Calculating a Relevant TWI

Richard SullivanReserve Bank of New Zealand

Trade weighted exchange rate

• What is a TWI/NEER/REER?• Why have one? What is it used for?• What currencies to use?• How to weight? Why not just trade weights?• How to calculate NEER• How to recalculate, and how often?• How to calculate REER

What is a TWI?

TWI = Trade Weighted IndexA multilateral exchange rate which is a weighted

average of exchange rates of foreign currencies, with the weight for currency based on its share in trade.

It measures the average price of goods relative to the average price of goods of trading partners.

What is it for?A tool for measuring:• direct influence of exchange rate movements on prices• indirect influence of the exchange rate on inflation

through influence on external sector competitivenessIf the index increases, the purchasing power of that

currency is higher (the currency strengthened against the country's trading partners).

A lower index means that the currency depreciated (devaluation) so that you need more of that currency to pay for imports.

Provides a measure of relative value against a range of currencies you are interested in.

NEER

•Nominal Effective Exchange Rate– a nominal TWI

•The weighted average value of a country's currency relative to a pool of currencies. •The weights are determined by the importance a home country places on the other currencies within the pool – usually based on trade.• Usually measured by trade flows (hence TWI).

TWI less volatile

2005 2006 2007 2008 200950

60

70

80

50

60

70

80Index NZD/USD (cents)

NZD TWI

NZD/USD

Pa’anga not as volatile as bilateral rates suggest

NZD

0.65

0.70

0.75

0.80

0.85

0.90

Jul-05 Jan-06 Jul-06 Jan-07 Jul-07 Jan-08 Jul-08 Jan-09 Jul-09

NEER

90

95

100

105

Jul-07 Jan-08 Jul-08 Jan-09 Jul-09

USD

0.44

0.46

0.48

0.50

0.52

0.54

0.56

Jul-05 Jan-06 Jul-06 Jan-07 Jul-07 Jan-08 Jul-08 Jan-09 Jul-09

AUD

0.55

0.58

0.61

0.64

0.67

0.70

Jul-05 Jan-06 Jul-06 Jan-07 Jul-07 Jan-08 Jul-08 Jan-09 Jul-09

REER

• Real Effective Exchange Rate– a real TWI

• Same as NEER, but adjusted for inflation• Better measure of competitiveness over time

– takes into account price movements

A higher REER indicates lower competitiveness as it costs more to produce similar goods.

NEER calculation

Important decisions

• Pick the relevant currencies– Trade flow?– Policy goals will provide guide

• Determine appropriate weights– Which way to weight?– How often to re-weight?

Choosing Appropriate Currencies

• Trade flows– Just exports?

• if export competitiveness is the primary goal– Just imports?

• If imported price inflation is key priority– All trade?

• Other currency flows– Remittances– Capital/grants

• Completeness vs ease of calculation

Factors to consider when determining weights

• Equal weighting to exports and imports?• Other currency flows• Foreign currency regimes

– Currency pegs (e.g to USD)– Similar ‘baskets’ (e.g Fiji and Tonga)

Third country competition

• Competition faced by exporters from countries not in ‘basket’– e.g squash from Mexico to Japan

• Studies show is good proxy for wider range of currencies within TWI

More currencies does not mean better coverage

TWI14 index includes the five TWI currencies with the addition of the currencies of: •China, •Malaysia, •Indonesia, •Thailand, •Taiwan, •Korea, •Singapore, •Hong Kong and• Canada.

Administrivia

• Arithmetic vs geometric mean• Update frequency• Ease of finding data

– What data to use

Data website

• IMF data– Currencies– GDP– Inflation

• http://www.imf.org/external/data.htm• WEO database for GDP and inflation• IFS if you need currencies

NEER Examples

Examples

• NZD TWI– 5 currency basket with 50% GDP weight

• Tonga NEER– 4 currency basket, all trade weight– 5 currency basket, 25% trade weight– What about the CNY?

NZD TWI

• GDP weight greatly increases importance of USD and euro

• Better reflects actual currency traded, and third country competition

TOP NEER

• Previous methodology– Trade only weights

• Subject to large changes in weights• No account for 3rd country competition

– Updated every 5 years• Weights can become inappropriate

TOP NEER

• Added 3rd country competition– 25% GDP weights/75% trade weights(50% made USA too dominant as other countries were so small relatively)

• Update more regularly• Stability in weight

Australia NEER weights

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Trade

Trade & GDP

China NEER weights

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Trade

Trade & GDP

Fiji NEER weights

0.00

0.05

0.10

0.15

0.20

0.25

Trade

Trade & GDP

Japan NEER weights

0.00

0.05

0.10

0.15

0.20

0.25

Trade

Trade & GDP

New Zealand NEER weights

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Trade

Trade & GDP

United States NEER weights

0.00

0.05

0.10

0.15

0.20

0.25

0.30Trade

Trade & GDP

Calculation of NEER 1. Get trade weights for appropriate year

– appropriate year will always be 2 years behind (e.g in January 2009, the data you need are for 2007)

– insert total annual import and export data into sheet "data" – Calculate trade weight as % of ‘basket’ currencies

2. Get GDP weights for appropriate year – enter GDP data into sheet "data" – enter average exchange rate for year to make – Convert GDP into USD – Calculate GDP weight as % of ‘basket’ currencies

3. NEER weights will be weighted average of both trade and GDP weight4. Calculate index

– Convert bilateral exchange rates to index with common base– Use new weights to calculate index = 100 for month in which you plan to

change – Multiply by factor so that it is splice with previous year (eg if NEER is 51.6,

multiply new index by 51.6/100)

1. Calculating trade weight

• Find import and export data for chosen currencies – In local currency

• Calculate as percentage of all trade with those chosen countries

2. Calculating GDP weight

• Find GDP data for chosen currencies– In levels– In common currency

• Calculate as percentage of total GDP of those chosen countries

3. Calculate NEER weight

Australia China Fiji Japan New Zealand United StatesExports 1121972 Exports 93930 Exports 95044 Exports 2063067 Exports 5445809 Exports 4835855Imports 32923572 Imports 17501268 Imports 37371747 Imports 7320487 Imports 94765689 Imports 28545054Total Trade 34045544 Total Trade 17,595,198 Total Trade 37,466,791 Total Trade 9,383,554 Total Trade 100,211,498 Total Trade 33,380,909GDP (AUDbn) 1021.062 GDP (CNYbn) 9927.757 GDP (FJDbn) 2.983 GDP (JPYbn) 561207.9 GDP (NZDbn) 134.743 GDP (USDbn) 11523.9AUD 0.836769483 CNY 7.587833333 FJD 0.6210 JPY 117.8 NZD 0.7349 USD 1.0000GDP (USDbn) 854.3935218 GDP (USDbn) 1308.378369 GDP (USDbn) 1.85 GDP (USDbn) 4766.0 GDP (USDbn) 99.0 GDP (USDbn) 11523.9

Total Exports 13,655,677Total Imports 218,427,817Total Trade 232,083,494Total GDP (USDbn) 18,554

Average exchange rate

for year

Sum of selected countries

3. Calculate NEER weight

Australia China Fiji Japan New ZealandUnited States0.147 0.076 0.161 0.040 0.432 0.144

Australia China Fiji Japan New ZealandUnited States0.046 0.071 0.000 0.257 0.005 0.621

Australia China Fiji Japan New ZealandUnited States0.122 0.074 0.121 0.095 0.325 0.263

Trade

GDP

NEER

Share of trade/sum of

trade

Share of GDP/sum of

GDP

Weighted average of

above

4. Calculate index

• Set bilateral exchange rates to common base index

• Multiply by NEER weights and aggregate• Splice with current series

ExampleFM EXRATES (Period Averages) Indices of exchanges rates NEER NEER

AUSTRALIA CHINA FIJI JAPANNEW

ZEALANDUNITED STATES

AUSTRALIA CHINA FIJI JAPAN

NEW ZEALAND

UNITED STATES 2005 weights2006 weights2007 weights

Dec-06 0.6349 3.9017 0.8001 58.4169 0.7207 0.4988 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00Jan-07 0.6326 3.8603 0.7938 59.6491 0.7123 0.4956 99.64 98.94 99.20 102.11 98.84 99.36 99.54 99.54Feb-07 0.6326 3.8358 0.7937 59.6708 0.7139 0.4948 99.64 98.31 99.20 102.15 99.05 99.20 99.55 99.55Mar-07 0.6286 3.8527 0.7938 58.4090 0.7129 0.4979 99.00 98.74 99.21 99.99 98.91 99.83 99.32 99.32Apr-07 0.6124 3.9125 0.7880 60.1851 0.6901 0.5065 96.45 100.28 98.48 103.03 95.75 101.54 98.80 98.80May-07 0.6118 3.8766 0.7871 60.9528 0.6885 0.5049 96.36 99.36 98.37 104.34 95.53 101.24 98.76 98.76Jun-07 0.6065 3.8968 0.7836 62.6045 0.6755 0.5106 95.52 99.88 97.94 107.17 93.73 102.38 98.69 98.69Jul-07 0.5980 3.9281 0.7808 63.0804 0.6593 0.5185 94.19 100.68 97.58 107.98 91.48 103.95 98.31 98.31

Aug-07 0.6047 3.7969 0.7795 58.5334 0.6904 0.5013 95.24 97.31 97.43 100.20 95.80 100.52 97.76 97.76Sep-07 0.5950 3.7721 0.7727 57.7015 0.7005 0.5014 93.71 96.68 96.57 98.78 97.19 100.53 97.65 97.65Oct-07 0.5749 3.8699 0.7737 59.7669 0.6792 0.5158 90.55 99.19 96.70 102.31 94.25 103.42 97.64 97.64Nov-07 0.5795 3.8533 0.7730 57.6125 0.6810 0.5192 91.27 98.76 96.61 98.62 94.49 104.10 97.47 97.47Dec-07 0.6010 3.8655 0.7847 58.9395 0.6814 0.5243 94.67 99.07 98.07 100.89 94.54 105.11 98.68 98.68Jan-08 0.6040 3.8553 0.7913 57.4268 0.6890 0.5320 95.13 98.81 98.90 98.31 95.60 106.66 99.23 99.47 99.23Feb-08 0.5946 3.8829 0.7852 58.0771 0.6805 0.5417 93.66 99.52 98.14 99.42 94.42 108.61 99.49 99.24Mar-08 0.5904 3.8687 0.7819 55.2278 0.6815 0.5464 92.99 99.15 97.73 94.54 94.56 109.56 99.02 98.78Apr-08 0.5858 3.8073 0.7842 55.6749 0.6889 0.5439 92.27 97.58 98.01 95.31 95.59 109.05 99.16 98.91May-08 0.5730 3.7917 0.7816 56.6977 0.6993 0.5437 90.24 97.18 97.68 97.06 97.02 109.01 99.41 99.17Jun-08 0.5680 3.7244 0.7798 57.7439 0.7092 0.5398 89.46 95.46 97.46 98.85 98.40 108.22 99.56 99.32Jul-08 0.5612 3.6951 0.7782 57.6917 0.7151 0.5404 88.39 94.71 97.26 98.76 99.22 108.36 99.60 99.36

Aug-08 0.5884 3.5577 0.7730 56.7787 0.7317 0.5192 92.67 91.18 96.61 97.20 101.52 104.10 99.11 98.87Sep-08 0.6143 3.4484 0.7832 53.8597 0.7460 0.5045 96.75 88.38 97.89 92.20 103.51 101.15 98.91 98.66Oct-08 0.6884 3.2446 0.7983 47.7000 0.7781 0.4747 108.42 83.16 99.77 81.65 107.97 95.18 98.79 98.55Nov-08 0.7007 3.1520 0.8049 44.8012 0.8169 0.4617 110.36 80.79 100.59 76.69 113.35 92.56 99.26 99.02Dec-08 0.6912 3.1739 0.7985 42.3216 0.8299 0.4631 108.86 81.35 99.80 72.45 115.15 92.86 99.02 98.78Jan-09 0.6822 3.1580 0.7965 41.7139 0.8354 0.4620 107.45 80.94 99.54 71.41 115.92 92.64 98.82 98.57Feb-09 0.6920 3.0731 0.7950 41.5564 0.8718 0.4496 108.99 78.76 99.36 71.14 120.96 90.14 99.51 99.26Mar-09 0.6825 3.0958 0.7986 44.2882 0.8559 0.4529 107.49 79.35 99.82 75.81 118.76 90.80 99.59 99.35Apr-09 0.6565 3.1949 0.9073 46.2006 0.8193 0.4677 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00May-09 0.6310 3.2800 0.9894 46.4911 0.8039 0.4807 96.11 102.66 109.06 100.63 98.12 102.79 101.01 101.01Jun-09 0.6170 3.3784 0.9845 47.7908 0.7751 0.4944 93.97 105.74 108.51 103.44 94.60 105.70 100.80 100.80Jul-09 0.6173 3.3944 1.0225 47.0004 0.7710 0.4969 94.02 106.24 112.70 101.73 94.12 106.23 101.17 101.17

Aug-09 0.6077 3.4667 1.0210 48.2091 0.7506 0.5074 92.56 108.51 112.53 104.35 91.62 108.49 101.17 101.17

Create common base

Multiply by weights to get

NEER

Splice index

To include the CNY?• Currency flows suggest it is a very important

currency to consider– Imports– Grants– Loans

• Pegged to USD– So no reason to add as new currency

• Peg is being loosened– Should increase importance of CNY– Consider inclusion as CNY moves become less tied to

USD

REER

Another important decision• What deflator to use?• Depends on policy goal• Core inflation is theoretically best

– But different countries measure core inflation differently

• Headline inflation is most accessible– All countries publish– Best for international comparison due to similarity

http://www.rbnz.govt.nz/research/bulletin/2007_2011/jun2007.html“A review of the trade weighted index”

Calculation

• Calculate bilateral real exchange rates– r = e*P/P´

• r = real exchange rate• e = nominal exchange rate• P = home price level• P´= foreign price level

• Index bilateral rates to common base• Multiply by NEER weights and aggregate• Splice with current index• Reweight at same time as NEER

Example NZD/TOPNZD/TOP NZ TONGA Real NZD/TOP

Dec-06 0.7207 1005 142.6 100.0Jan-07 0.7123 1006.25 140.9 97.5Feb-07 0.7139 1008.75 141.1 97.6Mar-07 0.7129 1010 141.7 97.8Apr-07 0.6901 1012.5 142 94.6May-07 0.6885 1017.5 142.8 94.5Jun-07 0.6755 1020 144 93.2Jul-07 0.6593 1021.25 147.9 93.3

Aug-07 0.6904 1023.75 149 98.2Sep-07 0.7005 1025 150.4 100.5Oct-07 0.6792 1028 150.9 97.5Nov-07 0.6810 1034 151.1 97.3Dec-07 0.6814 1037 152.3 97.8Jan-08 0.6890 1038.75 155.8 101.0Feb-08 0.6805 1042.25 158.3 101.0Mar-08 0.6815 1044 158.7 101.3Apr-08 0.6889 1048.25 159 102.1May-08 0.6993 1056.75 160.7 103.9Jun-08 0.7092 1061 161.6 105.6Jul-08 0.7151 1065 161.6 106.1

Aug-08 0.7317 1073 165.2 110.1Sep-08 0.7460 1077 165.9 112.3Oct-08 0.7781 1075.75 165.2 116.8Nov-08 0.8169 1073.25 163.1 121.4Dec-08 0.8299 1072 162 122.6Jan-09 0.8354 1072.75 161.8 123.2Feb-09 0.8718 1074.25 161.4 128.0Mar-09 0.8559 1075 162.5 126.5Apr-09 0.8193 1076.5 161.2 119.9May-09 0.8039 1079.5 163.8 119.2Jun-09 0.7751 1081 163.6 114.7Jul-09 0.7710 1084.5 163.6 113.7

Aug-09 0.7506 1091.5 166.1 111.7

CPI

Nominal exchange rate

CPI(index not inflation)

Nominal exchange rate*Tonga CPI/NZ CPI

*1023(to base at 100 in Dec 06)

Nominal vs Real

90

95

100

105

110

115

120

125

130

Real NZD/TOP

NZD/TOP

Why the difference?

0%

2%

4%

6%

8%

10%

12%

14%NZ

TONGA

CPI Inflation

Calculation

• Calculate bilateral real exchange rates– r = e*P/P´

• r = real exchange rate• e = nominal exchange rate• P = home price level• P´= foreign price level

• Index bilateral rates to common base• Multiply by NEER weights and aggregate• Splice with current index• Reweight at same time as NEER

Questions