move in the TWI directly influences the CA balance. An appreciating TWI tends to **worsen** the CA, while a depreciating TWI tends to **improve** it, provided the Marshall‑Lerner condition holds.
7. Marshall‑Lerner Condition & the J‑Curve
- Marshall‑Lerner condition: a depreciation improves the trade balance if
\[
\bigl|\varepsilon_{X}\bigr|+\bigl|\varepsilon_{M}\bigr|>1
\]
where \(\varepsilon_{X}\) is the export‑price elasticity and \(\varepsilon_{M}\) the import‑quantity elasticity (both weighted by trade shares).
- J‑curve: in the short run, a depreciation may **worsen** the trade balance because import volumes are price‑inelastic. Over time, volumes adjust and the balance improves – the TWI helps illustrate the timing of this adjustment.
8. Exchange‑Rate Regimes, Policy Tools & Evaluation (Syllabus 11.2)
8.1 Regimes & Typical Behaviour of the TWI
| Regime |
How the TWI is determined |
Typical policy response when TWI moves |
| Floating (pure market) |
All bilateral rates float; TWI reflects the net effect of market forces. |
Central bank may intervene only to smooth excessive volatility (rare). |
| Fixed / Pegged |
Policy rate is set; TWI shows the pressure of partner currencies on the peg. |
Intervention via foreign‑exchange (FX) reserves, possible re‑valuation or de‑valuation. |
| Managed (dirty‑float) |
Policy rate is the reference; occasional buying/selling of foreign currency moves the TWI. |
FX intervention, sterilised intervention, reserve management, capital‑flow controls. |
8.2 Main Policy Tools
- Direct FX intervention – buying domestic currency (to curb appreciation) or selling it (to curb depreciation).
- Reserve management – altering the composition of foreign‑exchange reserves to influence supply/demand.
- Sterilised intervention – offsetting the monetary impact of FX trades by open‑market operations.
- Capital controls – limiting inflows/outflows to reduce pressure on the exchange rate.
8.3 Evaluation (AO3)
- Floating: provides automatic adjustment to shocks (good for external balance) but can lead to excessive volatility, harming trade and investment.
- Fixed/peg: offers stability and low transaction costs; however, maintaining the peg can exhaust reserves and force painful de‑valuations if the TWI signals persistent misalignment.
- Managed float: combines stability with flexibility; the downside is the risk of “policy‑induced” distortions and the cost of continuous intervention.
9. Common Pitfalls & How to Avoid Them
- Weighting error – using the wrong trade direction. Fix: State clearly whether export‑share or import‑share weighting is used and keep it consistent.
- Out‑of‑date basket – failing to update partner shares. Fix: Re‑calculate \(w_i\) each year (or each exam question) with the latest data.
- Confusing nominal with real – treating the TWI as a real‑terms competitiveness measure. Fix: Always discuss the RTWI or note the effect of domestic inflation.
- Base‑year omission – not showing why the index equals 100 in the base year. Fix: Include a brief base‑year calculation (as in the example).
- Mis‑reading the denominator – forgetting that \(\sum w_i = 1\) when shares are percentages. Fix: Use percentages or keep the denominator explicit when raw weights are used.
10. Suggested Diagram for the Exam
- Bar chart showing export (or import) shares of the main partners.
- Superimposed line graph of the nominal TWI over a 10‑year period, highlighting a recent rise or fall.
- Optional: AD/AS diagram illustrating the shift in AD caused by a TWI movement.
11. Key Take‑aways for the Exam (AO1 & AO2)
- Define **nominal** and **real** exchange rates; state that the TWI is a **nominal** index.
- Write the TWI formula, explain each component, and show how the base‑year index of 100 is obtained.
- Carry out a full calculation: compute trade shares, apply the formula, and (if required) convert to a real index.
- Explain the economic intuition:
- Falling TWI → depreciation → cheaper exports, costlier imports → AD shifts right → potential improvement in the current account (subject to Marshall‑Lerner).
- Rising TWI → appreciation → opposite effects.
- Link the TWI to the **Marshall‑Lerner condition**, the **J‑curve**, and to **exchange‑rate policy** under floating, fixed and managed regimes.
- Identify limitations (choice of weighting, neglect of price levels, need for regular basket updates) and common errors.
- Briefly evaluate the advantages and disadvantages of each exchange‑rate regime and the policy tools available when the TWI moves.