1. 有效汇率 Effective Rate
The effective exchange index is the (weighted) average derived from the bilateral exchange indices (more than two), which are averaged with a unified base period.

2. Example: 1980为基期；
美元对英镑：2.121/3.326×100=91.2
美元对日元：226.7/219.6 ×100=103.5
美元对加拿大元汇率平均持平 100
美元对意大利里拉：856.4/830.9 ×100=103.1
美元对法国法郎：4.226/4.254 ×100=99.3
美元对德国马克：1.818/1.833 ×100=99.2
( ) ÷6=99.4

3. Effective exchange rates or multilateral ERs
Definition: an Effective ER is a weighted average of bilateral exchange rates
Construction of an effective ER proceeds as follows
Don’t simply average for if simply average the outcome depends on the units of measurement.

4. (1) Scale exchange rates, (2)Weight
(1)   Scaling
Purpose is to make magnitude of ERs comparable in some (base) period
Si0 = Spot rate (ER), period 0 (base period), country i
Sit = Spot rate period t (current period), country i

5. Construct index for each currency with base of 100 in period 0:
(2) Weight:

6. where wi = weight for country i
and w1 + w2 + … + wm = ∑wi = 1
How to choose wi? They should reflect country i’s importance to domestic country. Typically use trade weights so that they reflect the importance in trade but may use asset weights to reflect importance of international asset flows.

7. Nominal effective exchange rate index
It represents the ratio (i.e., on the base 1995=100) of an index of the period average exchange rate of the currency in question to a weighted geometric average of exchange rates for the currencies of selected countries.

8. Real effective exchange rate index
It is defined as a nominal effective exchange rate index adjusted for relative movements in national price or cost indicators of the home country and selected countries.

9. Real Effective ER
1. This is a combination of real and effective ERs. Thus either a weighted average of many bilateral real ERs or an effective ER adjusted for multilateral differences in inflation rates relative prices.
2. It can be used as a measure of competitiveness relative to major trading partners.
3. Weighted averages above are arithmetic averages. Geometric averages are also used.

10. Construct Real ER’s for countries 1,2,…,m
Weight Rit using trade weights, wi :