### Methodology for Calculating Regional and Global Estimates of Price Inflation

#### International Labor Organization

To satisfy an increasing need for global and regional estimates of price inflation, the International Labor Organization developed the following method for calculating them.

Basically the method calculates regional price changes as a weighted geometric average of the price changes that have been reported in each of the countries of the region, weighting each country's price changes by its share of GDP in the region. Inflation is then calculated as the percentage change in the average over some period, using one of two possible base periods. Either the same month of the previous year is used as the base period or the previous month is. There are many issues to deal with other than determining the basic method, such as what to do about gaps in data, and the approaches taken to these issues are described here as well.

Currently, the Cleveland Fed uses the ILO method to prepare inflation estimates for seven groups of countries: a global estimate and six regional ones.

#### Step 1. Gathering price data

Constructing the estimates begins with obtaining the consumer price index (general indices) of every country that prepares them. These data are gathered by the ILO and are available for download on the ILO website: http://laborsta.ilo.org/.

#### Step 2. Refine the dataset

After all the price series are gathered, there are some irregularities in the data that need to be dealt with. While most countries report monthly price data, a few report only quarterly, and two report semiannually. So for some months there will be "missing" data for the countries that don't report monthly data. Also, over the years some countries have changed the reference year on which their index is calculated but have not provided enough information to allow the entire series to be linked and rebased on one reference year. This leads to a "break" in the series when the inflation numbers are calculated (described in more detail below). Finally, most countries report only one consumer price index series, but some countries report more than one. For example, one country might report two or three general CPI series, each of which covers different geographical area or population group.

#### Step 2A. Adjust for different reporting frequencies

Some countries report CPI data only quarterly or semiannually (28 and 2, respectively, of the 200 total. Click here for a list). Instead of leaving these countries out of the monthly regional estimates, we include them by estimating (interpolating) values for the missing months. There are two estimation procedures for those countries reporting only quarterly or semiannually, one of which is used when the base period is the same month of the previous year, and one of which is used when the base period is the previous month.

#### i.When the base period is the same month of the previous year

In this case the procedure is to apply the quarterly estimate to each of the three months in a quarter, and likewise with semiannual data, to apply the semiannual estimate to each of the six months in the half-year. This procedure assumes that the price changes for the all months of the reporting period have the same price level as the one that was reported; because the number reported is the average for the period (the quarter or the half-year), this is reasonable.

#### ii.When the base period is the previous month

The method used for estimating missing months in the quarterly or semiannual series seems a little more complicated but is pretty straightforward.

To get the monthly index values

1. Take the CPI value from the current reporting period (quarter or half-year) and divide it by the CPI value from the previous reporting period.

2. Take the third root of this ratio for quarterly data, or the sixth root for semiannual data.

3. Multiply the index value from the previous reporting period by the resulting value from (a) to get the index value for the first month of the current period (note, it is really based on the final month of the previous period, not the previous month).

4. Multiply the previous period index value by the resulting value from (a) squared to get an index value for the second month of the current period.

5. Multiply the previous period index value by the resulting value from (a) cubed to get an index value for the third month of the current period.

Continue the process for semiannual data, multiplying the previous period index value by (a), but increasing the exponent by 1 for each successive month of the current period.

Here is an example.

Say there is a country that reports CPI data four times a year, in March, June, September, and December.

1995 fourth-quarter CPI is: 120.7

1996 first-quarter CPI is: 130.9

a. 130.9/120.7 = 1.084507. Third root of 1.084507 is 1.027411

b. 120.7 * 1.027411 = 124.0085 [The index for January 1996]

c. 120.7 * 1.027411 * 1.027411 = 127.4077 [The index for February 1996]

d. 120.7 * 1.027411 * 1.027411 * 1.027411 = 130.9 [The index for March 1996]

Note that the index values in (b), (c), and (d) above are really based on the previous quarter, but they will provide the correct inflation values. To check this, we can use the values computed with the previous-quarter base to calculate the index values for the months (Jan., Feb. and March 1996) that are based on the previous month:

Jan.1996: 124.0085/120.7 * 100 = 102.7411

Feb. 1996: 127.4077/124.0085 *100 = 102.7411

March 1996: 130.9/127.4077 * 100 = 102.7411

By multiplying these three indices (each one on base previous month):

102.7411*102.7411*102.7411/10000 =108.4507

we get the index for 1996IQ on base 1995IVQ.

#### Step 2.B. Adjust for "breaks" in the data

For those countries whose price series are not based on one single reference period, the calculation of month-to-month or month-over-the-same-month-of-the-previous-year inflation is problematic, In particular, it is not possible to calculate inflation values for any month that requires price data from both sets of numbers, that is, where one number is based on one reference year and the other number is based on another.

For example, a country X might have a consumer price series where the reference is 1990=100 for the years 1990 to 1995, but from 1996 to 2004 the reference is 2000=100. Calculating inflation will be a problem in each of the twelve months of 1996 when the same month from the previous year is used as the base period. When using the previous month as the base, there is a problem when calculating the inflation value in January 1996.

Because there are no reliable methods to estimate the missing data, the dataset must be adjusted so that the problem months are not included in the estimates. (Note that their inclusion will result in distorted estimates of period-to-period changes) Continuing with the example of country X, a value of "missing" has to be assigned to each of the months of 1995, when using the same month of the previous year as the base, so that no inflation values will be computed for that country in 1996. When using the previous month as the base, the value of "missing" is assigned to the final month of 1995 so that no inflation is calculated for that country in January 1996. These series thus will have breaks in them. Also, when GDP weights are calculated, the weights must be adjusted in the months where data are missing (see below). (Click here to view the list of countries that have breaks in their series.)

#### C. Adjust for countries reporting multiple price series

Some countries report multiple series. In these cases, all of the series are averaged together or one or a subset of series is selected and used. Preference is given to series having wider geographical coverage and relating to all income groups, provided they are no less current than more narrowly defined series. (Click here to view the list of countries reporting multiple series.)

#### Step 3. Preparing the weights

Another dataset is created with the GDP values for the countries that report GDP. The GDP values are from 1999, and to standardize the values across countries, they are deflated by purchasing power parity estimates (obtained from the World Bank*). It is difficult to be sure that an index based on weights that are seven years old and do not allow for the changing importance of a country within a region over time will provide a reliable and relevant measure of current inflation, but the 1999 GDP data were the most recent data available at the time this project started. A changing set of GDP weights will need to be introduced soon.

The relative weights of the countries in each regional estimate are then calculated. First the GDP totals for the various regional estimates are calculated, then the weights representing each country's share of the totals are calculated. As the same countries must be compared from one period to another, adjustments of weights are made each month for any changes in country coverage.

In calculating the total GDP and deriving the weights, only those countries that have price data available for both the starting month and the ending month of the calculation are included. That is, when using the same month of the previous year as the base to calculate inflation, only those countries that have price data available for the month in consideration and for the same month of the previous year are included in calculation of total GDP. Likewise, when calculating inflation using the previous month as the base, only those countries that have price data available for the month in consideration and for the previous month are included in the total GDP. This requirement means that countries that have missing price data are excluded from total GDP for that particular month. Separate sets of weights are calculated for each month.

GDP was chosen as the weighting variable over other some plausible alternatives, for example, population, because GDP seemed the most appropriate--a regional inflation estimate weighted by GDP indicates the general effect of inflation on the economy in the region. This weighting procedure is also similar to the one used to calculate national CPIs, which are expenditure-weighted indexes.

*World Bank estimates available at http://unstats.un.org/unsd/cdb/cdb_source_xrxx.asp?source_code=45

made each month for any changes in country coverage.

#### Step 4. Weighting the price data

The CPI data for each country that is included in a particular regional estimate is powered by its share of GDP in the region, expressed as percentage. These values, multiplied together, give the regional total. This is done for each month of data for each country that is part of a given regional estimate.

The calculation of regional totals and averages for the world takes account of the problem that data for some countries do not run through the end of the period for which world and regional data should be calculable. Regional totals are estimated by assuming that the rate of change in the unreported country data is the same as the rate of change in the weighted total or average of the reported country data for that region.

#### Step 5. Averaging

Regional price indexes are calculated as weighted geometric averages of the countries in the region. A geometric average is used because it is less affected than an arithmetic average by extreme values and is regarded as more suitable for groups where the dispersion of indices is considerable. (A geometric average is calculated as the nth root of the product of n observations or values. An arithmetic average is the result of the sum of n observations or values divided by n.)

#### Step 6. Calculating inflation estimates

Inflation is calculated from the series of index numbers as a percent change over some period. The 12-month rate of change is calculated as the percentage variation over 12 months for monthly series, over four quarters for quarterly series and over one year for annual series.

#### Regional groupings

Researchers and analysts might be interested in any number of potential groupings, but initially countries were assigned into one of six categories. The first two categories are developed and transition economies, and countries not assigned to either of these are then grouped by geographical location. Standard UNSD Country and Region Classification was used as a starting point for making decisions on the major groupings. Modifications were made to account for the specificity of the CPI. For example, the transition countries from Central and Eastern Europe were grouped in a separate group from other transition countries because of the similar trends in the price inflation they experienced at the beginning of 1990s.

CPI estimates are produced for the following main country groupings:

• Developed countries
• Transition countries
• Asia and Pacific
• Latin America and the Caribbean
• Sub-Saharian Africa
• Middle East and North Africa

The country composition of the world is all countries for which the series are available.

#### Table 2. Countries reporting quarterly or semi-annually

 Country Period Month of the quarter reported LS, Lesotho 1990-2001 1st SH, Saint Helena 1990-2001 2nd T1, Tanzania (Tanganyika) 1990-1993 3rd T2, Tanzania (Zanzibar) 1990-1998 2nd AI, Anguilla 2001-2004 3rd BZ, Belize 1990-2004 2nd KY, Cayman Islands 1990-2003 3rd FK, Falkland Is. (Malvinas) 1990-2002 2nd PM, Saint Pierre and Miquelon 1990-2001 3rd OM, Oman 1990-2001 2nd FO, Faeroe Islands 1990-2003 1st GI, Gibraltar 1990-2004 1st IE, Ireland 1990-1996 2nd JE, Jersey 1990-2003 3rd AS, American Samoa 1990-2004 2nd AU, Australia 1990-2004 3rd CK, Cook Islands 1990-2004 2nd GU, Guam 1990-2003 2nd KI, Kiribati 1990-2003 2nd MH, Marshall Islands 1991-2004 2nd NZ, New Zealand 1990-2004 2nd NU, Niue 1990-2003 2nd NF, Norfolk Island 1990-2004 3rd MP, Northern Mariana Island 1990-2004 2nd PG, Papua New Guinea 1990-2004 2nd WS, Samoa 1999-2003 3rd TV, Tuvalu 1990-2003 2nd VU, Vanuatu 1990-2003 2nd GL, Greenland 1990-2004 Half yearly, 1st BT, Bhutan 1990-2003 Half yearly 6th

#### Table 3.  Countries reporting multiple series

 Country Available series Series used Cape Verde CV –Cape Verde CV1 –Cape Verde (Praia) CV Ethiopia ET –Ethiopia ET1 –Ethiopia (Addis Ababa)) ET1 Madagascar MG –Madagascar MG1 –Madagascar (Antananarivo, Madagascar) MG2 –Madagascar (Antananarivo, Europe) MG1 (1990-2000) MG (>2000) Mozambique MZ –Mozambique MZ1 –Mozambique (Maputo) MZ1 Swaziland SZ –Swaziland SZ1 –Swaziland (Mbabane-Manzini) SZ1 (1994) SZ (all years except 1994) Zambia ZM –Zambia ZM2 –Zambia (low income group) ZM Brazil BR –Brazil BR1 –Brazil (Sao Paulo) BR French Guiana GF –French Guiana GF1 –French Guiana (Cayenne) GF1 (1990-1992) GF (>1992) Nicaragua NI –Nicaragua NI1 –Nicaragua (Managua) NI1 India IN4 –India (Agricultural workers) IN5 –India (Industrial workers) IN6 –India (Urban non-manual employees) IN7 –India (Delhi, Industrial workers) IN6 Lao People’s Dem. Rep. LA –Lao People’s Dem. Rep. LA1 –Lao People’s Dem. Rep. (Vientiane) LA1 (1990-1996) LA(>1996) Myanmar MM –Myanmar MM1 –Myanmar (Yangon) MM1 (1990-1998) MM (>1998) Saudi Arabia SA –Saudi Arabia (All cities) SA1 –Saudi Arabia (middle income group) SA

#### Table 4.  Countries that have breaks in their series

 Country Period of break MA, Morocco 1991 GA, Gabon 1991 BN, Brunei Darussalam 1991 DM, Dominica 1993 FI, Finland 1993 BH, Bahrain 1997 HT, Haiti 1996 ET, Ethiopia 1997 CI, Cote d’Ivoire 1996 GQ, Equatorial Guinea 2000